LIBRARY 

OF    THE 

UNIVERSITY  OF  CALIFORNIA. 
Gats 


GENERAL 


THE 

PHYSICAL  PAPERS 


OF 


HENRY  AUGUSTUS  ROWLAND 


THE 


PHYSICAL  PAPERS 


OF 


HENRY  AUGUSTUS  ROWLAND 

PH.D.,  LL.  D. 

Professor  of  Physics  and  Director  of  the  Physical  Laboratory  in 

The  Johns  Hopkins  University 

1876-1901 


COLLECTED  FOR  PUBLICATION  BY  A 
COMMITTEE  OF  THE  FACULTY  OF  THE  UNIVERSITY 


BALTIMORE 
THE  JOHNS  HOPKINS  PRESS 
1902 


Copyright,  1902,  by  the  JOHNS  HOPKINS  PRESS 


PRINTED   BY 


BALTIMORE,  RID.,    U.  S.  A. 


HENRY  AUGUSTUS  ROWLAND 

Born,  Honesdale,  Pennsylvania,  November  27,  1848 
Died,  Baltimore,  Maryland,  April  16,  1901 


Doctor  of  Philosophy  (Ph.  D.),  Johns  Hopkins  University,  1880.     (Hon- 
oris Causa.) 

Doctor  of  Laws  (LL.  D.),  Yale  University,  1895. 
Doctor  of  Laws  (LL.  D.),  Princeton  University,  1896. 

Fellow  or  Member  of 

The  British  Association  for  the  Advancement  of  Science. 

The  Physical  Society  of  London. 

The  Philosophical  Society  of  Cambridge,  England. 

The  Royal  Society  of  London. 

The  Royal  Society  of  Gottingen. 

The  Gioenian  Academy  of  Natural  Sciences,  Catania,  Sicily. 

The  French  Physical  Society. 

The  French  Academy  of  Sciences. 

The  Literary  and  Philosophical  Society  of  Manchester. 

The  Royal  Lyncean  Academy,  Rome. 

The  Academy  of  Sciences,  Stockholm. 

The  Italian  Society  of  Spectroscopists. 

The  Royal  Society  of  Edinburgh. 

The  Society  of  Arts,  London. 

The  Royal  Astronomical  Society  of  England. 

The  Royal  Society  of  Lombardy. 

The  Royal  Physiographic  Society  of  Lund. 

The  Royal  Academy  of  Sciences,  Berlin. 

The  Royal  Academy  of  Sciences  and  Letters,  Copenhagen. 

The  American  Philosophical  Society,  Philadelphia. 

The  American  Academy  of  Arts  and  Sciences,  Boston. 

The  National  Academy  of  Sciences,  Washington. 

The  American  Physical  Society, — its  first  President. 

The  Astronomical  and  Astrophysical  Society  of  America. 

Delegate  of  the  United  States  Government  to  the 
International  Congress  of  Electricians,  Paris,  1881. 
International  Congress  for  the  Determination  of  Electrical  Units,  Paris, 

1882.     Appointed  Officer  of  the  Legion  of  Honor  of  France. 
Electrical  Congress,  Philadelphia,  1884, — President. 
International  Chamber  of  Delegates  for  the  Determination  of  Electrical 

Units,  Chicago,  1893, — President. 


PRIZES  AND  MEDALS. 

Rumford  Medal,  American  Academy  of  Arts  and  Sciences. 
Draper  Medal,  National  Academy  of  Sciences. 
Matteucci  Medal. 

Prize  awarded  by  the  Venetian  Institute  in  competition  for  a  critical 
paper  on  the  Mechanical  Equivalent,  of  Heat. 


102497 


PREFACE 

Shortly  after  the  death  of  Professor  Rowland  in  April,  1901,  a  com- 
mittee of  the  Faculty  of  The  'Johns  Hopkins  University  was  appointed 
by  President  Gilman  to  suggest  to  the  Trustees  of  the  University  a  plan 
for  a  memorial  of  their  colleague.  The  committee,  consisting  of  Pro- 
fessors Remsen,  Welch  and  Ames  decided  to  recommend  that  a  volume 
be  prepared  containing  the  physical  papers  and  addresses  of  Professor 
Rowland,  and  also  a  detailed  description  of  the  dividing  engines  which 
had  been  designed  and  constructed  by  him  for  the  purpose  of  ruling 
diffraction  gratings,  and  that  this  volume  be  published  by  the  University 
Press.  This  recommendation  was  approved  by  the  Trustees  of  the 
University;  and  the  same  committee,  with  the  addition  of  Professor 
R.  W.  Wood,  was  empowered  to  prepare  the  volume  for  publication. 
The  editorial  supervision  has  been  mainly  undertaken  by  Professor 
Joseph  S.  Ames. 

In  deciding  upon  the  scope  of  the  proposed  volume,  it  was  thought 
best  to  include  only  the  distinctly  physical  papers,  inasmuch  as  Pro- 
fessor Rowland  himself  on  several  occasions  when  the  question  of  the 
collection  of  his  scientific  papers  was  raised,  had  expressed  himself  as 
opposed  to  the  republication  of  the  purely  mathematical  ones.  It  was 
also  decided  to  omit  tables  of  wave-lengths,  as  these  are  extremely 
bulky,  and  copies  can  be  easily  obtained.  Professor  Rowland  left  many 
thousand  pages  of  manuscript  notes  and  outlines  of  lectures,  but  none 
of  this  material  was  ready  for  publication,  and  the  committee  were  not 
in  a  position  to  undertake  the  task  of  its  preparation.  No  attempt  has 
been  made  to  include  a  biography  of  Professor  Rowland,  for  this  would 
properly  form  a  volume  by  itself,  and  would  require  much  time  for  its 
preparation.  There  was  at  hand,  moreover,  the  memorial  address  of 
Dr.  Mendenhall,  which  tells  so  well,  though  briefly,  the  story  of  his  life. 


vi  PREFACE 

It  was  with  difficulty,  and  only  after  a  careful  examination  of  many 
hundred  volumes  of  scientific  journals  and  transactions,  that  the  com- 
mittee were  able  to  obtain  copies  of  all  of  Professor  Eowland's  numerous 
and  scattered  articles;  but  they  are  convinced  that  no  paper  of  import- 
ance has  escaped  their  notice.  In  preparing  for  publication  these  me- 
moirs and  addresses,  no  alterations  other  than  typographical  have  been 
made. 

For  permission  to  reprint  some  of  the  most  valuable  papers,  thanks 
are  due  to  various  publishers.  The  committee  wish  especially  to  express 
their  appreciation  of  the  kindness  of  Messrs.  A.  and  C.  Black,  and  of 
The  Times  (London)  for  permission  to  reprint  from  the  Encyclopaedia 
Britannica  the  articles  on  "  The  Screw  "  and  on  "  Diffraction  Gratings," 
and  of  the  Engineering  Magazine  Company,  of  New  York,  for  permis- 
sion to  reprint  the  article  on  "  Modern  Theories  as  to  Electricity." 

The  committee  acknowledge  their  indebtedness  also  to  Mr.  1ST.  Mur- 
ray, Librarian  of  The  Johns  Hopkins  University,  who  has  personally 
superintended  the  details  of  publication,  and  whose  advice  has  been 
often  needed.  The  proofs  have  been  revised  by  Mr.  E.  P.  Hyde,  Fellow 
in  The  Johns  Hopkins  University,  who  has  thus  been  of  the  greatest 
assistance  to  the  committee. 

THE  JOHNS  HOPKINS  UNIVERSITY, 

BALTIMORE,  MARYLAND, 

DECEMBER  1,  1902. 


CONTENTS 


PAGE 

PREFACE    v 

ADDRESS  BY  DR.  T.  C.  MENDENHALL  1 

SCIENTIFIC   PAPERS    19 

PART  I.    EAKLY  PAPERS.  21 

*1.  The   Vortex   Problem    23 

Scientific  American  XIII,  308,  1865. 

2.  Paine's  Electro-magnetic  Engine    24 

Scientific  American  XXV,  21,  1871. 

3.  Illustration  of  Resonances  and  Actions  of  a  Similar  Nature 28 

Journal  of  the  Franklin  Institute  XCIV,  275-278,  1872. 

4.  On  the  Auroral  Spectrum  31 

American  Journal  of  Science  (3),  V,  320,  1873. 

PART  II.    MAGNETISM  AND  ELECTRICITY.  33 

5.  On  Magnetic  Permeability,  and  the  Maximum  of  Magnetism  of  Iron, 

Steel  and  Nickel   35 

Philosophical  Magazine  (4),  XL VI,  140-159,  1873. 

6.  On  the  Magnetic  Permeability  and  Maximum  of  Magnetism  of  Nickel 

and   Cobalt    56 

Philosophical  Magazine  (4),  XLVHI,  321-340,  1874. 

7.  On  a  new  Diamagnetic  Attachment  to  the  Lantern,  with  a  Note  on 

the  Theory  of  the  Oscillations  of  Inductively  Magnetized  Bodies..     75 
American  Journal  of  Science  (3),  IX,  357-361,  1875. 

8.  Notes   on   Magnetic  Distribution    80 

Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  XI,  191,  192, 
1876. 

9.  Note  on  Kohlrausch's  Determination  of  the  Absolute  Value  of  the 

Siemens  Mercury  Unit  of  Electrical  Resistance   82 

Philosophical  Magazine  (4),  L,  161-163,  1875. 

10.  Preliminary  Note  on  a  Magnetic  Proof  Plane  85 

American  Journal  of  Science  (3),  X,  14-17,  1875. 

*  The  numbers  refer  to  corresponding  ones  in  the  Bibliography,  page  681. 


viii  CONTENTS 

PAGE 

11.  Studies  on  Magnetic  Distribution    89 

American  Journal  of  Science  (3),  X,  325-335,  451-450,   1875. 

Ibid.,  XI,  17-29,  103-108,  1876. 

Philosophical  Magazine  (i\  L,  257-277,  348-367, 1875. 

12.  On  the  Magnetic  Effect  of  Electric  Convection 128 

American  Journal  of  Science  (3),  XV,  30-38,  1878. 

13.  Note  on  the  Magnetic  Effect  of  Electric  Convection  138 

Philosophical  Magazine  (5),  VII,   442-443,   1879. 

14.  Note  on  the  Theory  of  Electric  Absorption   139 

American  Journal  of  Mathematics,  I,  53-58,  1878. 

15.  Eesearch  on  the  Absolute  Unit  of  Electrical  Eesistance   145 

American  Journal  of  Science  (3),  XV,  281-291,  325-336,  430-439,  1878. 

17.  On  Professors  Ayrton  and  Perry's  NeAv  Theory  of  the  Earth's  Mag- 

netism, with  a  Note  on  a  New  Theory  of  the  Aurora 179 

Philosophical  Magazine   (5),   VIII,    102-106,   1879. 
Proceedings  of  the  Physical  Society,  III,  93-98,  1879. 

18.  On  the  Diamagnetic  Constants  of  Bismuth  and  Calc-spar  in  Absolute 

Measure.     By  H.  A.  Rowland  and  W.  W.  Jacques 184 

American  Journal  of  Science  (3),  XVIII,  360-371,  1879. 

19.  Preliminary  Notes  on  Mr.  Hall's  recent  Discovery  197 

American  Journal  of  Mathematics,  II,  354-356,  1879. 
Philosophical   Magazine  (5),    IX,    432-434,   1880. 
Proceedings  of  the  Physical  Society,  IV,  10-13,  1880. 

22.  On  the  Efficiency  of  Edison's  Electric  Light.     By  H.  A.  Rowland  and 

G.   F.   Barker    200 

American  Journal  of  Science  (3),  XIX,  337-339,  1880. 

27.  Electric    Absorption    of    Crystals.     By    H.    A.    Rowland    and    E.    L. 

Nichols     204 

Philosophical  Magazine  (5),  XI,  414-419,  1881. 
Proceedings  of  the  Physical  Society,  IV,  215-221,  1881. 

28.  On  Atmospheric  Electricity    212 

Johns  Hopkins  University  Circulars  Xo.  19,  pp.  4,  5,  1882. 

34.  The  Determination  of  the  Ohm.     Extract  from  a  letter  to  the  Inter- 

national  Congress  at  Paris,   1884    217 

Proces-Verbaux,  Deuxieme    Session,  p.  37.     Paris,  1884. 

35.  The  Theory  of  the  Dynamo   219 

Report  of  the  Electrical  Conference  at  Philadelphia  in  November,   1884, 
pp.     72-83,   90,  91,   104,   107.     Washington,   1886. 

36.  On   Lightning  Protection    236 

Report  of  the  Electrical  Conference  at  Philadelphia  in  November,   1884, 
pp.  172-174. 

37.  On  the  Value  of  the  Ohm  239 

La  Lumiere  Electrique,  XXVI,  pp.  188,  477,  1887. 


CONTEXTS 


PAOE 

38.  On  a  Simple  and  Convenient  Form  of  Water-battery  ...............   241 

American  Journal  of  Science  (3),  XXXIII,  147,  1887. 

Philosophical  Magazine  (5),  XXIII,  303,  1887. 

Johns  Hopkins  University  Circulars  No.  57,  p.  80,  1887. 

40.  On  an  Explanation  of  the  Action  of  a  Magnet  on  Chemical  Action. 

By  H.  A.  Rowland  and  Louis  Bell  ................................   242 

American  Journal  of  Science  (3),  XXXVI,  39-47,  1888. 
Philosophical  Magazine  (5),  XXVI,  105-114,  1888. 

43.  On   the  Electromagnetic  Effect   of  Convection-Currents.    By  H.  A. 

Kowland  and  C.  T.  Hutchinson   ..................................  251 

Philosophical  Magazine  (5),  XXVH,  445-460,  1889. 

44.  On  the  Ratio  of  the  Electro-static  to  the  Electro-magnetic  Unit  of 

Electricity.     By  H.  A.  Rowland,  E.  H.  Hall,  and  L.  B.  Fletcher.  .  .   266 
American  Journal  of  Science  (3),  XXXVIII,  289-298,  1889. 
Philosophical  Magazine  (5),  XXVIII,  304-315,  1889. 

47.  Notes  on  the  Theory  of  the  Transformer   ..........................  276 

Philosophical  Magazine  (5),  XXXIV,  54-57,  1892. 

Electrical  World,   XX,  20,   1892. 

Johns  Hopkins  University  Circulars  No.  99,   pp.  104,   105,  1892. 

48.  Notes  on  the  Effect  of  Harmonics  in  the  Transmission  of  Power  by 

Alternating  Currents    ............................................   280 

Electrical  World,  XX,  368,  1892. 

La  Lumiere  Electrique,  XLVII,   42-44,   1893. 

53.  Modern  Theories  as  to  Electricity    .................................   285 

The  Engineering  Magazine,  VIII,  589-596,   1895. 

60.  Electrical  Measurement  by  Alternating  Currents   ..................  294 

American  Journal  of  Science  (4),  IV,  429-448,  1897. 
Philosophical  Magazine  (5),  XLV,  66-85,  1898. 

62.  Electrical  Measurements.     By  H.  A.  Rowland  and  T.  D.  Penniman..   314 

American  Journal  of  Science  (4),  VIII,  35-57,  1899. 

63.  Resistance  to  Ethereal  Motion.     By  H.  A.  Rowland,  N.  E.  Gilbert  and 

P.  C.  McJunckin   ................................................     338 

Johns  Hopkins  University  Circulars  No.  146,  p.  60,  1900. 

PART  III.    HEAT.  341 

16.  On  the  Mechanical  Equivalent  of  Heat,  with  Subsidiary  Researches 
on  the  Variation  of  the  Mercurial  from  the  Air-Thermometer  and 
on  the  Variation  of  the  Specific  Heat  of  Water  ...................  343 

Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  XV,  75-200, 

1880. 
21.  Appendix  to  Paper  on  the  Mechanical  Equivalent  of  Heat,  Contain- 

ing the  Comparison  with  Dr.  Joule's  Thermometer  ...............  469 

Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  XVI,  38-45, 

1881. 
20.  Physical  Laboratory;   Comparison  of  Standards    ...................  477 

Johns  Hopkins  University  Circulars  No.  3,  p.  31,  1880. 


x  CONTENTS 

PAGE 

26.  On  Geissler  Thermometers   481 

American  Journal  of  Science  (3),  XXI,  451-453,   1881. 

PART  IV.    LIGHT.  485 

29.  Preliminary  Notice  of  the  Eesults  Accomplished  in  the  Manufacture 

and  Theory  of  Gratings  for  Optical  Purposes   487 

Johns  Hopkins  University   Circulars  No.   17,   pp.   248,   249,   1882. 
Philosophical  Magazine   (4),   XIII,   469-474,   1882. 
Nature,  26,  211-213,  1882. 

30.  On  Concave  Gratings  for  Optical  Purposes    492 

American  Journal  of  Science  (3),  XXVI,   87-98,  1883. 
Philosophical  Magazine  (5),  XVI,  197-210,  1883. 

31.  On  Mr.  Glazebrook's  Paper  on  the  Aberration  of  Concave  Gratings.   505 

American  Journal  of  Science  (3),  XXVI,  214,  1883. 
Philosophical  Magazine  (5),  XVI,  210,  1883. 

33.  Screw     506 

Encyclopaedia  Britannica,  Ninth  Edition,  Vol.  21. 

39.  On  the  Relative  Wave-lengths  of  the  Lines  of  the  Solar  Spectrum  . . .   512 
American  Journal  of  Science  (3),   XXXIII,  182-190,   1887. 
Philosophical  Magazine  (5),  XXIII,  257-265,  1887. 

41.  Table   of   Standard   Wave-lengths    517 

Philosophical  Magazine  (5),  XXVII,  479-484,  1889. 

42.  A  Few  Notes  on  the  Use  of  Gratings   519 

Johns  Hopkins  University  Circulars  No.  73,  pp.   73,  74,   1889. 

46.  Report  of  Progress  in  Spectrum  Work   521 

The  Chemical  News,  LXIII,  133,  1891. 

Johns  Hopkins  University  Circulars  No.   85,  pp.   41,  42,   1891. 

American  Journal  of  Science  (3),  XLI,  243,  244,  1891. 

49.  Gratings  in  Theory  and  Practice  525 

Philosophical   Magazine   (5),   XXXV,    397-419,    1893. 
Astronomy  and  Astro-Physics,  XII,  129-149,  1893. 

50.  A  New  Table  of  Standard  Wave-lengths   545 

Philosophical  Magazine  (5),  XXXVI,  49-75,  1893. 
Astronomy  and  Astro-Physics,   XII,.  321-347,   1893. 

51.  On  a  Table  of  Standard  Wave-lengths  of  the  Spectral  Lines  548 

Memoirs  of  the  American  Academy  of  Arts  and  Sciences,   XII,   101-186, 
1896. 

52.  The   Separation   of  the  Rare   Earths    565 

Johns  Hopkins  University  Circulars  No.  112,  pp.  73,  74,  1894. 

57.  Notes  of  Observation  on  the  Rontgen  Rays.     By  H.  A.  Rowland,  N. 

R.   Carmichael  and  L.  J.  Briggs    571 

American  Journal  of  Science  (4),  I,  247,  248,  1896. 
Philosophical  Magazine   (5),   XLI,  381-382,   1896. 


CONTENTS  xi 

PAGE 

58.  Notes  on  Rontgen  Bays.     By  H.  A.  Rowland,  N.  R.  Carmichael  and 

L.  J.  Briggs   573 

Electrical  World,  XXVII,  452,  1896. 

59.  The  Eontgen  Ray  and  its  Relation  to  Physics   576 

Transactions  of  the  American  Institute  of  Electrical  Engineers,  XIII, 
403-410,  430,  431,  1896. 

64.  Diffraction   Gratings    587 

Encyclopaedia  Britannica,  New  Volumes,  III,  458,  459,  1902. 

ADDRESSES    591 

1.  A  Plea  for  Pure  Science.     Address  as  Vice-President  of  Section  B  of 

the  American  Association  for  the  Advancement  of  Science,  Minne- 
apolis, August  15,  1883  593 

Proceedings  of  the  American  Association  for  the  Advancement  of  Science, 
XXXII,  105-126,  1883. 

Science,  II,  242-250,  1883. 

Journal  of   the  Franklin  Institute,   CXVI,   279-299,   1883. 

2.  The  Physical  Laboratory  in  Modern  Education.    Address  for  Com- 

memoration Day  of  the  Johns  Hopkins  University,  February  22, 

1886      614 

Johns  Hopkins  University  Circulars  No.  50,  pp.  103-105,  1886. 

3.  Address  as  President  of  the  Electrical  Conference  at  Philadelphia, 

September  8,   1884    619 

Report  of  the  Electrical  Conference  at  Philadelphia  in  September,  1884, 
Washington,  1886. 

4.  The   Electrical   and   Magnetic   Discoveries   of   Faraday.     Address   at 

The  Opening  of  the  Electrical  Club  House  of  New  York  City,  1888 .  638 
Electrical  Review,  Feb.  4,  1888. 

5.  On  Modern  Views  with  Respect  to  Electric  Currents.     Address  Be- 

fore the  American  Institute  of  Electrical   Engineers,   New  York, 

May    22,    1889    653 

Transactions  of  the  American  Institute  of  Electrical  Engineers,  VI,  342- 
357,  1889. 

6.  The  Highest  Aim   of  the  Physicist.    Address  as   President  of   the 

American  Physical  Society,  New  York,  October  28,  1899   668 

Science,  X,  825-833,  1899. 

American  Journal  of  Science  (4),  VIII,  401-411,  1899. 

Johns  Hopkins  University  Circulars  No.  143,  pp.  17-20,  1900. 

BIBLIOGRAPHY    679 

DESCRIPTION   OF    THE    DIVIDING    ENGINES   DESIGNED   BY    PRO- 
FESSOR   ROWLAND    689 

INDEX.  699 


HENRY  A.  ROWLAND 
COMMEMORATIVE  ADDRESS 

BY 

DR.  THOMAS  C.  MENDENHALL 

[Delivered  before  an  assembly  of  friends,  Baltimore,  October  26,  1901.] 


In  reviewing  the  scientific  work  of  Professor  Kowland  one  is  most 
impressed  by  its  originality.  In  quantity,  as  measured  by  printed  page 
or  catalogue  of  titles,  it  has  been  exceeded  by  many  of  his  contem- 
poraries; in  quality  it  is  equalled  by  that  of  only  a  very,  very  small 
group.  The  entire  collection  of  his  important  papers  does  not  exceed 
thirty  or  forty  in  number  and  his  unimportant  papers  were  few.  When, 
at  the  unprecedentedly  early  age  of  thirty-three  years,  he  was  elected 
to  membership  in  the  National  Academy  of  Sciences,  the  list  of  his 
published  contributions  to  science  did  not  contain  over  a  dozen  titles, 
but  any  one  of  not  less  than  a  half-dozen  of  these,  including  what  may 
properly  be  called  his  very  first  original  investigation,  was  of  such 
quality  as  to  fully  entitle  him  to  the  distinction  then  conferred. 

Fortunately  for  him,  and  for  science  as  well,  he  liijed  during  a  period 
of  almost  unparalleled  intellectual  activity,  and  his  work  was  done 
during  the  last  quarter  of  that  century  to  which  we  shall  long  turn 
with  admiration  and  wonder.  During  these  twenty-five  years  the  num- 
ber of  industrious  cultivators  of  his  own  favorite  field  increased  enor- 
mously, due  in  large  measure  to  the  stimulating  effect  of  his  own  enthu- 
siasm, and  while  there  was  only  here  and  there  one  possessed  of  the 
divine  afflatus  of  true  genius,  there  were  many  ready  to  labor  most  assid- 
uously in  fostering  the  growth,  development,  and  final  fruition  of  germs 
which  genius  stopped  only  to  plant.  A  proper  estimate  of  the  magni- 
tude and  extent  of  Eowland's  work  would  require,  therefore,  a  careful 
examination,  analytical  and  historical,  of  the  entire  mass  of  contribu- 
tions to  physical  science  during  the  past  twenty-five  years,  many  of 
his  own  being  fundamental  in  character  and  far-reaching  in  their  influ- 
ence upon  the  trend  of  thought,  in  theory  and  in  practice.  But  it  was 
1 


2  HENRY  A.  ROWLAND 

quality,  not  quantity,  that  he  himself  most  esteemed  in  any  perform- 
ance; it  was  quality  that  always  commanded  his  admiration  or  excited 
him  to  keenest  criticism;  no  one  recognized  more  quickly  than  he  a 
real  gem,  however  minute  or  fragmentary  it  might  be,  and  by  quality 
rather  than  by  quantity  we  prefer  to  judge  his  work  to-day,  as  he  would 
himself  have  chosen. 

Rowland's  first  contribution  to  the  literature  of  science  took  the 
form  of  a  letter  to  The  Scientific  American,  written  in  the  early  Autumn 
of  1865,  when  he  was  not  yet  seventeen  years  old.  Much  to  his  sur- 
prise this  letter  was  printed,  for  he  says  of  it,  "  I  wrote  it  as  a  kind  of 
joke  and  did  not  expect  them  to  publish  it."  Neither  its  humor  nor 
its  sense,  in  which  it  was  not  lacking,  seems  to  have  been  appreciated 
by  the  editor,  for  by  the  admission  of  certain  typographical  errors  he 
practically  destroyed  both.  The  embryo  physicist  got  nothing  but  a 
little  quiet  amusement  out  of  this,  but  in  a  letter  of  that  day  he  de- 
clares his  intention  of  some  time  writing  a  sensible  article  for  the 
journal  that  so  unexpectedly  printed  what  he  meant  to  be  otherwise. 
This  resolution  he  seems  not  to  have  forgotten,  for  nearly  six  years 
later  there  appeared  in  its  columns  what  was,  as  far  as  is  known,  his 
second  printed  paper  and  his  first  serious  public  discussion  of  a  scientific 
question.  It  was  a  keen  criticism  of  an  invention  which  necessarily 
involved  the  idea  of  perpetual  motion,  in  direct  conflict  with  the  great 
law  of  the  Conservation  of  Energy  which  Rowland  had  already  grasped. 
It  was,  as  might  be  expected,  thoroughly  well  done,  and  received  not  a 
little  complimentary  notice  in  other  journals.  This  was  in  1871,  the 
year  following  that  in  which  he  was  graduated  as  a  Civil  Engineer  from 
the  Rensselaer  Polytechnic  Institute,  and  the  article  was  written  while 
in  the  field  at  work  on  a  preliminary  railroad  survey.  A  year  later, 
having  returned  to  the  Institute  as  instructor  in  physics,  he  published 
in  the  Journal  of  the  Franklin  Institute  an  article  entitled  "  Illustra- 
tions of  Resonances  and  Actions  of  a  Similar  Nature,"  in  which  he 
described  and  discussed  various  examples  of  resonance  or  "  sympa- 
thetic "  vibration.  This  paper,  in  a  way,  marks  his  admission  to  the 
ranks  of  professional  students  of  science  and  may  be  properly  con- 
sidered as  his  first  formal  contribution  to  scientific  literature;  his  last 
was  an  exhaustive  article  on  spectroscopy,  a  subject  of  which  he,  above 
all  others,  was  master,  prepared  for  a  new  edition  of  the  Encyclopaedia 
Britannica,  not  yet  published.  Early  in  1873  the  American  Journal  of 
Science  printed  a  brief  note  by  Rowland  on  the  spectrum  of  the  Aurora, 
sent  in  response  to  a  kindly  and  always  appreciated  letter  from  Pro- 


COMMEMORATIVE  ADDRESS  3 

fessor  George  F.  Barker,  one  of  the  editors  of  that  journal.  It  is  inter- 
esting as  marking  the  beginning  of  his  optical  work.  For  a  year,  or 
perhaps  for  several  years  previous  to  this  time,  however,  he  had  been 
busily  engaged  on  what  proved  to  be,  in  its  influence  upon  his  future 
career,  the  most  important  work  of  his  life.  To  climb  the  ladder  of 
reputation  and  success  by  simple,  easy  steps  might  have  contented 
Eowland,  but  it  would  have  been  quite  out  of  harmony  with  his  bold 
spirit,  his  extraordinary  power  of  analysis  and  his  quick  recognition  of 
the  relation  of  things.  By  the  aid  of  apparatus  entirely  of  his  own 
construction  and  by  methods  of  his  own  devising,  he  had  made  an  inves- 
tigation both  theoretical  and  experimental  of  the  magnetic  permea- 
bility and  the  maximum  magnetization  of  iron,  steel  and  nickel,  a 
subject  in  which  he  had  been  interested  in  his  boyhood.  On  June  9, 
1873,  in  a  letter  to  his  sister,  he  says:  " I  have  just  sent  off  the  results 
of  my  experiments  to  the  publisher  and  expect  considerable  from  it; 
not,  however,  filthy  lucre,  but  good,  substantial  reputation."  What 
he  did  get  from  it,  at  first,  was  only  disappointment  and  discourage- 
ment. It  was  more  than  once  rejected  because  it  was  not  understood, 
and  finally  he  ventured  to  send  it  to  Clerk  Maxwell,  in  England,  by 
whose  keen  insight  and  profound  knowledge  of  the  subject  it  was 
instantly  recognized  and  appraised  at  its  full  value.  Eegretting  that 
the  temporary  suspension  of  meetings  made  it  impossible  for  him  to 
present  the  paper  at  once  to  the  Eoyal  Society,  Maxwell  said  he  would 
do  the  next  best  thing,  which  was  to  send  it  to  the  Philosophical  Maga- 
zine for  immediate  publication,  and  in  that  journal  it  appeared  in 
August,  1873,  Maxwell  himself  having  corrected  the  proofs  to  avoid 
delay.  The  importance  of  the  paper  was  promptly  recognized  by 
European  physicists,  and  abroad,  if  not  at  home,  Eowland  at  once  took 
high  rank  as  an  investigator. 

In  this  research  he  unquestionably  anticipated  all  others  in  the  dis- 
covery and  announcement  of  the  beautifully  simple  law  of  the  magnetic 
circuit,  the  magnetic  analogue  of  Ohm's  law,  and  thus  laid  the  founda- 
tion for  the  accurate  measurement  and  study  of  magnetic  permea- 
bility, the  importance  of  which,  both  in  theory  and  practice  during 
recent  years,  it  is  difficult  to  overestimate.  It  has  always  seemed  to 
me  that  when  consideration  is  given  to  his  age,  his  training,  and  the 
conditions  under  which  his  work  was  done,  this  early  paper  gives  a 
better  measure  of  Eowland's  genius  than  almost  any  performance  of 
his  riper  years.  During  the  next  year  or  two  he  continued  to  work 
along  the  same  lines  in  Troy,  publishing  not  many,  but  occasional, 


4  HENRY  A.  BOWLAND 

additions  to  and  developments  of  his  first  magnetic  research.  There 
was  also  a  paper  in  which  he  discussed  Kohlrausch's  determination  of 
the  absolute  value  of  the  Siemens  unit  of  electrical  resistance,  fore- 
shadowing the  important  part  which  he  was  to  play  in  later  years  in  the 
final  establishment  of  standards  for  electrical  measurement. 

In  1875,  having  been  appointed  to  the  professorship  of  physics  in 
the  Johns  Hopkins  University,  the  faculty  of  which  was  just  then 
being  organized,  he  visited  Europe,  spending  the  better  part  of  a  year 
in  the  various  centres  of  scientific  activity,  including  several  months  at 
Berlin  in  the  laboratory  of  the  greatest  Continental  physicist  of  his 
time,  von  Helmholtz.  While  there  he  made  a  very  important  investi- 
gation of  the  magnetic  effect  of  moving  electrostatic  charges,  a  question 
of  first  rank  in  theoretical  interest  and  significance.  His  manner  of 
planning  and  executing  this  research  made  a  marked  impression  upon 
the  distinguished  Director  of  the  laboratory  in  which  it  was  done,  and, 
indeed,  upon  all  who  had  any  relations  with  Eowland  during  its  pro- 
gress. He  found  what  von  Helmholtz  himself  had  sought  for  in  vain, 
and  when  the  investigation  was  finished  in  a  time  which  seemed  incred- 
ibly short  to  his  more  deliberate  and  painstaking  associates,  the  Director 
not  only  paid  it  the  compliment  of  an  immediate  presentation  to  the 
Berlin  Academy,  but  voluntarily  met  all  expenses  connected  with  its 
execution. 

The  publication  of  this  research  added  much  to  Eowland's  rapidly- 
growing  reputation,  and  because  of  that  fact,  as  well  as  on  account  of 
its  intrinsic  value,  it  is  important  to  note  that  his  conclusions  have 
been  held  in  question,  with  varying  degrees  of  confidence,  from  the  day 
of  their  announcement  to  the  present.  The  experiment  is  one  of  great 
difficulty  and  the  effect  to  be  looked  for  is  very  small  and  therefore 
likely  to  be  lost  among  unrecognized  instrumental  and  observational 
errors.  It  was  characteristic  of  Eowland's  genius  that  with  compara- 
tively crude  apparatus  he  got  at  the  truth  of  the  thing  in  the  very  start. 
Others  who  have  attempted  to  repeat  his  work  have  not  been  uniformly 
successful,  some  of  them  obtaining  a  wholly  negative  result,  even  when 
using  apparatus  apparently  more  complete  and  effective  than  that  first 
employed  by  Eowland.  Such  was  the  experience  of  Lecher  in  1884, 
but  in  1888  Eoentgen  confirmed  Eowland's  experiments,  detecting  the 
existence  of  the  alleged  effect.  The  result  seeming  to  be  in  doubt, 
Eowland  himself,  assisted  by  Hutchinson,  in  1889  took  it  up  again, 
using  essentially  his  original  method  but  employing  more  elaborate  and 
sensitive  apparatus.  They  not  only  confirmed  the  early  experiments, 


COMMEMORATIVE  ADDRESS  5 

but  were  able  to  show  that  the  results  were  in  tolerably  close  agreement 
with  computed  values.  The  repetition  of  the  experiment  by  Himstedt 
in  the  same  year  resulted  in  the  same  way,  but  in  1897  the  genuineness 
of  the  phenomenon  was  again  called  in  question  by  a  series  of  experi- 
ments made  at  the  suggestion  of  Lippmann,  who  had  proposed  a  study 
of  the  reciprocal  of  the  Rowland  effect,  according  to  which  variations 
of  a  magnetic  field  should  produce  a  movement  of  an  electrostatically 
charged  body.  This  investigation,  carried  out  by  Cremieu,  gave  an 
absolutely  negative  result,  and  because  the  method  was  entirely  differ- 
ent from  that  employed  by  Eowland  and,  therefore,  unlikely  to  be 
subject  to  the  same  systematic  errors,  it  naturally  had  much  weight 
with  those  who  doubted  his  original  conclusions.  Realizing  the  neces- 
sity for  additional  evidence  in  corroboration  of  his  views,  in  the  Fall 
of  the  year  1900,  the  problem  was  again  attacked  in  his  own  laboratory 
and  he  had  the  satisfaction,  only  a  short  time  before  his  death,  of 
seeing  a  complete  confirmation  of  the  results  he  had  announced  a 
quarter  of  a  century  earlier,  concerning  which,  however,  there  had 
never  been  the  slightest  doubt  in  his  own  mind.  It  is  a  further  satis- 
faction to  his  friends  to  know  that  a  very  recent  investigation  at  the 
Jefferson  Physical  Laboratory  of  Harvard  University,  in  which  Row- 
land's methods  were  modified  so  as  to  meet  effectively  the  objections 
made  by  his  critics,  has  resulted  in  a  complete  verification  of  his 
conclusions. 

On  his  return  from  Europe,  in  1876,  his  time  was  much  occupied 
with  the  beginning  of  the  active  duties  of  his  professorship,  and 
especially  in  putting  in  order  the  equipment  of  the  laboratory  over 
which  he  was  to  preside,  much  of  which  he  had  ordered  while  in  Europe. 
In  its  arrangement  great,  many  of  his  friends  thought  undue,  promi- 
nence was  given  to  the  workshop,  its  machinery,  tools,  and  especially 
the  men  who  were  to  be  employed  in  it.  He  planned  wisely,  however, 
for  he  meant  to  see  to  it  that  much,  perhaps  most,  of  the  work  under 
his  direction  should  be  in  the  nature  of  original  investigation,  for  the 
successful  execution  of  which  a  well-manned  and  equipped  workshop  is 
worth  more  than  a  storehouse  of  apparatus  already  designed  and  used 
by  others. 

He  shortly  found  leisure,  however,  to  plan  an  elaborate  research  upon 
the  Mechanical  Equivalent  of  Heat,  and  to  design  and  supervise  the 
construction  of  the  necessary  apparatus  for  a  determination  of  the 
numerical  value  of  this  most  important  physical  constant,  which  he 
determined  should  be  exhaustive  in  character  and,  for  some  time  to 


6  HENRY  A.  EOWLAND 

come,  at  least,  definitive.  While  this  work  lacked  the  elements  of 
originality  and  boldness  of  inception  by  which  many  of  his  principal 
researches  are  characterized,  it  was  none  the  less  important.  While 
doing  over  again  what  others  had  done  before  him,  he  meant  to  do  it, 
and  did'  do  it,  on  a  scale  and  in  a  way  not  before  attempted.  It  was  one 
of  the  great  constants  of  nature,  and,  besides,  the  experiment  was  one 
surrounded  by  difficulties  so  many  and  so  great  that  few  possessed  the 
courage  to  undertake  it  with  the  deliberate  expectation  of  greatly  ex- 
celling anything  before  accomplished.  These  things  made  it  attractive 
to  Eowland. 

The  overthrow  of  the  materialistic  theory  of  heat,  accompanied  as 
it  was  by  the  experimental  proof  of  its  real  nature,  namely,  that  it  is 
essentially  molecular  energy,  laid  the  foundation  for  one  of  those  two 
great  generalizations  in  science  which  will  ever  constitute  the  glory  of 
the  nineteenth  century.  The  mechanical  equivalent  of  heat,  the  num- 
ber of  units  of  work  necessary  to  raise  one  pound  of  water  one  degree 
in  temperature,  has,  with  much  reason,  been  called  the  Golden  Number 
of  that  century.  Its  determination  was  begun  by  an  American,  Count 
Eumford,  and  finished  by  Rowland  nearly  a  hundred  years  later.  In 
principle  the  method  of  Eowland  was  essentially  that  of  Eumford. 
The  first  determination  was,  as  we  now  know,  in  error  by  nearly  40 
per  cent;  the  last  is  probably  accurate  within  a  small  fraction  of  1  per 
cent.  Eumford  began  the  work  in  the  ordnance  foundry  of  the  Elector 
of  Bavaria  at  Munich,  converting  mechanical  energy  into  heat  by  means 
of  a  blunt  boring  tool  in  a  cannon  surrounded  by  a  definite  quantity 
of  water,  the  rise  in  temperature  of  which  could  be  measured.  Eowland 
finished  it  in  an  establishment  founded  for  and  dedicated  to  the  in- 
crease and  diffusion  of  knowledge,  aided  by  all  the  resources  and  refine- 
ments in  measurement  which  a  hundred  years  of  exact  science  had 
made  possible.  As  the  mechanical  theory  of  heat  was  the  germ  out 
of  which  grew  the  principle  of  the  conservation  of  energy,  an  exact 
determination  of  the  relation  of  work  and  heat  was  necessary  to  a 
rigorous  proof  of  that  principle,  and  Joule,  of  Manchester,  to  whom 
belongs  more  of  the  credit  for  this  proof  than  to  any  other  one  man  or, 
perhaps,  to  all  others  put  together,  experimented  on  the  mechanical 
equivalent  of  heat  for  more  than  forty  years.  He  employed  various 
methods,  finally  recurring  to  the  early  method  of  heating  water  by 
friction,  improving  on  Eumford's  device  by  creating  friction  in  the 
water  itself.  Joule's  last  experiments  were  made  in  1878,  and  most 
of  Eowland's  work  was  done  in  the  year  following.  It  excelled  that  of 


COMMEMOBATIVE    ADDRESS  7 

Joule,  not  only  in  the  magnitude  of  the  quantities  to  be  observed,  but 
especially  in  the  greater  attention  given  to  the  matter  of  thermometry. 
In  common  with  Joule  and  other  previous  investigators,  he  made  use 
of  mercury  thermometers,  but  this  was  only  for  convenience,  and  they 
were  constantly  compared  with  an  air  thermometer,  the  results  being 
finally  reduced  to  the  absolute  scale.  By  experimenting  with  water  at 
different  initial  temperatures  he  obtained  slightly  different  values  for 
the  mechanical  equivalent  of  heat,  thus  establishing  beyond  question 
the  variability  of  the  specific  heat  of  water.  Indeed,  so  carefully  and 
accurately  was  the  experiment  worked  out  that  he  was  able  to  draw 
the  variation  curve  and  to  show  the  existence  of  a  minimum  value  at 
30  degrees  C. 

This  elaborate  and  painstaking  research,  which  is  now  classical,  was 
everywhere  awarded  high  praise.  It  was  published  in  full  by  the  Amer- 
ican Academy  of  Arts  and  Sciences  with  the  aid  of  a  fund  originally 
established  by  Count  Eumford,  and  in  1881  it  was  crowned  as  a  prize 
essay  by  the  Venetian  Institute.  Its  conclusions  have  stood  the  test 
of  twenty  years  of  comparison  and  criticism. 

In  the  meantime,  Rowland's  interest  had  been  drawn,  largely  per- 
haps through  his  association  with  his  then  colleague,  Professor  Hast- 
ings, toward  the  study  of  light.  He  was  an  early  and  able  exponent 
of  Maxwell's  Magnetic  Theory  and  he  published  important  theoretical 
discussions  of  electro-magnetic  action.  Recognizing  the  paramount  im- 
portance of  the  spectrum  as  a  key  to  the  solution  of  problems  in  ether 
physics,  he  set  about  improving  the  methods  by  which  it  was  produced 
and  studied,  and  was  thus  led  into  what  will  probably  always  be  re- 
garded as  his  highest  scientific  achievement. 

At  that  time,  the  almost  universally  prevailing  method  of  studying 
the  spectrum  was  by  means  of  a  prism  or  a  train  of  prisms.  But  the 
prismatic  spectrum  is  abnormal,  depending  for  its  character  largely 
upon  the  material  made  use  of.  The  normal  spectrum  as  produced  by 
a  grating  of  fine  wires  or  a  close  ruling  of  fine  lines  on  a  plane  reflect- 
ing or  transparent  surface  had  been  known  for  nearly  a  hundred  years, 
and  the  colors  produced  by  scratches  on  polished  surfaces  were  noted 
by  Eobert  Boyle,  more  than  two  hundred  years  ago.  Thomas  Young 
had  correctly  explained  the  phenomenon  according  to  the  undulatory 
theory  of  light,  and  gratings  of  fine  wire  and,  later,  of  rulings  on  glass 
were  used  by  Fraunhofer  who  made  the  first  great  study  of  the  dark 
lines  of  the  solar  spectrum.  Imperfect  as  these  gratings  were,  Fraun- 
hofer succeeded  in  making  with  them  some  remarkably  good  measures 


8  HENRY  A.  ROWLAND 

of  the  length  of  light  waves,  and  it  was  everywhere  admitted  that  for 
the  most  precise  spectrum  measurements  they  were  indispensable.  In 
their  construction,  however,  there  were  certain  mechanical  difficulties 
which  seemed  for  a  time  to  be  insuperable.  There  was  no  special 
trouble  in  ruling  lines  as  close  together  as  need  be ;  indeed,  Nobert,  who 
was  long  the  most  successful  maker  of  ruled  gratings,  had  succeeded  in 
putting  as  many  as  a  hundred  thousand  in  the  space  of  a  single  inch. 
The  real  difficulty  was  in  the  lack  of  uniformity  of  spacing,  and  on 
uniformity  depended  the  perfection  and  purity  of  the  spectrum  pro- 
duced. Nobert  jealously  guarded  his  machine  and  method  of  ruling 
gratings  as  a  trade  secret,  a  precaution  hardly  worth  taking,  for  before 
many  years  the  best  gratings  in  the  world  were  made  in  the  United 
States.  More  than  thirty  years  ago  an  amateur  astronomer,  in  New 
York  City,  a  lawyer  by  profession,  Lewis  M.  Rutherfurd,  became  inter- 
ested in  the  subject  and  built  a  ruling  engine  of  his  own  design.  In 
this  machine  the  motion  of  the  plate  on  which  the  lines  were  ruled 
was  produced  at  first  by  a  somewhat  complicated  set  of  levers,  for  which 
a  carefully  made  screw  was  afterwards  substituted.  Aided  by  the  skill 
and  patience  of  his  mechanician,  Chapman,  Rutherfurd  continued  to 
improve  the  construction  of  his  machine  until  he  was  able  to  produce 
gratings  on  glass  and  on  speculum  metal  far  superior  to  any  made  in 
Europe.  The  best  of  them,  however,  were  still  faulty  in  respect  to 
uniformity  of  spacing,  and  it  was  impossible  to  cover  a  space  exceeding 
two  or  three  square  inches  in  a  satisfactory  manner.  When  Rowland 
took  up  the  problem,  he  saw,  as,  indeed,  others  had  seen  before  him, 
that  the  dominating  element  of  a  ruling  machine  was  the  screw  by 
means  of  which  the  plate  or  cutting  tool  was  moved  along.  The  ruled 
grating  would  repeat  all  of  the  irregularities  of  this  screw  and  would 
be  good  or  bad  just  as  these  were  few  or  many.  The  problem  was, 
then,  to  make  a  screw  which  would  be  practically  free  from  periodic 
and  other  errors,  and  upon  this  problem  a  vast  amount  of  thought  and 
experiment  had  already  been  expended.  Rowland's  solution  of  it  was 
characteristic  of  his  genius;  there  were  no  easy  advances  through  a 
series  of  experiments  in  which  success  and  failure  mingled  in  varying 
proportions ;  "  fire  and  fall  back  "  was  an  order  which  he  neither  gave 
nor  obeyed,  capture  by  storm  being  more  to  his  mind.  He  was  by 
nature  a  mechanician  of  the  highest  type,  and  he  was  not  long  in  devis- 
ing a  method  for  removing  the  irregularities  of  a  screw,  which  aston- 
ished everybody  by  its  simplicity  and  by  the  all  but  absolute  perfection 
of  its  results.  Indeed,  the  very  first  screw  made  by  this  process  ranks 


COMMEMORATIVE  ADDRESS  9 

to-day  as  the  most  perfect  in  the  world.  But  such  an  engine  as  this 
might  only  be  worked  up  to  its  highest  efficiency  under  the  most  favor- 
able physical  conditions,  and  in  its  installation  and  use  the  most  careful 
attention  was  given  to  the  elimination  of  errors  due  to  variation  of  tem- 
perature, earth  tremors,  and  other  disturbances.  Not  content,  how- 
ever, with  perfecting  the  machinery  by  which  gratings  were  ruled,  Kow- 
land  proceeded  to  improve  the  form  of  the  grating  itself,  making  the 
capital  discovery  of  the  concave  grating,  by  means  of  which  a  large 
part  of  the  complex  and  otherwise  troublesome  optical  accessories  to 
the  diffraction  spectroscope  might  be  dispensed  with.  Calling  to  his 
aid  the  wonderful  skill  of  Brashear  in  making  and  polishing  plane  and 
concave  surfaces,  as  well  as  the  ingenuity  and  patience  of  Schneider, 
for  so  many  years  his  intelligent  and  loyal  assistant  at  the  lathe  and 
workbench,  he  began  the  manufacture  and  distribution,  all  too  slowly 
for  the  anxious  demands  of  the  scientific  world,  of  those  beautifully 
simple  instruments  of  precision  which  have  contributed  so  much  to 
the  advance  of  physical  science  during  the  past  twenty  years.  While 
willing  and  anxious  to  give  the  widest  possible  distribution  to  these 
gratings,  thus  giving  everywhere  a  new  impetus  to  optical  research, 
Eowland  meant  that  the  principal  spoils  of  the  victory  should  be  his, 
and  to  this  end  he  constructed  a  diffraction  spectrometer  of  extra- 
ordinary dimensions  and  began  his  classical  researches  on  the  Solar 
Spectrum.  Finding  photography  to  be  the  best  means  of  reproducing 
the  delicate  spectral  lines  shown  by  the  concave  grating,  he  became  at 
once  an  ardent  student  and,  shortly,  a  master  of  that  art.  The  out- 
come of  this  was  that  wonderful  "  Photographic  Map  of  the  Normal 
Solar  Spectrum,"  prepared  by  the  use  of  concave  gratings  six  inches 
in  diameter  and  twenty-one  and  a  half  feet  radius,  which  is  recognized 
as  a  standard  everywhere  in  the  world.  As  a  natural  supplement  to 
this  he  directed  an  elaborate  investigation  of  absolute  wave-lengths, 
undertaking  to  give,  finally,  the  wave-length  of  not  only  every  line  of 
the  solar  spectrum,  but  also  of  the  bright  lines  of  the  principal  ele- 
ments, and  a  large  part  of  this  monumental  task  is  already  completed, 
mostly  by  Rowland's  pupils  and  in  his  laboratory. 

Time  will  not  allow  further  expositions  of  the  important  conse- 
quences of  his  invention  of  the  ruling  engine  and  the  concave  grating. 

Indeed,  the  limitations  to  which  I  must  submit  compel  the  omission 
of  even  brief  mention  of  many  interesting  and  valuable  investigations 
relating  to  other  subjects  begun  and  finished  during  these  years  of 
activity  in  optical  research,  many  of  them  by  Eowland  himself  and 


10  HENRY  A.  KOWLAND 

many  of  them  by  his  pupils,  working  out  his  suggestions  and  con- 
stantly stimulated  by  his  enthusiasm.  A  list  of  titles  of  papers  ema- 
nating from  the  physical  laboratory  of  the  Johns  Hopkins  University 
during  this  period  would  show  somewhat  of  the  great  intellectual  fertil- 
ity which  its  director  inspired,  and  would  show,  especially,  his  continued 
interest  in  magnetism  and  electricity,  leading  to  his  important  investi- 
gations relating  to  electric  units  and  to  his  appointment  as  one  of  the 
United  States  Delegates  at  important  International  Conventions  for 
the  better  determination  and  definition  of  these  units.  In  1883  a  com- 
mittee appointed  by  the  Electrical  Congress  of  1881,  of  which  Rowland 
was  a  member,  adopted  106  centimetres  as  the  length  of  the  mercury 
column  equivalent  to  the  absolute  ohm,  but  this  was  done  against  his 
protest,  for  his  own  measurements  showed  that  this  was  too  small  by 
about  three-tenths  of  one  per  cent.  His  judgment  was  confirmed  by 
the  Chamber  of  Delegates  of  the  International  Congress  of  1893,  of 
which  Rowland  was  himself  President,  and  by  which  definitive  values 
were  given  to  a  system  of  international  units. 

Rowland's  interest  in  applied  science  cannot  be  passed  over,  for  it 
was  constantly  showing  itself,  often,  perhaps,  unbidden,  an  unconscious 
bursting  forth  of  that  strong  engineering  instinct  which  was  born  in 
him,  to  which  he  often  referred  in  familiar  discourse,  and  which  would 
unquestionably  have  brought  him  great  success  and  distinction  had  he 
allowed  it  to  direct  the  course  of  his  life.  Although  everywhere  looked 
upon  as  one  of  the  foremost  exponents  of  pure  science,  his  ability  as  an 
engineer  received  frequent  recognition  in  his  appointment  as  expert 
and  counsel  in  some  of  the  most  important  engineering  operations  in 
the  latter  part  of  the  century.  He  was  an  inventor,  and  might  easily 
have  taken  first  rank  as  such  had  he  chosen  to  devote  himself  to  that 
sort  of  work.  During  the  last  few  years  of  his  life  he  was  much  occu- 
pied with  the  study  of  alternating  electric  currents  and  their  applica- 
tion to  a  system  of  rapid  telegraphy  of  his  own  invention.  A  year  ago 
his  system  received  the  award  of  a  grand  prix  at  the  Paris  Exposition, 
and  only  a  few  weeks  after  his  death  the  daily  papers  published  cable- 
grams from  Berlin  announcing  its  complete  success  as  tested  between 
Berlin  and  Hamburg,  and  also  the  intention  of  the  German  Postal 
Department  to  make  extensive  use  of  it. 

But  behind  Rowland,  the  profound  scholar  and  original  investigator, 
the  engineer,  mechanician  and  inventor,  was  Rowland  the  man,  and 
any  estimate  of  his  influence  in  promoting  the  interests  of  physical 
science  during  the  last  quarter  of  the  nineteenth  century  would  be 


COMMEMORATIVE  ADDRESS  11 

quite  inadequate  if  not  made  from  that  point  of  view.  Born  at  Hones- 
dale,  Pennsylvania,  on  November  27,  1848,  he  had  the  misfortune,  at 
the  age  of  11  years,  to  lose  his  father  by  death.  This  loss  was  made 
good,  as  far  as  it  is  possible  to  do  so,  by  the  loving  care  of  mother  and 
sisters  during  the  years  of  his  boyhood  and  youthful  manhood.  From 
his  father  he  inherited  his  love  for  scientific  study,  which  from  the  very' 
first  seems  to  have  dominated  all  of  his  aspirations,  directing  and  con- 
trolling most  of  his  thoughts.  His  father,  grandfather,  and  great- 
grandfather were  all  clergymen  and  graduates  of  Yale  College.  His 
father,  who  is  described  as  one  "  interested  in  chemistry  and  natural 
philosophy,  a  lover  of  nature  and  a  successful  trout-fisherman,"  had 
felt,  in  his  early  youth,  some  of  the  desires  and  ambitions  that  after- 
ward determined  the  career  of  his  distinguished  son,  but  yielding,  no 
doubt,  to  the  influence  of  family  tradition  and  desire,  he  followed  the 
lead  of  his  ancestors.  It  is  not  unlikely,  and  it  would  not  have  been 
unreasonable,  that  similar  hopes  were  entertained  in  regard  to  the 
future  of  young  Henry,  and  his  preparatory  school  work  was  arranged 
with  this  in  view.  Before  being  sent  away  from  home,  however,  he  had 
quite  given  himself  up  to  chemical  experiments,  glass-blowing  and  other 
similar  occupations,  and  the  members  of  his  family  were  often  sum- 
moned by  the  enthusiastic  boy  to  listen  to  lectures  which  were  fully 
illustrated  by  experiments,  not  always  free  from  prospective  danger. 
His  spare  change  was  invested  in  copper  wire  and  the  like,  and  his  first 
five-dollar  bill  brought  him,  to  his  infinite  delight,  a  small  galvanic 
battery.  The  sheets  of  the  New  York  Observer,  a  treasured  family 
newspaper,  he  converted  into  a  huge  hot-air  balloon,  which,  to  the 
astonishment  of  his  family  and  friends,  made  a  brilliant  ascent  and 
flight,  coming  to  rest,  at  last,  and  in  flames,  on  the  roof  of  a  neighbor- 
ing house,  and  resulting  in  the  calling  out  of  the  entire  fire  department 
of  the  town.  When  urged  by  his  boy  friends  to  hide  himself  from 
the  rather  threatening  consequences  of  his  first  experiment  in  aero- 
nautics, he  courageously  marched  himself  to  the  place  where  his  balloon 
had  fallen,  saying,  "  No !  I  will  go  and  see  what  damage  I  have  done/' 
When  a  little  more  than  sixteen  years  old,  in  the  spring  of  1865,  he 
was  sent  to  Phillips  Academy  at  Andover,  to  be  fitted  for  entering  the 
academic  course  at  Yale.  His  time  there  was  given  entirely  to  the 
study  of  Latin  and  Greek,  and  he  was  in  every  way  out  of  harmony 
with  his  environment.  He  seems  to  have  quickly  and  thoroughly  ap- 
preciated this  fact,  and  his  very  first  letter  from  Andover  is  a  cry  for 
relief.  "Oh,  take  me  home!"  is  the  boyish  scrawl  covering  the  last 


12  HENRY  A.  ROWLAND 

page  of  that  letter,  on  another  of  which  he  says,  "  It  is  simply  horrible; 
I  can  never  get  on  here."  It  was  not  that  he  could  not  learn  Latin  and 
Greek  if  he  was  so  minded,  but  that  he  had  long  ago  become  wholly 
absorbed  in  the  love  of  nature  and  in  the  study  of  nature's  laws,  and 
the  whole  situation  was  to  his  ambitious  spirit  most  artificial  and  irk- 
some. Time  did  not  soften  his  feelings  or  lessen  his  desire  to  escape 
from  such  uncongenial  surroundings,  and,  at  his  own  request,  Dr.  Far- 
rand,  Principal  of  the  Academy  at  Newark,  New  Jersey,  to  which  city 
the  family  had  recently  removed,  was  consulted  as  to  what  ought  to- 
be  done.  Fortunately  for  everybody,  his  advice  was  that  the  boy  ought 
to  be  allowed  to  follow  his  bent,  and,  at  his  own  suggestion,  he  was 
sent,  in  the  autumn  of  that  year,  to  the  Eensselaer  Polytechnic  Institute 
at  Troy,  where  he  remained  five  years,  and  from  which  he  was  graduated 
as  a  Civil  Engineer  in  1870. 

It  is  unnecessary  to  say  that  this  change  was  joyfully  welcomed  by 
young  Rowland.  At  Andover  the  only  opportunity  that  had  offered 
for  the  exercise  of  his  skill  as  a.  mechanic  was  in  the  construction  of  a 
somewhat  complicated  device  by  means  of  which  he  outwitted  some  of 
his  schoolmates  in  an  early  attempt  to  haze  him  and  in  this  he  took 
no  little  pride.  At  Troy  he  gave  loose  rein  to  his  ardent  desires,  and 
his  career  in  science  may  almost  be  said  to  begin  with  his  entrance  upon 
his  work  there  and  before  he  was  seventeen  years  old. 

He  made  immediate  use  of  the  opportunities  afforded  in  Troy  and 
its  neighborhood  for  the  examination  of  machinery  and  manufacturing 
processes,  and  one  of  his  earliest  letters  to  his  friends  contained  a  clear 
and  detailed  description  of  the  operation  of  making  railroad  iron,  the 
rolls,  shears,  saws,  and  other  special  machines  being  represented  in 
uncommonly  well  executed  pen  drawings.  One  can  easily  see  in  this 
letter  a  full  confirmation  of  a  statement  that  he  occasionally  made  later 
in  life,  namely,  that  he  had  never  seen  a  machine,  however  complicated 
it  might  be,  whose  working  he  could  not  at  once  comprehend.  In 
another  letter,  written  within  a  few  weeks  of  his  arrival  in  Troy,  he 
shows  in  a  remarkable  way  his  power  of  going  to  the  root  of  things 
which  even  at  that  early  age  was  sufficiently  in  evidence  to  mark  him 
for  future  distinction  as  a  natural  philosopher.  On  the  river  he  saw 
two  boats  equipped  with  steam  pumps,  engaged  in  trying  to  raise  a 
half -sun  ken  canal  boat  by  pumping  the  water  out  of  it.  He  described 
engine?,  pumps,  etc.,  in  much  detail,  and  adds,  "But  there  was  one 
thing  that  I  did  not  like  about  it;  they  had  the  end  of  their  discharge 
pipe  about  ten  feet  above  the  water  so  that  they  had  to  overcome  a 


COMMEMORATIVE  ADDRESS  13 

pressure  of  about  five  pounds  to  the  square  inch  to  raise  the  water  so 
high,  and  yet  they  let  it  go  after  they  got  it  there,  whereas  if  they  had 
attached  a  pipe  to  the  end  of  the  discharge  pipe  and  let  it  hang  down 
into  the  water,  the  pressure  of  water  on  that  pipe  would  just  have 
balanced  the  five  pounds  to  the  square  inch  in  the  other,  so  that  they 
could  have  used  larger  pumps  with  the  same  engines  and  th«s  have  got 
more  water  out  in  a  given  time." 

The  facilities  for  learning  physics,  in  his  day,  at  the  Eensselaer  Poly- 
technic Institute  were  none  of  the  best,  a  fact  which  is  made  the  subject 
of  keen  criticism  in  his  home  correspondence,  but  he  made  the  most  of 
whatever  was  available  and  created  opportunity  where  it  was  lacking. 
The  use  of  a  turning  lathe  and  a  few  tools  being  allowed,  he  spent  all 
of  his  leisure  in  designing  and  constructing  physical  apparatus  of  var- 
ious kinds  with  which  he  experimented  continually.  All  of  his  spare 
money  goes  into  this  and  he  is  always  wishing  he  had  more.  While  he 
pays  without  grumbling  his  share  of  the  expense  of  a  class  supper,  he 
cannot  help  declaring  that  "  it  is  an  awful  price  for  one  night's  pleas- 
ure; why,  it  would  buy  another  galvanic  battery."  During  these  early 
years  his  pastime  was  the  study  of  magnetism  and  electricity,  and  his 
lack  of  money  for  the  purchase  of  insulated  wire  for  electro-magnetic 
apparatus  led  him  to  the  invention  of  a  method  of  winding  naked 
copper  wire,  which  was  later  patented  by  some  one  else  and  made 
much  of.  Within  six  months  of  his  entering  the  Institute  he  had  made 
a  delicate  balance,  a  galvanometer,  and  an  electrometer,  besides  a  small 
induction  coil  and  several  minor  pieces.  A  few  weeks  later  he  an- 
nounces the  finishing  of  a  Euhmkorff  coil  of  considerable  power,  a 
source  of  much  delight  to  him  and  to  his  friends.  In  December,  1866, 
he  began  the  construction  of  a  small  but  elaborately  designed  steam 
engine  which  ran  perfectly  when  completed  and  furnished  power  for 
his  experiments.  A  year  later  he  is  full  of  enthusiasm  over  an  investi- 
gation which  he  wishes  to  undertake  to  explain  the  production  of 
electricity  when  water  comes  in  contact  with  red-hot  iron,  which  he 
attributes  to  the  decomposition  of  a  part  of  the  water.  Along  with  all 
of  this  and  much  more  he  maintains  a  good  standing  in  his  regular  work- 
in  the  Institute,  in  some  of  which  he  is  naturally  the  leader.  He  occa- 
sionally writes: — "I  am  head  of  my  class  in  mathematics," — or  "I  lead 
the  class  in  Natural  Philosophy,"  but  official  records  show  that  he  was 
now  and  then  "  conditioned  "  in  subjects  in  which  he  had  no  special 
interest.  As  early  as  1868,  before  his  twentieth  birthday,  he  decided 
that  he  must  devote  his  life  to  science.  While  not  doubting  his  ability 


14  HENRY  A.  EOWLAND 

"to  make  an  excellent  engineer"  as  he  declares,  he  decides  against 
engineering,  saying,  "  You  know  that  from  a  child  I  have  been  ex- 
tremely fond  of  experiment;  this  liking  instead  of  decreasing  has  gradu- 
ally grown  upon  me  until  it  has  become  a  part  of  my  nature,  and  it 
would  be  folly  for  me  to  attempt  to  give  it  up;  and  I  don't  see  any 
reason  why  I  should  wish  it,  unless  it  be  avarice,  for  I  never  expect 
to  be  a  rich  man.  I  intend  to  devote  myself  hereafter  to  science.  If 
she  gives  me  wealth,  I  will  receive  it  as  coming  from  a  friend,  but  if 
not,  I  will  not  murmur." 

He  realized  that  his  opportunity  for  the  pursuit  of  science  was  in 
becoming  a  teacher,  but  no  opening  in  this  direction  presenting  itself 
he  spent  the  first  year  after  graduation  in  the  field  as  a  civil  engineer. 
This  was  followed  by  a  not  very  inspiring  experience  as  instructor  in 
natural  science  in  a  Western  college,  where  he  acquired,  however, 
experience  and  useful  discipline. 

In  the  spring  of  1872  he  returned  to  Troy  as  instructor  in  physics, 
on  a  salary  the  amount  of  which  he  made  conditional  on  the  purchase 
by  the  Institute  of  a  certain  number  of  hundreds  of  dollars'  worth  of 
physical  apparatus.  If  they  failed  in  this,  as  afterward  happened,  his 
pay  was  to  be  greater,  and  he  strictly  held  them  to  the  contract.  His 
three  years  at  Troy  as  instructor  and  assistant  professor  were  busy, 
fruitful  years.  In  addition  to  his  regular  work  he  did  an  enormous 
amount  of  study,  purchasing  for  that  purpose  the  most  recent  and  most 
advanced  books  on  mathematics  and  physics.  He  built  his  electro- 
dynamometer  and  carried  out  his  first  great  research.  As  already 
stated,  this  quickly  brought  him  reputation  in  Europe  and  what  he 
prized  quite  as  highly,  the  personal  friendship  of  Maxwell,  whose  ardent 
admirer  and  champion  he  remained  to  the  end  of  his  life.  In  April, 
1875,  he  wrote,  "  It  will  not  be  very  long  before  my  reputation  reaches 
this  country,"  and  he  hoped  that  this  would  bring  him  opportunity  to 
devote  more  of  his  time  and  energy  to  original  research. 

This  opportunity  for  which  he  so  much  longed  was  nearer  at  hand 
than  he  imagined.  Among  the  members  of  the  Visiting  Board  at  the 
West  Point  Military  Academy  in  June,  1875,  was  one  to  whom  had 
come  the  splendid  conception  of  what  was  to  be  at  once  a  revelation  and 
a  revolution  in  methods  of  higher  education.  In  selecting  the  first 
faculty  for  an  institution  of  learning  which,  within  a  single  decade,  was 
to  set  the  pace  for  real  university  work  in  America,  and  whose  influence 
was  to  be  felt  in  every  school  and  college  of  the  land  before  the  end  of 
the  first  quarter  of  a  century,  Dr.  Oilman  was  guided  by  an  instinct 


15 

which  more  than  all  else  insured  the  success  of  the  new  enterprise. 
A  few  words  about  Eowland  from  Professor  Michie,  of  the  Military 
Academy,  led  to  his  being  called  to  West  Point  by  telegraph,  and  on 
the  banks  of  the  Hudson  these  two  walked  and  talked,  "  he  telling  me," 
Dr.  Oilman  has  said,  "  his  dreams  for  science  and  I  telling  him  my 
dreams  for  higher  education/'  Eowland,  with  characteristic  frank- 
ness, writes  of  this  interview,  "  Professor  Gilman  was  very  much 
pleased  with  me,"  which,  indeed,  was  the  simple  truth.  The  engage- 
ment was  quickly  made.  Eowland  was  sent  to  Europe  to  study  labor- 
atories and  purchase  apparatus,  and  the  rest  is  history,  already  told  and 
everywhere  known. 

Eowland's  personality  was  in  many  respects  remarkable.  Tall,  erect 
and  lithe  in  figure,  fond  of  athletic  sports,  there  was  upon  his  face  a 
certain  look  of  severity  which  was,  in  a  way,  an  index  of  the  exacting 
standard  he  set  for  himself  and  others.  It  did  not  conceal,  however, 
what  was,  after  all,  his  most  striking  characteristic,  namely,  a  perfectly 
frank,  open  and  simple  straightforwardness  in  thought,  in  speech  and 
in  action.  His  love  of  truth  held  him  in  supreme  control,  and,  like 
Galileo,  he  had  no  patience  with  those  who  try  to  make  things  appear 
otherwise  than  as  they  actually  are.  His  criticisms  of  the  work  of 
others  were  keen  and  merciless,  and  sometimes  there  remained  a  sting 
of  which  he  himself  had  not  the  slightest  suspicion.  "I  would  not 
have  done  it  for  the  world,"  he  once  said  to  me  after  being  told  that 
his  pitiless  criticism  of  a  scientific  paper  had  wounded  the  feelings  of 
its  author.  As  a  matter  of  fact  he  was  warm-hearted  and  generous,  and 
his  occasionally  seeming  otherwise  was  due  to  the  complete  separation, 
in  his  own  mind,  of  the  product  and  the  personality  of  the  author.  He 
possessed  that  rare  power,  habit  in  his  case,  of  seeing  himself,  not  as 
others  see  him,  but  as  he  saw  others.  He  looked  at  himself  and  his  own 
work  exactly  as  if  he  had  been  another  person,  and  this  gave  rise  to  a 
frankness  of  expression  regarding  his  own  performance  which  some- 
times impressed  strangers  unpleasantly,  but  which,  to  his  friends,  was 
one  of  his  most  charming  qualities.  Much  of  his  success  as  an  investi- 
gator was  due  to  a  firm  confidence  in  his  own  powers,  and  in  the  unerring 
course  of  the  logic  of  science  which  inspired  him  to  cling  tenaciously 
to  an  idea  when  once  he  had  given  it  a  place  in  his  mind.  At  a  meeting 
of  the  National  Academy  of  Science  in  the  early  days  of  our  knowledge 
of  electric  generators,  he  read  a  paper  relating  to  the  fundamental 
principles  of  the  dynamo.  A  gentleman  who  had  had  large  experience 
with  the  practical  working  of  dynamos  listened  to  the  paper,  and  at  the 


16  HENRY  A.  ROWLAND 

end  said  to  the  Academy  that  unfortunately  practice  directly  contra- 
dicted Professor  Rowland's  theory,  to  which  instantly  replied  Rowland, 
"  So  much  the  worse  for  the  practice,"  which,  indeed,  turned  out  to  be 
the  case. 

Like  all  men  of  real  genius,  he  had  phenomenal  capacity  for  concen- 
tration of  thought  and  effort.  Of  this,  one  who  was  long  and  intimately 
associated  with  him  remarks,  "  I  can  remember  cases  when  he  appeared 
as  if  drugged  from  mere  inability  to  recall  his  mind  from  the  pursuit 
of  all-absorbing  problems,  and  he  had  a  triumphant  joy  in  intellectual 
achievement  such  as  we  would  look  for  in  other  men  only  from  the 
gratification  of  an  elemental  passion."  So  completely  consumed  was 
he  by  fires  of  his  own  kindling  that  he  often  failed  to  give  due  attention 
to  the  work  of  others,  and  some  of  his  public  utterances  give  evidence 
of  this  curious  neglect  of  the  historic  side  of  his  subject. 

As  a  teacher  his  position  was  quite  unique.  Unfit  for  the  ordinary 
routine  work  of  the  class  room  he  taught  as  more  men  ought  to  teach, 
by  example  rather  than  by  precept.  Says  one  of  his  most  eminent 
pupils,  "  Even  of  the  more  advanced  students  only  those  who  were  able 
to  brook  severe  and  searching  criticism  reaped  the  full  benefit  of  being 
under  him,  but  he  contributed  that  which,  in  a  University,  is  above  all 
teaching  of  routine,  the  spectacle  of  scientific  work  thoroughly  done 
and  the  example  of  a  lofty  ideal." 

Returning  home  about  twenty  years  ago  after  an  expatriation  of 
several  years,  and  wishing  to  put  myself  in  touch  with  the  development 
of  methods  of  instruction  in  physics  and  especially  in  the  equipment  of 
physical  laboratories,  I  visited  Rowland  very  soon  after,  as  it  happened, 
the  making  of  his  first  successful  negative  of  the  solar  spectrum.  That 
he  was  completely  absorbed  in  his  success  was  quite  evident,  but  he  also 
seemed  anxious  to  give  me  such  information  as  I  sought.  I  questioned 
him  as  to  the  number  of  men  who  were  to  work  in  his  laboratory,  and 
although  the  college  year  had  already  begun  he  appeared  to  be  unable 
to  give  even  an  approximate  answer.  "  And  what  will  you  do  with 
them  ?  "  I  said.  "  Do  with  them  ?  "  he  replied,  raising  the  still  drip- 
ping negative  so  as  to  get  a  better  light  through  its  delicate  tracings, 
"  Do  with  them  ? — I  shall  neglect  them."  The  whole  situation  was  in- 
tensely characteristic,  revealing  him  as  one  to  whom  the  work  of  a  drill- 
master  was  impossible,  but  ready  to  lead  those  who  would  be  led  and 
could  follow.  To  be  neglected  by  Rowland  was  often,  indeed,  more 
stimulating  and  inspiring  than  the  closest  personal  supervision  of  men 
lacking  his  genius  and  magnetic  fervor. 


COMMEMORATIVE  ADDRESS  17 

In  the  fulness  of  his  powers,  recognized  as  America's  greatest  physi- 
cist, and  one  of  a  very  small  group  of  the  world's  most  eminent,  he  died 
on  April  16,  1901,  from  a  disease  the  relentless  progress  of  which  he  had 
realized  for  several  years  and  opposed  with  a  splendid  but  quiet  courage. 

It  was  Eowland's  good  fortune  to  receive  recognition  during  his  life 
in  the  bestowal  of  degrees  by  higher  institutions  of  learning;  in  elec- 
tion to  membership  in  nearly  all  scientific  societies  worthy  of  note  in 
Europe  and  America;  in  being  made  the  recipient  of  medals  of  honor 
awarded  by  these  societies;  and  in  the  generously  expressed  words  of 
his  distinguished  contemporaries.  It  will  be  many  years,  however,  be- 
fore full  measure  can  be  had  of  his  influence  in  promoting  the  interests 
of  physical  science,  for  with  his  own  brilliant  career,  sufficient  of  itself 
to  excite  our  profound  admiration,  must  be  considered  that  of  a  host 
of  other,  younger,  men  who  lighted  their  torches  at  his  flame  and  who 
will  reflect  honor  upon  him  whose  loss  they  now  mourn  by  passing  on 
something  of  his  unquenchable  enthusiasm,  something  of  his  high 
regard  for  pure  intellectuality,  something  of  his  love  of  truth  and  his 
sweetness  of  character  and  disposition. 


SCIENTIFIC  PAPERS 


PART  I 

EARLY  PAPERS 


THE  VOKTEX  PROBLEM 

[Scientific  American,  XIII,  308,  1865] 

Messrs.  Editors: — In  a  late  number  of  your  paper  an  inquiry  was 
made  why  a  vortex  was  formed  over  the  orifice  of  an  outlet1  pipe;  as, 
for  instance,  in  a  bath  tub,  when  the  water  is  running  out.  If  the 
water  be  first  started,  the  explanation  will  be  on  the  same  principle 
that  a  ball  and  string  will,  if  started,  wind  itself  up  upon  the  hand;  the 
ball  being  attached  to  the  string  will,  as  the  string  winds  up,  get  nearer 
the  hand,  and,  consequently,  will  have  less  far  to  go  to  make  one  revo- 
lution, and  thus  the  momentum,  though  perhaps  not  great  enough  to 
carry  it  around  in  the  great  circle,  is  still  sufficient  to  make  it  revolve 
in  the  smaller  one. 

Therefore,  as  the  string  is  continually  winding  up,  and  the  ball  con- 
tinually nearing  the  hand,  it  will,  if  the  resistance  of  the  air  is  not  too 
great,  continue  to  revolve  until  the  string  is  wound  up.  Now,  in  the 
case  of  the  water,  each  particle  of  it  will  represent  the  ball,  the  force 
of  the  water  rushing  toward  the  outlet  will  be  the  string,  and,  the  water 
running  out,  and  thus  causing  the  particles  to  come  nearer  the  center 
at  every  revolution,  will  represent  the  winding-up  process.  Thus,  we 
see  this  case  is  analogous  to  the  preceding,  and  the  same  reason  that 
will  apply  to  one  will  apply  to  the  other.  I  suppose  that  some  slight 
motion  existing  among  the  particles  of  the  water,  united  to  the  motion 
produced  by  the  outlet,  causes  the  vortex  to  begin,  and,  once  begun,  it 
will  continue  until  the  water  is  exhausted. 

Such  motion  could  either  previously  exist,  or  might  be  produced  by 
the  form  *  of  the  vessel,  which  would  cause  the  water,  in  running  to 
the  outlet,  to  assume  a  certain  direction. 

H.  A.  R. 

Troy,  N.  T.,  October,  1865. 

'[In  the  original  article  this  reads  "outlet  of  an  orifice,"  an  obvious  misprint.] 
MIn  the  original  article  this  word  is  "power,"  an  obvious  misprint.] 


PAINE'S  ELECTRO-MAGNETIC  ENGINE 

[Scientific  American,  XXV,  21,  1871] 

To  the  Editor  of  the  Scientific  American: 

Having  noticed  several  articles  in  your  paper  with  reference  to 
Paine's  electro-magnetic  machine,  I  believe  I  cannot  do  better  than 
describe  a  visit  which  I  paid  it  about  three  months  ago. 

Entering  the  office  in  company  with  a  friend,  at  about  twelve  o'clock 
one  day,  I  was  told  that  the  machine  was  not  running  then,  but  would 
be  in  operation  at  one.  Proceeding  there  alone,  at  about  that  time,  I 
was,  after  the  formality  of  sending  up  my  name,  conducted  by  a  small 
boy,  through  numerous  by-ways  and  passages,  to  the  second  story  of  a 
back  building,  where  I  was  met  by  the  illustrious  inventor  and  a  few 
select  friends.  Mr.  Paine  began  by  showing  the  small  model  machines, 
which  he  set  in  motion  by  a  battery  of  four  cups,  of  about  a  gallon 
capacity  each.  These  models  revolved  very  well,  but  apparently  with  no 
power,  for  they  could  be  stopped  easily.  I  then  began  to  reason  with 
him  on  the  absurdity  of  his  position,  and  adduced  in  my  support  the 
experiments  of  Joule,  Mayer,  Faraday  and  others.  He,  evidently,  had 
no  very  high  opinion  of  these,  and  pronounced  the  conservation  of  force 
an  old  fashioned  idea,  which  had  been  overthrown  in  these  enlightened 
days  by  his  "  experiments,"  though  what  the  latter  were  I  have  never 
determined. 

After  conversing  some  time,  to  no  purpose,  he  prepared  to  over- 
throw me  and  my  authority  at  one  blow,  by  an  exhibition  of  The 
Machine.  This  was  standing  in  front  of  a  chimney,  on  one  side  of  the 
room,  with  the  axis  of  its  wheels  parallel  to  the  wall.  The  wheel  to 
which  the  magnets  were  attached  was,  unlike  the  models,  inclosed  in  a 
cast  iron  case,  which  enveloped  it  closely  above,  but  spread  out  into  a 
rectangular  base  below.  The  latter  rested  directly  on  the  floor.  The 
axis  of  the  wheel  projected  on  each  side,  and,  to  one  end,  a  pulley  was 
attached,  and  to  the  other,  the  brake  for  operating  the  magnets.  The 
machine  had  the  general  appearance  of  a  fan  blower  with  an  enlarged 
pulley.  The  battery  was  attached  to  two  binding  screws,  fixed  to  a 


PAINE'S  ELECTBO-MAGNETIC  ENGINE  25 

standard  on  the  chimney,  and  the  current  was  supposed  to  pass  from 
these,  along  wires,  to  the  break  piece,  and  thence  to  the  magnets.  A 
belt  on  the  pulley  connected  with  a  shaft  overhead,  whence  another  belt 
proceeded  to  the  pulley  of  a  small  circular  saw. 

As  soon  as  the  connection  was  made  with  the  battery,  the  whole 
apparatus  began  to  move,  and  soon  the  saw  attained  great  velocity, 
shaking  the  building  with  violence.  The  latter  effect  was  caused  by  a 
heavy  fly  wheel  on  the  saw  arbor,  which  probably  was  not  well  balanced. 
When  well  in  motion,  boards  were  applied  and  sawed  with  the  greatest 
ease.  To  show  the  excess  of  power,  they  were  sometimes  placed  on 
edge  and  passed  over  the  saw,  so  as  wholly  to  envelop  it,  and  the  cut 
made  from  end  to  end,  without  the  velocity  being  at  all  diminished. 
On  throwing  off  the  belt  from  the  saw,  the  machine  still  proceeded  at 
the  same  velocity,  with  entire  indifference  to  external  resistance.  On 
mentioning  this  to  Mr.  Paine,  he  informed  me  that  when  the  saw  was 
attached,  and  the  resistance  greater,  the  increased  pull  on  the  magnets 
brought  them  nearer  together,  by  bending  the  heavy  iron  frame;  and, 
as  magnetic  attraction  varies  inversely  as  the  square  of  the  distance,  it 
only  required  a  small  change  of  distance  to  account  for  the  increased 
power.  I  clearly  indicated  that  I  was  skeptical  on  this  point,  and  sug- 
gested that  it  would  also  work  without  variation  if  the  power  pro- 
ceeded from  some  well  governed  steam  engine  in  the  neighborhood. 
On  this  he  intimated  that,  if  I  were  not  careful,  a  force  might  proceed 
from  his  body  which  would  act  in  conjunction  with  gravitation  in 
causing  me  to  be  projected  through  the  window,  and  strike  with  vio- 
lence on  the  ground  below. 

The  exhibition  being  over,  on  going  down  stairs  in  company  with  the 
rest,  I  tried  the  door  of  the  room  below,  but  found  it  locked,  and  the 
windows  covered  with  papers.  I  desired  to  get  in,  but  was  met  with 
the  assurance  that  the  room  was  rented  by  a  man  who  was  then  absent. 

This,  1  believe,  is  the  last  visit  paid  by  an  outsider  to  this  wonderful 
invention.  I  have  been  there  several  times  since,  but  there  has  been 
no  admittance  to  me,  or  to  any  one  else.  I  have  since  been  to  the 
owner  of  the  building,  and  find  that  Mr.  Paine  rents  the  room  to  which 
I  sought  admittance,  and  also  rents  power  in  that  same  room,  which  is 
directly  below  that  containing  his  machine.  The  engine  from  which 
the  power  comes  generally  stops  work  at  twelve  and  starts  again  at 
one,  but  sometimes  works  all  day. 

My  visits  there  have  established  the  following  facts:  First,  That 
my  friend  and  I  were  denied  admittance  at  twelve  o'clock,  but  were 


26  HENEY  A.  KOWLAND 

invited  to  come  at  one.  Second,  That  the  shaft  in  the  room  below  does 
not  revolve  between  the  hours  of  twelve  and  one.  Third,  That  the 
room  below,  containing  power,  was  rented  by  Mr.  Paine,  but  that  he 
kept  it  carefully  locked,  and  misguided  me  as  to  the  tenant.  Fourth, 
That  the  working  parts  are  concealed  in  an  unnecessarily  strong  case, 
well  adapted  to  the  concealment  of  another  source  of  power.  Fifth, 
That  part  of  the  apparatus  is  attached  to  the  wall,  so  that  the  machine 
must  always  occupy  the  same  position  on  the  floor.  Sixth,  That  the 
models  have  not  a  power  proportionate  to  their  size.  Seventh,  That 
the  machine  runs  at  the  same  velocity,  whether  producing  one  horse 
power  or  a  fraction  of  a  horse  power,  and  this  without  a  governor. 

These  are  the  facts  of  the  case.  Where  the  power  of  the  machine 
comes  from  I  am  unable  to  say.  Is  there  some  secret  connection  be- 
tween this  machine  and  the  shaft  below,  and  does  the  battery  serve 
only  to  make  this  connection?  Or  does  the  battery,  when  applied, 
connect  the  apparatus  with  a  larger  battery?  I  leave  these  questions 
to  others;  but,  unless  the  reasoning  and  experiments  of  a  host  of  our 
greatest  men  be  false,  and  unless  the  greatest  development  of  modern 
science  be  overthrown,  this  machine  cannot  but  derive  its  power  from 
some  extraneous  source. 

In  a  late  communication  to  your  paper,  Mr.  Paine  sets  himself  up 
as  the  peer  of  Faraday,  Tyndall  and  others,  and  gives  as  the  reason, 
his  long  devotion  to  science.  He  evidently  does  not  consider  that  to 
be  ranked  with  such  men  requires  something  more  than  devotion;  it 
requires  brains;  brains  to  discriminate  between  true  science  and  quack- 
ish  nonsense;  brains  to  discover  and  originate.  And  pray  what  fact, 
among  the  thousands  of  science,  does  Mr.  Paine  pretend  to  have  proved 
beyond  doubt  ?  Let  him  answer.  As  to  Mr.  Paine's  "  science,"  I 
assert  that  it  is  a  tissue  of  error  and  ignorance,  from  beginning  to  end. 
Even  his  vaunted  invention  of  metallic  foil,  wherewith  to  envelop  his 
magnets  or  wire,  can  operate  in  no  other  manner  than  to  the  detriment 
of  his  machine,  as  any  such  metallic  coating  lengthens  the  demagneti- 
zation, which  is  the  very  thing  to  be  guarded  against.  This  is  due  to 
an  induced  current,  which  forms  in  the  coating,  and,  being  in  the  same 
direction  as  the  primary  current,  operates  in  the  same  manner  to  keep 
up  the  magnetism.  His  reason  for  the  machine's  keeping  at  the  same 
velocity  also  shows  great  ignorance  of  the  subject.  In  the  first  place, 
the  law  of  magnetic  force,  under  these  circumstances,  is  stated  entirely 
wrong.  For  this  case,  the  true  law  is  complex,  but  most  nearly  ap- 
proaches to  that  of  inversely  as  the  distance,  instead  of  as  the  square  of 


PAINE'S  ELECTRO-MAGNETIC  ENGINE  27 

the  distance.  (See  Joule,  and  also  Tyndall,  in  the  London,  Edinburgh 
and  Dublin  Philosophical  Magazine  for  1850.)  And,  in  the  second 
place,  approach  of  the  poles  would  not  necessarily  increase  the  effi- 
ciency; in  this  kind  of  machine  there  is  a  distance  of  maximum  effi- 
ciency; and  if  the  magnets  revolve  at  a  distance  greater  than  this,  the 
attraction  becomes  too  small;  and  if  at  a  less  distance,  the  times  of 
magnetizing  and  demagnetizing  the  magnets  become  too  great,  and  the 
machine  goes  too  slowly.  The  distance  in  this  machine  is,  undoubtedly, 
within  the  limit,  for  Mr.  Paine  prides  himself  upon  its  smallness,  and 
so  further  reduction,  could  it  take  place,  can  act  in  no  other  manner 
than  the  opposite  of  that  claimed.  But  it  is  my  opinion  that  all  the 
force  brought  to  bear  on  the  magnets  could  not  move  them  one  two- 
hundredth  of  an  inch,  when  attached  to  such  a  frame. 

As  to  Mr.  Paine's  disregard  for  the  conservation  of  force,  I  have 
little  to  say.  His  assertions  are  made  directly  in  the  face  of  this 
principle,  and  yet  he  has  never  adduced  one  experiment,  or  even  a  plaus- 
ible reason,  to  prove  what  he  says.  He  takes  you  into  a  building  where 
shafts  are  revolving  by  the  vulgar  power  of  steam,  and  directs  you  to 
look  while  he  evokes  power  from  nothing.  You  must  not  touch  any- 
thing; you  must  not  enter  the  room  below;  you  must  not  be  there  while 
the  engine  next  door  is  at  rest;  but  you  must  simply  look,  and  by  that 
renowned  maxim  of  fools,  that  "  seeing  is  believing/'  you  must  believe 
that  the  whole  structure  of  science  has  fallen,  and  that  above  its  ruins 
nothing  remains  but  Mr.  Paine  and  his  wonderful  electro-magnetic 

machine. 

HENRY  A.  EOWLAND,  C.  E. 

Newark,  N.  J. 


ILLUSTRATION  OF  RESONANCES  AND  ACTIONS  OF  A 
SIMILAR  NATURE 

[Journal  of  the  Franklin  Institute,  XCIV,  275-278,  18721 

At  the  present  day,  when  scientific  education  is  beginning  to  take 
its  proper  place  in  the  public  estimation,  anything  which  can  help 
toward  imparting  a  clear  idea  of  any  physical  phenomenon  becomes  im- 
portant. There  are  a  number  of  these  phenomena,  of  which  resonance 
is  one,  which  play  quite  an  important  part  in  nature,  but  which  as  yet 
have  not  been  illustrated  with  sufficient  clearness  in  the  lecture-room. 
Among  these  are  the  following:  A  person  carrying  water  may  so  time 
his  steps  as  to  produce  waves  which  shall  rise  and  fall  in  unison  with 
the  motion  of  his  body;  soldiers  in  crossing  a  bridge  must  not  keep 
step,  or  they  may  transmit  such  a  vibration  to  it  as  to  break  it  down; 
window-panes  are  sometimes  cracked  by  sounding  a  powerful  organ- 
pipe  to  which  they  can  vibrate ;  a  tuning-fork  will  respond  to  another  of 
equal  pitch  sounded  near  it;  and  others  will  readily  suggest  themselves 
to  the  reader.  In  all  these  cases  we  have  two  bodies  which  can  vibrate 
in  equal  times,  connected  together  either  directly  or  by  some  medium 
which  transmits  the  motion  from  one  to  the  other.  We  can,  then, 
readily  reproduce  the  circumstances  in  the  lecture-room. 

The  vibrating  bodies  which  I  have  found  most  convenient  are  pendu- 
lums; they  are  easily  made,  are  seen  well  at  a  distance,  and  their  time 
of  vibration  can  be  easily  and  quickly  regulated.  The  apparatus  can 
be  prepared  in  the  following  manner:  Fix  a  board,  about  a  foot  long, 
in  a  horizontal  position;  suspend  a  piece  cf  small  stiff  wire,  of  equal 
length,  beneath  its  edge,  parallel  to  it,  and  an  inch  or  two  distant,  by 
means  of  threads.  To  one  end  of  the  board  suspend  a  pendulum,  con- 
sisting of  a  thread  about  ten  or  twenty  inches  long,  to  which  is  attached 
a  ball  weighing  two  or  three  ounces;  join  the  thread  of  this  pendulum 
to  the  horizontal  wire  by  taking  a  turn  of  it  around  the  wire,  so  that 
when  the  pendulum  oscillates,  it  causes  the  wire  to  move  back  and 
forth  in  unison  with  it.  To  complete  the  apparatus,  prepare  a  number 
of  small  pendulums  by  suspending  bullets  to  threads,  and  let  them  have 
small  hooks  of  wire  to  hang  by. 


ILLUSTRATION  OF  KESONANCES  29 

Having  then  set  the  heavy  pendulum  in  motion,  hang  some  of  the 
light  ones  on  the  horizontal  wire,  and  note  the  result:  those  which  are 
shorter  or  longer  than  the  heavy  one  will  not  be  affected,  but  if  any  of 
them  are  nearly  of  the  same  length,  they  will  begin  to  vibrate  to  a 
small  extent,  but  will  soon  come  to  rest,  after  which  they  will  com- 
mence again,  but  stop  as  before ;  but  if  any  one  happens  to  be  of  exactly 
the  proper  length,  its  motion  will  soon  become  very  great,  and  im- 
mensely surpass  in  amplitude  that  of  the  heavy  one,  although  the  motion 
is  derived  from  it.  Of  course  the  heavy  pendulum  must  be  retarded  in 
giving  motion  to  the  light  one,  but  it  is  hardly  perceptible  when  there  is 
great  difference  in  the  weight.  In  the  same  manner  a  tuning-fork  will 
undoubtedly  come  to  rest  sooner  when  producing  resonance  than  when 
vibrating  freely.  To  show  this  retardation  more  clearly,  suspend  two 
pendulums,  equal  in  weight  and  length,  to  the  edge  of  a  horizontal 
board,  and  connect  their  two  threads  together  by  a  horizontal  thread 
tied  to  each  at  a  point  an  inch  or  two  from  the  top,  and  drawn  so  tight 
as  to  pull  each  of  the  pendulums  a  little  out  of  plumb.  On  starting  one 
of  these  pendulums  the  other  will  gradually  move,  and  finally  absorb 
all  the  motion  from  the  first,  and  bring  it  entirely. to  rest;  the  action 
will  then  begin  anew,  and  the  motion  will  be  entirely  given  back  to  the 
first  ball.  This  experiment  differs  from  that  of  resonance,  inasmuch 
as  in  the  case  of  the  pendulums  all  the  motion  of  the  first  ball  is  finally 
stored  up  in  the  second;  but  in  the  case  of  resonance  the  confined  air 
is  constantly  giving  out  its  motion  to  the  atmosphere  in  waves  of  sound. 
To  imitate  this  to  some  extent  we  must  attach  a  rather  large  piece  of 
paper  to  the  second  pendulum,  so  that  it  will  meet  with  resistance,  and 
then  both  balls  will  come  to  rest  sooner  than  otherwise.  If  one  of  the 
balls  is  only  two  or  three  times  heavier  than  the  other,  they  will  then 
also  interchange  motions;  but  when  the  heavy  ball  has  the  motion, 
the  arc  of  its  vibration  will  not  be  so  great  as  that  of  the  other  when 
it  vibrates. 

To  illustrate  the  use  of  Helmholtz  resonance  globes,  or  Koenig's 
apparatus  for  the  analysis  of  sounds,  we  can  enlarge  and  modify  the 
first  apparatus  somewhat.  Make  the  board  six  or  eight  feet  long,  and 
suspend  at  one  end  four  or  five  of  the  heavy  pendulums,  and  at  the 
other  the  same  number  of  light  ones,  each  of  which  corresponds  in  time 
of  vibration  with  one  of  the  heavy  ones.  On  now  causing  any  of  the 
heavy  pendulums  to  vibrate,  as  No.  3,  we  shall  meet  with  no  response 
from  any  of  the  light  ones  except  No.  7.  If  Nos.  1,  2  and  4  are  set 
going  at  one  time,  the  wire  A  will  be  drawn  hither  and  thither  by  the 


30 


HENKY  A.  ROWLAND 


conflicting  pulls  with  no  seeming  regularity,  but  each  of  the  balls  5, 
6  and  8  will  pick  out  from  the  confused  motion  the  vibration  due  to 
itself,  and  will  move  in  unison,  but  No.  7  will  remain  quiet.  The  short 
pendulums  always  produce  the  effect  sooner  than  the  long  ones.  To 
remedy  this  to  some  extent  it  is  well  to  bend  the  wire  A  into  the  shape 
shown  in  the  figure.  It  is  not  well  to  make  the  pendulum  more  than 
twenty  inches  long,  if  a  quick  response  is  wished.  There  seems  to  be 
no  limit  to  the  number  of  pendulums  which  can  be  used  or  the  distance 
to  which  the  effect  can  be  transmitted,  though  it  is  more  decided  when 
there  are  but  few  pendulums  and  they  are  near  together.  It  may  some- 
times be  more  convenient  to  suspend  the  pendulums  from  a  wire, 


:wm 


tightly  stretched,  than  from  a  board.  To  make  the  balls  visible  at  a 
distance,  it  may  be  well  in  some  cases  to  make  them  of  polished  steel, 
and  illuminate  them  by  a  beam  from  the  electric  lamp. 

These  experiments  have  many  advantages  which  recommend  them  to 
teachers;  they  can  be  performed  without  purchased  apparatus,  and 
can  be  made  to  illustrate  resonance  and  the  kindred  phenomena  in  all 
their  details.  Indeed,  any  one  will  be  well  repaid  for  spending  an  hour 
in  performing  them,  simply  for  their  own  beauty. 


4 

ON  THE  AUKORAL  SPECTRUM 

I  American  Journal  of  Science  [3],   F,  320,  1873] 

A  letter  from  Henry  A.  Rowland,  at  present  Instructor  in  Physics  in 
the  Rensselaer  Polytechnic  Institute  at  Troy,  informs  us  that  he 
observed  the  line  of  wave-length  431  in  the  auroral  spectrum  of  last 
October.  He  says :  "  The  observations  were  made  with  an  ordinary 
chemical  spectroscope  of  one  prism,  in  which  the  scale  was  read  by 
means  of  a  lamp.  Great  care  was  taken  in  the  readings,  and  after  com- 
pleting them  the  spectroscope  was  set  aside  until  morning,  when  the 
readings  were  taken  on  the  lines  of  comparison  without  altering  the 
instrument  in  any  way  or  even  regulating  the  slit.  The  wave-lengths 
of  the  known  lines  were  taken  from  Watts's  *  Index  of  Spectra/  but  as 
he  does  not  give  the  wave-lengths  of  lines  in  the  flame  spectrum  I  am 
not  quite  certain  that  they  are  correct."  On  the  scale  of  his  instru- 
ment, Li  a  was  at  13.5°,  Caa21°,  Naa27.50,  Ca/3360,  Car95.5°,  and 
K/s  110°.  The  aurora  lines  were  as  follows: 

Scale-reading.  Wave-lengths. 

1  19  628.3 

2  35.5  554.3 

3  95  425 

"  The  wave-lengths  of  the  auroral  lines  were  obtained  by  graphical 
interpolation  on  such  a  large  scale  as  to  introduce  little  or  no  error." 


PART  II 

MAGNETISM  AND  ELECTRICITY 


ON  MAGNETIC  PERMEABILITY,1  AND  THE  MAXIMUM  OF 
MAGNETISM  OF  IRON,  STEEL,  AND  NICKEL 

[Philosophical  Magazine  [4],  XL  VI,  140-159,  1873] 

More  than  three  years  ago  I  commenced  the  series  of  experiments 
the  results  of  which  I  now  publish  for  the  first  time.  Many  of  the 
facts  which  I  now  give  were  obtained  then;  but,  for  satisfactory  reasons, 
they  were  not  published  at  that  time.  The  investigations  were  com- 
menced with  a  view  to  determine  the  distribution  of  magnetism  on 
iron  bars  and  steel  magnets;  but  it  was  soon  found  that  little  could  be 
done  without  new  experiments  on  the  magnetic  permeability  of  sub- 
stances. 

Few  observations  have  been  made  as  yet  for  determining  the  mag- 
netic permeability  of  iron,  and  none,  I  believe,  of  nickel  and  cobalt,  in 
absolute  measure.  The  subject  is  important,  because  in  all  theories  of 
induced  magnetism  a  quantity  is  introduced  depending  upon  the  mag- 
netic properties  of  the  substance,  and  without  a  knowledge  of  which 
the  problem  is  of  little  but  theoretical  interest;  this  quantity  has 
always  been  treated  as  a  constant,  although  the  experiments  on  the 
maximum  of  magnetism  show  that  it  is  a  variable.  However,  the  form 
of  the  function  has  never  been  determined,  except  so  far  as  we  may 
deduce  it  from  the  equation  of  Miiller, 


which,  as  will  be  shown,  leads  to  wrong  results.  The  quantities  used 
by  different  persons  are  as  follows:  — 

«,  Neumann's  coefficient,  or  magnetic  susceptibility  (Thomson). 

Tc,  Poisson's  coefficient. 

/*,  coefficient  of  magnetization  (Maxwell),  or  magnetic  permeability 
(Thomson). 

^-,  introduced  for  convenience  in  the  following  paper. 

1  The  word  "permeability"  has  been  proposed  by  Thomson,  and  has  the  same 
meaning  as  "conductivity"  as  used  by  Faraday  ('Papers  on  Electricity  and  Magnet- 
ism,' Thomson,  p.  484;  Maxwell's  'Electricity  and  Magnetism,'  vol.  ii,  p.  51.) 


36  HEXRY  A.  ROWLAND 

The  relations  of  these  quantities  are  given  by  the  following  equa- 
tions :  — 

,  _ 
- 


3k  A— 


The  first  determination  of  the  value  of  any  of  these  quantities  was 
made  by  Thalen.  But  more  important  experiments  have  been  made 
by  Weber,  Von  Quintus  Icilius,  and  more  recently  by  M.  Eeicke  and 
Dr.  A.  Stoletow.2  The  first  three  of  these  in  their  experiments  used 
long  cylindrical  rods,  or  ellipsoids  of  great  length;  the  last,  who  has 
made  by  far  the  most  important  experiments  on  this  subject,  has  used 
an  iron  ring.  The  method  of  the  ring  was  first  used  by  Dr.  Stoletow 
in  September,  1871;  but  more  than  eight  months  before  that,  in  Jan- 
uary, 1871,  I  had  used  the  same  method,  but  with  different  apparatus, 
to  measure  the  magnetism.  He  plots  a  curve  showing  the  variation  of 
K  ;  but  he  plots  it  with  reference  to  E  as  abscissa  instead  of  R  * ,  and 
thus  fails  to  determine  the  law.  His  method  of  experiment  is  much 
more  complicated  than  mine,  so  that  he  could  only  obtain  results  for 
one  ring;  while  by  my  method  I  have  experimented  on  about  a  dozen 
rings  and  on  numerous  bars,  so  that  I  believe  I  have  been  enabled  to 
find  the  true  form  of  the  function  according  to  which  /*  varies  with  the 
magnetism  of  the  bar  or  the  magnetizing-force. 

Many  experiments  have  been  made  on  the  magnetism  of  iron  without 
giving  the  results  in  absolute  measure.  Among  these  are  the  experi- 
ments of  Muller,  Joule,  Lenz  and  Jacobi,  Dub,  and  others.  The  ex- 
periments have  been  made  by  the  attraction  of  electromagnets,  by  the 
deflection  of  a  compass-needle,  or,  in  one  case,  by  measuring  the  in- 
duced current  in  a  helix  extending  the  whole  length  of  the  bar.  By 
the  last  two  methods  the  change  in  the  distribution  of  magnetism  over 
the  bar  when  the  magnetism  of  the  bar  varies  is  disregarded,  if  indeed 
it  was  thought  of  at  all :  even  in  a  recent  memoir  of  M.  Cazin  *  we  have 
the  statement  made  that  the  position  of  the  poles  is  independent  of  the 
strength  of  the  current.  He  does  not  give  the  experiment  from  which 
he  deduces  this  result.  Now  it  is  very  easy  to  show,  from  the  formula 

'Phil.  Mag.,  January,  1873. 

3  Annales  de  Chimie  et  de  Physique,  Feb.,  1873,  p.  171. 


MAGNETIC  PERMEABILITY  OF  IROX,  STEEL  AND  XICKEL         37 

of  Green  for  the  distribution  of  magnetism  on  a  bar-magnet  combined 
with  the  known  variation  of  K,  that  this  can  only  be  true  for  short  and 
thick  bars;  and  it  has  also  been  remarked  by  Thomson  that  this  should 
be  the  case.4  An  experiment  made  in  1870  places  this  beyond  doubt. 
A  small  iron  wire  (No.  16),  8  inches  long,  was  wound  with  two  layers  of 
fine  insulated  wire;  a  small  hard  steel  magnet  £  inch  long  suspended  by 
a  fibre  of  silk  was  rendered  entirely  astatic  by  a  large  magnet  placed 
about  2  feet  distant;  the  wire  electromagnet  was  then  placed  near  it, 
so  that  the  needle  hung  H  inch  from  it  and  about  2  inches  back  from 
the  end.  On  now  exciting  the  magnet  with  a  weak  current,  the  needle 
took  up  a  certain  definite  position,  indicating  the  direction  of  the  line 
of  force  at  that  point.  When  the  current  was  very  much  increased,  the 
needle  instantly  moved  into  a  position  more  nearly  parallel  to  the 
magnet,  thus  showing  that  the  magnetism  was  now  distributed  more 
nearly  at  the  ends  than  before.  This  shows  that  nearly  all  the  experi- 
ments hitherto  made  on  bar-magnets  contain  an  error;  but,  owing  to 
its  small  amount,  we  can  accept  the  results  as  approximately  true. 

I  believe  mine  are  the  first  experiments  hitherto  made  on-this  subject 
in  which  the  results  are  expressed  and  the  reasoning  carried  out  in  the 
language  of  Faraday's  theory  of  lines  of  magnetic  force ;  and  the  utility 
of  this  method  of  thinking  is  shown  in  the  method  of  experimenting 
adopted  for  measuring  magnetism  in  absolute  measure,  for  which  I 
claim  that  it  is  the  simplest  and  most  accurate  of  any  yet  devised. 
Whether  Faraday's  theory  is  correct  or  not,  it  is  well  known  that  its 
use  will  give  correct  results;  at  the  present  time  the  tendency  of  the 
most  advanced  thought  is  toward  the  theory5;  and  indeed  it  has  been 
pointed  out  by  Sir  William  Thomson  that  it  follows,  from  dynamical 
reasoning  upon  the  magnetic  rotation  of  the  plane  of  polarization  of 
light,  that  the  medium  in  which  this  takes  place  must  itself  be  in 
rotation,  the  axis  of  rotation  being  in  the  direction  of  the  lines  of 
force.8  Some  substances  must  of  necessity  be  more  capable  of  assum- 
ing this  rotary  motion  than  others;  and  hence  arises  the  notion  of 
magnetic  "  conductivity  '"'  and  "  permeability." 

Thomson  has  pointed  out  several  analogies  which  may  be  used  in 
calculating  the  distribution  and  direction  of  the  lines  of  force  under 
various  circumstances.  He  has  shown  that  the  mathematical  treatment 

4  Papers  on  Electricity  and  Magnetism,  p.  512. 

5  "On  Action  at  a  Distance,"  Maxwell,  'Nature,'  Feb.  27  and  March  6  and  13,  1873. 
"Thomson's  'Papers  on  Electricity  and  Magnetism,' p.  419,  note;   and  Maxwell's 

'Treatise  on  Electricity  and  Magnetism,'  vol.  ii,  chap.  xxi. 


38  HENRY  A.  EOWLAND 

of  magnetism  is  the  same  as  that  of  the  flow  of  heat  in  a  solid,  as  the 
static  induction  of  electricity,  and  as  the  flow  of  a  frictionless  incom- 
pressible liquid  through  a  porous  solid.  It  is  evident  that  to  these 
analogies  we  may  add  that  of  the  conduction  of  electricity.7  We  readily 
see  that  the  reason  of  the  treatment  being  the  same  in  each  case  is  that 
the  elementary  law  of  each  is  similar  to  Ohm's  law.  Mr.  Webb  8  has 
shown  that  this  law  is  useful  in  electrostatics;  and  I  hope,  in  a  sequel 
to  this  paper,  to  apply  it  to  the  distribution  of  magnetism:  I  give  two 
equations  derived  in  this  way  further  on. 

The  absolute  units  to  which  I  have  reduced  my  results  are  those  in 
which  the  metre,  gramme,  and  second  are  the  fundamental  units.  The 
unit  of  magnetizing-force  of  helix  I  have  taken  as  that  of  one  turn 
of  wire  carrying  the  unit  current  per  metre  of  length  of  helix,  and  is 
4?r  times  the  unit  magnetic  field.  This  is  convenient  in  practice,  and 
also  because  in  the  mathematical  solution  of  problems  in  electrodynam- 
ics the  magnetizing-force  of  a  solenoid  naturally  comes  out  in  this  unit. 
The  magnetizing-force  of  any  helix  is  reduced  to  this  unit  by  multiply- 
ing the  strength  of  current  in  absolute  units  by  the  number  of  coils  in 
the  helix  per  metre  of  length.  These  remarks  apply  only  to  endless 
solenoids,  and  to  those  which  are  very  long  compared  with  their  diam- 
eter. The  unit  of  number  of  lines  of  force  I  have  taken  as  the  number 
in  one  square  metre  of  a  unit  field  measured  perpendicular  to  their 
direction.  As  my  data  for  reducing  my  results  to  these  units,  I  have 
taken  the  horizontal  force  of  the  earth's  magnetism  at  Troy  as  1-641, 
and  the  total  force  as  6-27. 

The  total  force,  which  will  most  seriously  affect  my  results,  is  well 
'known  to  be  nearly  constant  at  any  one  place  for  long  periods  of  time. 

From  the  analogy  of  a  magnet  to  a  voltaic  battery  immersed  in  water 
I  have  obtained  the  following,  on  the  assumption  that  //  is  constant, 
and  that  the  resistance  to  the  lines  of  force  passing  out  into  the  medium 
is  the  same  at  every  point  of  the  bar. 

Let  R  =  resistance  to  lines  of  force  of  one  metre  of  length  of  bar. 
E'  =  resistance  of  medium  along  1  metre  of  length  of  bar. 
Q'  =  lines  of  force  in  bar  at  any  point. 
Qf=  lines  of  force  passing  from  bar  along  small  distance  I. 
e  =base  of  Napierian  system  of  logarithms. 
x   =  distance  from  one  end  of  helix. 

1  Maxwell's  'Treatise  on  Electricity  and  Magnetism,'  arts.  243,  244  and  245. 
s  "Application  of  Ohm's  Law  to  Problems  in  Electrostatics,"  Phil.  Mag.  S.  4,  vol. 
xxxv,  p.  325  (18«8). 


MAGNETIC  PERMEABILITY  OF  IRON,  STEEL  AND  NICKEL        39 

&    =  total  length  of  helix. 

s'  =  resistance  at  end  of  helix  of  the  rest  of  bar  and  medium. 
M  =  magnetizing-f  orce  of  helix. 
We  then  obtain 

Ml  -A        /  rx  r  (»-*)-)  (l\ 


1M  M      1  A 

m  -  ~  A    fer»4-1  —  sn—  er(»-*)^      f9\ 

s'   ~f      2R  A^-  I  ( 


IJE 

-VTT 


in  which 


and 


for  near  the  centre  of  an  infinitely  long  bar,  where  x  >  0  and  <  &,  and 
6=00  ,  we  have 

Q.=  0,and  V=%.  .    .-•'•.    •    •    (3) 
For  a  ring-magnet,  s'  =  0; 

.-.  &  =  0,and  Q=X  ......    (4) 

And  if  a  is  the  area  of  the  bar  or  ring, 

al=B  =  -irori  =  iSr  .....  (5) 

in  which  A  is  the  same  as  in  the  equations  previously  given.  These 
equations  show  that  we  may  find  the  value  of  ^,  and  hence  the  permea- 
bility, by  experimenting  either  on  an  infinitely  long  bar  or  on  a  ring- 
magnet.  Equations  (4)  evidently  apply  to  the  case  where  the  diameter 
of  the  ring  is  large  as  compared  with  its  section.  The  fact  given  by 
these  equations  can  be  demonstrated  in  another  and,  to  some  persons, 
more  satisfactory  manner.  If  n  is  the  number  of  coils  per  metre  of 
helix  and  n'  the  number  on  a  ring-magnet,  i  the  strength  of  current, 
and  p  the  distance  from  the  axis  of  the  ring  to  a  given  point  in  the 

»  Formulae  giving  the  same  distribution  as  this  have  been  obtained  by  Biot  and 
also  by  Green.  See  Biot's  Traite  de  Physique,  vol.  iii,  p.  77,10  and  'Essay  on  the  Ap- 
plication of  Mathematical  Analysis  to  the  Theories  of  Electricity  and  Magnetism,' 
by  Green,  17th  section. 

IO[In  the  original  paper  this  was  "  vol.  iv,  p.  669."  The  correction  was  made  later 
by  Professor  Rowland.] 


40  HENRY  A.  KOWLAND 

interior  of  the  ring-solenoid,  the  magnetic  field  at  that  point  will,  as  is 
well  known,  be 

2n'i  -  , 
f> 

and  at  a  point  within  an  infinitely  long  solenoid 


If  the  solenoid  contain  any  magnetic  material,  the  field  will  be  for 
the  ring 


and  for  the  infinite  solenoid 

4x/ttft, 

Therefore  the  number  of  lines  of  force  in  the  whole  section  of  a  ring- 
magnet  of  circular  section  will  be,  if  a  is  the  mean  radius  of  the  ring, 


S 


Q'=  ±n'  in  —     dx  = 

J   —B     a  —  x 

or,  since  n'  =  2  *  an  and  M  =  in,  we  have,  by  developing, 

Qf=  ^jfoorj?)  (i  +  \  f  +  i  jr  +  &c.y  .  .  (6) 

For  the  infinite  electromagnet  we  have  in  the  same  way  for  a  circular 
section, 

Q'  =  4*Mn(*B*)  .........     (7) 

When  the  section  of  the  ring  is  thin,  equation  (6)  becomes  the  same 
as  equation  (7),  and  either  of  them  will  give 


which  is  the  same  as  equation  (5). 

In  all  the  rings  used  the  last  parenthesis  of  (6)  is  so  nearly  unity 
that  the  difference  has  in  most  cases  been  neglected,  the  slightest  change 
in  the  quality  of  the  iron  producing  many  times  more  effect  on  the 
permeability  than  this.  Whenever  the  difference  amounted  to  more 
than  -^TT  it  was  not  rejected. 

The  apparatus  used  to  measure  Q'  was  based  upon  the  fact  discovered 
by  Faraday,  that  the  current  induced  in  a  closed  circuit  is  proportional 
to  the  number  of  lines  of  force  cut  by  the  wire,  and  that  the  deflection 
of  the  galvanometer-needle  is  also,  for  small  deflections,  proportional 
to  that  number.  In  the  experiments  of  1870-71  an  ordinary  astatic 
galvanometer  was  used;  but  in  those  made  this  year  a  galvanometer  was 


MAGNETIC  PERMEABILITY  OF  IRON,  STEEL  AND  XICKEL         41 

specially  constructed  for  the  purpose.  It  was  on  the  principle  of  Thom- 
son's reflecting  instrument,  but  was  modified  to  suit  the  case  by  increas- 
ing the  size  of  the  mirror  to  £  of  an  inch,  by  adding  an  astatic  needle 
just  above  the  coil  without  adding  another  coil,  by  loading  the  needle 
to  make  it  vibrate  slowly,  and,  lastly,  by  looking  at  the  reflected  image 
of  the  scale  through  a  telescope  instead  of  observing  the  reflection  of  a 
lamp  on  the  scale.  The  galvanometer  rested  on  a  firm  bracket  attached 
to  the  wall  of  the  laboratory  near  its  foundation.  In  most  of  the  ex- 
periments the  needle  made  about  five  single  vibrations  per  minute. 
The  astatic  needle  was  added  to  prevent  any  external  magnetic  force 
from  deflecting  the  needle;  and  directive  force  was  given  by  the  magnet 
above.  Each  division  of  the  scale  was  •  075  inch  long;  and  the  extrem- 
ities of  the  scale  were  reached  by  a  deflection  of  7°  in  the  needle  from  0. 
The  scale  was  bent  to  a  radius  of  4  feet,  and  was  3  feet  from  the  instru- 
ment. At  first  a  correction  was  made  for  the  resistance  of  the  air,  &c. ; 
but  it  was  afterwards  found  by  experiment  that  the  correction  was  very 
exactly  proportional  to  the  deflection,  and  hence  could  be  dispensed 
with.  This  instrument  gave  almost  perfect  satisfaction;  and  its  accu- 
racy will  be  shown  presently. 

The  tangent-galvanometer  was  also  a  very  fine  instrument,  and  was 
constructed  expressly  for  this  series  of  experiments.  The  needle  was 
1*1  inch  long,  of  hardened  steel;  and  its  deflections  were  read  on  a 
circle  graduated  to  half  degrees,  and  5  inches  in  diameter.  The  aver- 
age diameter  of  the  ring  was  16^  inches  nearly,  and  was  wound  with 
several  coils;  so  that  the  sensibility  could  be  increased  or  diminished 
at  pleasure,  and  so  give  the  instrument  a  very  wide  range.  The  value 
of  each  coil  in  producing  deflection  was  experimentally  determined  to 
within  at  least  ^  of  1  per  cent  by  a  method  which  I  shall  soon  publish. 
The  numbers  to  multiply  the  tangent  of  the  deflection  by,  in  order  to 
reduce  the  current  to  absolute  measure,  were  as  follows: — 

Number  of  coils.  Multiplier. 

1 -05377 

3  -01800 

9 "  .  -006007 

27 -002018 

48 "  .  -001143 

By  this  instrument  I  had  the  means  of  measuring  currents  which 
varied  in  strength  several  hundred  times  with  the  same  accuracy  for 
a  large  as  for  a  small  current.  For  greater  accuracy  a  correction  was 


42  HENEY  A.  ROWLAND 

applied  according  to  the  formula  of  Blanchet  and  De  la  Prevostaye  for 
the  length  of  the  needle,  the  position  of  the  poles  being  estimated;  this 
correction  in  the  deflections  used  was  always  less  than  -6  per  cent.  To 
eliminate  any  error  in  the  position  of  the  zero-point,  two  readings  were 
always  taken  with  the  currents  in  opposite  directions,  each  one  being 
estimated  with  considerable  accuracy  to  ^  of  a  degree. 

The  experiments  were  carried  on  in  the  assay  laboratory  of  the 
Institute,  which  was  not  being  used  at  that  time;  and  precautions  were 
taken  that  the  different  parts  of  the  apparatus  should  not  interfere 
with  each  other.  The  disposition  of  the  apparatus  is  represented  in 
Plate  II. 

The  current  from  the  battery  A,  of  from  two  to  six  large  Chester's 
"  electropoion  "  cells  No.  2,  joined  according  to  circumstances,  passed 
to  the  commutator  B,  thence  to  the  tangent-galvanometer  C,  thence 
to  another  commutator  D,  thence  around  the  magnet  E  (in  this  case  a 
ring),  and  then  back  through  the  resistance-coils  K  to  the  battery.  To 
measure  the  magnetism  excited  in  E,  a  small  coil  of  wire  F  was  placed 
around  it,11  which  connected  with  the  galvanometer  H,  so  that,  when 
the  magnetism  was  reversed  by  the  commutator  D,  the  current  induced 
in  the  coil  F,  due  to  twice  cutting  the  lines  of  force  of  the  ring, 
produced  a  sudden  swing  of  the  needle  of  H.  As  the  needle  swung 
very  freely  and  would  not  of  itself  come  to  rest  in  ten  or  fifteen  min- 
utes, the  little  apparatus  7  was  added :  this  consisted  of  a  small  horse- 
shoe magnet,  on  one  branch  of  which  was  a  coil  of  wire ;  and  by  sliding 
this  back  and  forth,  induced  currents  could  be  sent  through  the  wire, 
which,  when  properly  timed,  soon  brought  the  needle  to  rest.  This 
arrangement  was  very  efficient;  and  without  it  this  form  of  galvano- 
meter could  hardly  have  been  used.  To  compare  the  magnetism  of 
the  ring  with  the  known  magnetism  of  the  earth,  and  thus  reduce  it  to 
absolute  measure,  a  ring  G  supported  upon  a  horizontal  surface  was 
included  in  the  circuit;  when  this  was  suddenly  turned  over,  it  produced 
an  induced  current,  due  to  twice  cutting  the  lines  of  magnetic  force 
which  pass  through  the  ring  from  the  earth's  magnetism.  The  induced 
current  in  the  case  of  either  coil,  F  or  G,  is  proportional  to  the  number 
of  the  lines  of  force  cut  by  the  coils  "  and  to  the  number  of  wires  in  the 
coil,  which  latter  is  self  evident,  but  may  be  deduced  from  the  law  of 
Gaugain.1*  It  is  evident,  then,  that  if  c  is  the  deflection  from  coil  G, 

11  If  a  bar  was  used,  this  coil  was  placed  at  its  centre. 

12  Faraday's  Experimental  Researches,  vol.  iii,  series  29. 
13Dagnin's  Traite  de  Physique,  vol.  iii,  p.  691. 


MAGNETIC  PERMEABILITY  OF  IRON,  STEEL  AND  NICKEL         43 

and  h  that  from  helix  F,  the  number  of  lines  of  force  passing  through 
the  magnet  E,  expressed  in  the  unit  we  have  chosen,  will  he 


(9) 


where  ri  is  the  number  of  coils  in  the  ring  G,  n  the  number  in  the 
helix  F,  R  the  radius  of  G,  6-  27  the  total  magnetism  of  the  earth,  and 
74°50'  the  dip.  The  quantity  2n'(6-27  sin  74°50')^E2  is  constant  for 
the  coil,  and  had  the  value  14*  15.  This  is  the  number  of  square  metres 
of  a  unit  field  which,  when  cut  once  by  a  wire  from  the  galvanometer, 
would  produce  the  same  deflection  as  the  coil  when  turned  over. 

The  experiments  being  made  by  reversing  the  magnetism  of  the  bars, 
a  rough  experiment  was  made  to  see  whether  they  had  time  to  change 
in  half  a  single  vibration  of  the  needle;  it  was  found  that  this  varied 
from  sensibly  0  to  nearly  1  second,  so  that  there  was  ample  time.  It 
was  also  proved  that  the  sudden  impulse  given  to  the  needle  by  the 
change  of  current  produced  the  same  deflection  as  when  the  change  was 
more  gradual,  which  has  also  been  remarked  by  Faraday,  though  he 
did  not  use  such  sudden  induced  currents.  As  a  test  of  the  method, 
the  horizontal  force  of  the  earth's  magnetism  was  determined  by  means 
of  a  vertical  coil;  it  was  found  to  be  1'  634.  while  the  true  quantity  is 
1-641. 

It  is  sometimes  assumed  that  some  of  the  action  in  a  case  like  the 
present  is  due  to  the  direct  induction  of  the  helix  around  the  magnet  on 
the  coil  F.  I  think  that  this  is  not  correct;  for  when  the  helix  is  of 
fine  wire  closely  surrounding  the  bar  or  ring,  all  the  lines  of  force 
which  affect  F  must  pass  through  the  bar,  and  so  no  correction  should 
be  made.  However,  the  correction  is  so  small  that  it  will  hardly  affect 

the  result.     If  it  were  to  be  made,  -^  (equation  5)  should  be  diminished 

CL 

by  47r/lf  ;  but,  for  the  above  reasons,  it  has  not  been  subtracted.  As  a 
test  of  the  whole  arrangement,  I  have  obtained  the  number  of  lines  of 
force  in  a  very  long  solenoid:  the  mean  of  two  solenoids  gave  me 

Q'  =  12-67  M(xR<); 
while  from  theory  we  obtain,  by  equation  (7)  (n  —  1), 


which  is  within  the  limits  of  error  in  measuring  the  diameter  of  the 
tubes,  &c. 

All  the  rings  and  bars  with  which  I  have  experimented  have  had  a 
circular  section.     In  selecting  the  iron,  care  must  be  used  to  obtain  a 


44 


HEXET  A.  KOWLAND 


homogeneous  bar;  in  the  case  of  a  ring  I  believe  it  is  better  to  have  it 
welded  than  forged  solid;  it  should  then  be  well  annealed,  and  after- 
wards have  the  outside  taken  off  all  round  to  about  -J  of  an  inch  deep  in 
a  lathe.  This  is  necessary,  because  the  iron  is  "  burnt "  to  a  consider- 
able depth  by  heating  even  for  a  moment  to  a  red  heat,  and  a  sort  of 
tail  appears  on  the  curve  showing  the  permeability,  as  seen  on  plotting 
Table  III.  To  get  the  normal  curve  of  permeability,  the  ring  must  only 
be  used  once;  and  then  no  more  current  must  be  allowed  to  pass  through 
the  helix  than  that  with  which  we  are  experimenting  at  the  time.  If 
by  accident  a  stronger  current  passes,  permanent  magnetism  is  given  to 
the  ring,  which  entirely  changes  the  first  part  of  the  curve,  as  seen  on 
comparing  Table  I  with  Table  II.  The  areas  of  the  bars  and  rings  were 
always  obtained  by  measuring  their  length  or  diameter  across,  and  then 
calculating  the  area  from  the  loss  of  weight  in  water.  The  following 
is  a  list  of  a  few  of  the  rings  and  bars  used,  the  dimensions  being  given 
in  metres  and  grammes.  In  the  fourth  column  "  annealed "  means 
heated  to  a  red  heat  and  cooled  in  open  air,  "  C  annealed  "  means  placed 
in  a  large  crucible  covered  with  sand,  and  placed  in  a  furnace,  where, 
after  being  heated  to  redness,  the  fire  was  allowed  to  die  out ;  "  natural  " 
means  that  its  temper  was  not  altered  from  that  it  had  when  bought. 


Results 
given  in 
Table. 

Quality  of 
substance. 

How  made. 

Temper. 

Spec, 
grav. 

Weight. 

Mean 
diam. 

Area. 

State. 

•0000 

M 

"Burden 
best"  iron. 

Welded  and 
turned. 

Annealed. 

17-63 

148-61 

•0677 

916 

Normal. 

II. 

«           u 

11        <{ 

u 

7-63 

148-61 

•0677 

916 

Magnetic. 

III. 

It           II 

"    M 

C  an- 
nealed. 

17-63 

148-01 

•0677 

912 

Burnt. 

:v.j 

Bessemer 
steel. 

Turned  from 
large  bar. 

Natural. 

7-84 

38-34 

•0420 

371 

Normal. 

M 

Norway 
iron 

Welded  and 
turned. 

C  an- 
nealed. 

J7-83 

39-78 

•0656 

7695 

Magnetic. 

VI.    { 

Cast 
nickel.14 

Turned  from 
button. 

.... 

8-83 

4-806 

•0200 

0869 

Normal. 

VII.    | 

Stubs' 
steel. 

Hard-drawn 
wire. 

Natural. 

7-73 

0969 

Normal. 

The  first  three  Tables  are  from  the  same  ring. 

Besides  these  I  have  used  very  many  other  bars  and  rings ;  but  most 
of  them  were  made  before  I  had  discovered  the  effect  of  burning  upon 


14  Almost  chemically  pure  before  melting. 


MAGNETIC  PERMEABILITY  OF  IKON,  STEEL  AND  NICKEL         45 

the  iron,  and  hence  did  not  give  a  normal  curve  for  high  magnetizing- 
powers.  However,  I  have  collected  in  Table  VIII  some  of  the  results 
of  these  experiments;  but  I  have  many  more  which  are  not  worked 
up  yet. 

In  the  following  Tables  Q=  -^  has  been  measured  as  previously 

described.  It  is  evident  that  if,  instead  of  reversing  the  current,  we 
simply  break  it,  we  shall  obtain  a  deflection  due  to  the  temporary  mag- 
netism alone.  In  this  manner  the  temporary  magnetism  has  been 
measured;  and  on  subtracting  this  from  Q,  we  can  obtain  the  permanent 
magnetism. 

The  following  abbreviations  are  made  use  of  in  the  Tables,  the  other 
quantities  being  the  same  as  previously  described. 

C.T.G.  Number  of  coils  of  tangent-galvanometer  used. 
D.T.G.  Deflection  of  tangent-galvanometer. 
D.C.     Deflection  from  coil  G. 
D.F.     Deflection  from  helix  F  on  reversing  the  current. 

Q.      Magnetic  field  in  interior  of  bar  (total). 
D.B.     Deflection  from  F  on  breaking  current. 

T.  Magnetic  field  of  bar  due  to  temporary  magnetism. 
P.  Magnetic  field  of  bar  due  to  permanent  magnetism. 
n.  Number  of  coils  in  helix  F. 


Each  observation  given  is  almost  always  the  mean  of  several.  D.T.G. 
is  the  mean  of  four  readings,  two  before  and  two  after  the  observations 
on  the  magnetism;  D.C.  is  the  mean  of  from  four  to  ten  readings;  D.F. 
mean  of  three;  D.B.  mean  of  two,  except  in  Table  I,  where  the  deflec- 
tion was  read  only  once.  In  all  these  Tables  the  column  containing 
the  temporary  magnetism  T  can  only  be  accepted  as  approximate,  the 
experiments  having  been  made  more  to  determine  Q  than  T. 

The  value  of  n  was  generally  varied  by  coiling  a  wire  more  or  less 
around  the  ring,  but  leaving  its  length  the  same. 

The  change  in  the  value  of  D.C.  is  due  to  the  change  in  the  resist- 
ance of  the  galvanometer  from  change  of  temperature,  copper  wire 
increasing  in  resistance  about  1  per  cent  for  every  2°  -60.  rise.  In 
Table  I  the  temperature  first  increased  slowly,  and  then,  after  remain- 
ing stationary  for  a  while,  fell  very  fast. 


46 


HEXEY  A.  BOWLAND 


STABLE  i. 

" BURDEN  BEST"  IRON,  NORMAL. 


T. 
M? 

C.T.G. 

D.T.G. 

M. 

B.C. 

71. 

D.F. 

D.F. 
2n.  ' 

D.B. 

n. 

Q. 

A 

A 

Calcu- 
lated. 

A 
^=S- 

T. 

P. 

P. 
M.' 

3627- 

48 

4-5 

•1456 

23-4 

30 

6-6 

•1083 

1 
•08    715 

4910 

5845 

390-7 

528 

187- 

1284- 

7080- 

16-45 

•5501 

54-6 

•910 

•59 

6005 

10920 

10885 

868-7 

3894 

2111- 

3838- 

7746- 

20-2 

•6815 

87-9 

1-465 

•80 

9667 

14180 

14074 

1129 

5280 

4387- 

6437- 

8786- 

28-6  !  1-011 

23-3 

io 

74-2 

3-71 

1-34 

24600 

24330 

24000 

1936 

8882 

15718- 

15550- 

8766- 

31-1 

1-119 

88-2 

4-41 

1-48 

29230 

26120  26050 

2078 

9811 

19419- 

naso- 

8819- 

31-9 

1.155 

92'6 

4-63 

1-53 

30820 

26690}  26660 

2124    10180;  20640' 

17870- 

?8205- 

41-12 

1-623 

"z 

28-8 

7-45 

2-0 

49590 

30570 

30740 

2433   13310  36280- 

22370- 

94BO- 

27 

28-35 

1-766 

23-1 

32-8 

8-20 

2-5 

54820 

31030 

31050 

2470 

16710  38110- 

21570- 

9517- 

29-6 

1-861 

34-6 

8-65 

2-65 

57820 

31070 

31100 

2472   17710  40110' 

21550- 

8812- 

33-4 

2-162 

23-1 

39-8!  9-95 

2-85 

66510 

30770 

30776  2448   190501  47460- 

21950- 

8115- 

37-45 

2-512 

44-711-18 

3-05 

74730 

29750 

29930  :  2367   20390 

54340- 

21630- 

7985- 

44-45 

3-223 

53-513-38 

3-85 

89430 

27750  27390  !  2208   25740 

63690- 

19760- 

7674- 

52-1 

4-225 

60-315-08 

4-85 

100800 

23860  24730  :  1899   32420!  67380' 

15950" 

7070- 

'9 

34-65 

6-744 

73-1 

18-28 

7-10 

122700 

18210 

18410  1448   47680  75020- 

11130- 

6519- 

39-8 

8-136 

23-0 

77-319-32 

7-90 

129700 

15940 

16130  1  1269   53040  76660- 

9423- 

6403- 

44-3 

9-543 

"\ 

40-620-30 

9-1 

136300 

14280 

13920  1137   611001  75200' 

7881- 

4666- 

55-1  14-04 

43-521-75 

9-8 

145400 

10360 

10760 

824'1  65510-  79890- 

5690- 

2816- 

'3 

42-95  27-18 

47-423-70 

11-5 

157700 

5803 

6350 

461-8 

76540;  81160- 

2985- 

2300- 

51-3  36-60 

49-124-55 

12-7 

162700 

4445 

4523 

353.8 

84180!  78520- 

2145- 

1702- 

60-15  51-18 

23-4 

50-325-15 

13-2 

166000 

3243 

3310 

358.0 

87120,  78880- 

1541- 

00 

175000 

0 

1 

TABLE  II. 
"BURDEN  BEST"  IRON,  MAGNETIC. 


M. 

Q. 

A. 

M. 

M. 

Q. 

A. 

M. 

•1456 

426 

2920 

232 

2-930 

82720 

28240 

2247 

•5699 

3346 

5987 

476 

4-210 

100900 

23950 

1906 

•6962 

5700 

8189 

652 

6-769 

122800 

18140 

1444 

1-080 

24350 

22550 

1795 

7.273 

124300 

17090 

1360 

1-191 

29280 

24580 

1956 

7-626 

127100 

16670 

1326 

1-537 

46150 

30020 

2389 

11-10 

139500 

12570 

1000 

1-590 

49070 

30260 

2408 

13-61 

144700 

10630 

846 

1-933 

59680 

30860 

2456 

22-10 

154600 

6965 

554 

2-377 

71660 

30150 

2399 

>«  TABLE  III. 
BURDEN  BEST"  IRON,  BURNT. 


M. 

Q. 

A. 

M- 

T. 

M. 

Q. 

A. 

M. 

T. 

P. 

P. 

•143 

1001 

7039 

560 

1020 

3.810 

116900 

30730 

2446 

8 

.553 

9395 

16980 

1351 

5115 

4-283 

120200 

28060 

2233 

4280- 

•682 

16550 

24240 

1929 

6835 

4-722 

123900 

26240 

2088 

30830 

9715- 

•962 

37330 

38780 

3086 

9454 

6.565 

133100 

20270 

1613 

27876- 

1-070 

42920 

40130 

3194 

10300 

9-326 

141200 

15140 

1200 

3981032620- 

1-153 

48830 

42340 

3369 

10530 

11-00 

144400 

13120 

1045 

38300- 

1-317 

59490 

45180 

3595 

11650 

13-44 

147500 

10970 

873 

44070 

47840- 

103430- 

1-340 

59580 

44450 

3538 

13700 

23-41 

155500 

6642 

529 

51030 

45880- 

104470- 

a  •  127 

90180 

42400 

3374 

18470 

32-73 

159400 

4870 

387 

71710- 

2-501 

98560 

39400 

3136 

19920 

32-56 

158400 

48641  387 

78640- 

2-864 

104000 

36310 

2890 

24600 

51-03 

165800 

3250 

259 

56100 

79400- 

109700- 

3-151 

108200 

34330 

2732 

24610 

83590- 

15  [Columns  1,  15,   16  were   added  to   the  original   paper   by  Professor  Rowland, 
after  its  publication.] 

16  [The  last  two  columns  of  Tables  III,  IV,  V,  VII  were  added  by  Professor  Row- 
land after  the  paper  was  published.] 


MAGNETIC  PEEMEABILITY  or  IKON,  STEEL  AND  XICKEL        47 


STABLE  iv. 

BESSEMER  STEEL,  NORMAL. 


M. 

Q. 

A. 

M- 

T. 

M. 

Q. 

A. 

»*. 

T. 

P. 

P. 

•1356 

327 

2412 

192 

309 

2-756 

39960 

14500 

1154 

13080 

IS- 

26880- 

•2793 

817 

2995 

238 

727 

3-219 

50550 

15700 

1250 

16350 

90- 

34200- 

•5287 

1726 

3264 

260 

1471   3-551 

56310 

15860 

1262 

15980 

255- 

40330- 

•  9398  3833 

4079 

325  3106 

4-469 

71380 

15970 

1271 

18340 

727- 

53040- 

1-421   7702 

5421 

431 

5576 

5-698 

85530,  15010 

1195 

23610 

2126- 

61920- 

1-880 

14080 

7487   596 

8972 

11-44 

119550  10450 

832 

28020 

5108- 

91530- 

1-947 

15420 

7920 

630 

8938 

20-69 

138300  6685 

532 

41360 

6482- 

96940- 

2-300 

24830 

10800 

859 

11320 

38-99 

153700  3942 

314 

52930 

13510- 

100770- 

"TABLE  V. 
NORWAY  IRON,  MAGNETIC. 


M. 

Q. 

A. 

/*• 

T. 

M. 

Q. 

A. 

M. 

T. 

P. 

P. 

•1344 

865 

6439 

512 

2-290 

105900 

46240 

3680 

35240 

70660- 

•2673 

2550 

9910 

759   1892 

4-393)134100 

30520 

2429 

54970 

658- 

79130- 

•516l!  13000  25200 

2005    5857 

5-910 

142400 

24090 

1917 

62810 

7143- 

79590- 

•5572 

15310)  27480 

2187 

8110 

7-874 

149100 

18940 

1507 

68490 

7200- 

80610- 

•6725 

30140  44820 

3567 

8921 

13-77  156800 

11390 

906 

77060 

21220- 

79740  • 

•  9305 

53800J  57820  4602 

13970  26-84  165800 

6038 

480 

84710 

39830- 

81090- 

1-362 

77700  57110  4545 

21630 

36-86 

168500 

4572 

364 

87860 

56070- 

80740- 

1-788 

93000 

52020 

4140 

28200 

64800- 

TABLE  VI. 
CAST  NICKEL,  NORMAL. 


M. 

Q. 

A. 

M- 

T. 

M. 

Q. 

A. 

(*• 

T. 

1-433 

852 

595 

47-4 

13-43 

27100 

2018 

160-6 

11260 

2-904     2377 

819 

65-1 

16-53 

31050 

1878 

149-5 

13530 

3-527 

3685 

1070 

85-1 

21-02 

34950 

1663 

132-3 

16480 

5-555 

10080 

1815 

144-4 

32-17 

41980 

1305 

103-8 

22300 

6-783 

13680 

2017 

160-5 

5120 

33-92 

42650 

1257 

100-0 

23360 

7-401    15270 

2063 

164-2 

5614 

60-91 

50860 

855 

66-4 

29540 

9-273 

19600 

2114 

168-2 

7644 

82-36 

53650 

651 

51.8 

33460 

11.78     24720 

2098 

167-0 

9902 

105-2 

55230 

525 

41-8 

35120 

STABLE  vn. 

STUBS'  STEEL  WIRE,  NORMAL. 


M.           Q.           A. 

M. 

T. 

M. 

Q. 

A. 

/*• 

T 

P. 

P. 

•1673      159        953        75-9 

13-65 

54300 

3978 

316-6 

20900 

33400- 

•6237     678     1087       86-5 

598 

19-35 

77770    4020      319-9    29480 

80- 

48290- 

1.084  !  1197      1104        87-9 

1101 

27-43100800    3676      292-6    38590 

96- 

62210- 

2-043  !  2448      1199 

95-4 

2257 

33-39111300   3335 

265-4 

45110 

191- 

66190- 

2-714  j  3446      1270 

101-0 

3095 

35-58115000    3228 

256-9 

45950 

351- 

69050- 

4-221  i  6278     1487      118-4 

5145 

38-64 

119400 

3092 

246-0   48060 

1133- 

71340- 

10-26     33700     3286 

261  •  5 

16170 

17530- 

48  HENUY  A.  EOWLAND 

The  best  method  of  studying  these  Tables  is  to  plot  them:  one 
method  of  doing  this  is  to  take  the  value  of  the  magnetizing-force  as 
the  abscissa,  and  that  of  the  permeability  as  the  ordinate;  this  is  the 
method  used  by  Dr.  Stoletow;  but,  besides  making  the  complete  curve 
infinitely  long,  it  forms  a  very  irregular  curve,  and  it  is  impossible  to 
get  the  maximum  of  magnetism  from  it.  Another  method  is  to  employ 
the  same  abscissas,  but  to  use  the  magnetism  of  the  bar  as  ordinates; 
this  gives  a  regular  curve,  but  has  the  other  two  disadvantages  of  the 
first  method;  however,  it  is  often  employed,  and  gives  a  pretty  good 
idea  of  the  action.  In  Plate  II,  I  have  given  a  plot  of  Table  V  with 
the  addition  of  the  residual  or  permanent  magnetism,  which  shows  the 
general  features  of  these  curves  as  drawn  from  any  of  the  Tables.  It 
is  observed  that  the  total  magnetism  of  the  iron  at  first  increases  very 
fast  as  the  magnetizing-force  increases,  but  afterwards  more  and  more 
slowly  until  near  the  maximum  of  magnetism,  where  the  curve  is 
parallel  to  the  axis  of  Q.  The  concavity  of  the  curve  at  its  commence- 
ment, which  indicates  a  rapid  increase  of  permeability,  has  been  noticed 
by  several  physicists,  and  was  remarked  by  myself  in  my  experiments  of 
January,  1871;  it  has  now  been  brought  most  forcibly  before  the  public 
by  Dr.  Stoletow,  whose  paper  refers  principally  to  this  point.17  M. 
Miiller  has  given  an  equation  of  the  form 


to  represent  this  curve;  but  it  fails  to  give  any  concavity  to  the  first 
part  of  the  curve.  A  formula  of  the  same  form  has  been  used  by  M. 
Cazin  ;  18  but  his  experiments  carry  little  weight  with  them,  on  account 
of  the  small  variation  of  the  current  which  he  used,  this  being  only 
about  five  times,  while  I  have  used  a  variation  in  many  cases  of  more 
than  three  hundred  times. 

Weber  has  obtained,  from  the  theory  that  the  particles  of  the  iron 
are  always  magnetic  and  merely  turn  round  when  the  magnetizing- 
force  is  applied,  an  equation  which  would  make  the  first  part  of  the 
curve  coincide  with  the  dotted  line  in  Plate  II  ;  19  and  Maxwell,  by  addi- 
tion to  the  theory,  has  obtained  an  equation  which  replaces  the  first 

17  On  the  Magnetizing  Function  of  Soft  Iron,  especially  with  the  weaker  decom- 
posing powers.     By  Dr.  A.  Stoletow,  of  the  University  of  Moscow.     Translated  in 
the  Phil.  Mag.,  January,  1873.     See  particularly  p.  43. 

18  Annales  de  Chimie  et  de  Physique,  February  1873,  p.  182. 

19  This  is  according  to  Maxwell's  integration  of  Weber's  equation,  Weber  having 
made  some  mistake  in  the  integration. 


MAGNETIC  PERMEABILITY  OF  IRON,  STEEL  AND  NICKEL        49 

part  of  the  curve  by  the  broken  line.20  I  believe  that  I  have  obtained 
at  the  least  a  very  close  approximation  to  the  true  equation  of  the  curve, 
and  will  show  further  on  that  Q  and  M  must  satisfy  the  equation 


—  D 

It  is  very  probable  that  Weber's  theory  may  be  so  modified  as  to 
give  a  similar  equation. 

Space  will  not  permit  me  to  discuss  the  curves  of  temporary  and 
permanent  magnetism;  but  I  will  call  attention  to  the  following  facts 
which  the  Tables  seem  to  establish. 

1.  Nearly  or  quite  all  the  magnetism  of  a  bar  is,  with  weak  magnetizing- 
forces,  temporary;  and  this  is  more  apparent  in  steel  than  in  soft  iron. 

2.  The  temporary  magnetism  increases  continually  with  the  current. 

3.  The  permanent  magnetism  at  first  increases  very  fast  with  the  current, 
but  afterwards  diminishes  as  the  current  increases,  when  the  iron  is  near 
its  maximum  of  magnetism.21 

I  have  now  described  the  methods  of  plotting  the  Tables  hitherto 
used;  and  I  will  now  describe  the  third,  which  is,  I  believe,  new.  This 
is  by  using  the  values  of  the  magnetism  of  the  bar  as  abscissas,  and 
those  of  the  permeability  as  ordinates.  In  this  way  we  obtain  a  per- 
fectly regular  curve,  which  is  of  finite  dimensions,  and  from  which  the 
maximum  of  magnetism  can  be  readily  obtained.  Plate  III  shows  this 
method  of  plotting  as  applied  to  Table  I.  If  we  draw  straight  lines 
across  the  curve  parallel  to  the  axis  of  Q  and  mark  their  centres,  we 
find  that  they  always  fall  very  exactly  upon  a  straight  line,  which  is 
therefore  a  diameter  of  the  curve.  The  curve  of  nickel  shown  upon 
the  same  Plate  has  this  property  in  common  with  iron.  I  have  made 
several  attempts  to  get  a  ring  of  cobalt;  but  the  button  has  always 
been  too  porous  to  use.  However,  I  hope  soon  to  obtain  one,  and  thus 
make  the  law  general  for  all  the  magnetic  metals.  There  are  two 
equations  which  may  be  used  to  express  the  curve  :  one  is  the  equation 
of  an  inclined  parabola;  but  this  fails  for  the  two  ends  of  the  curve; 
the  other  is  an  equation  of  the  general  form 


(11) 


20  Treatise  on  Electricity  and  Magnetism,  Maxwell,  vol.  ii,  chap.  vi. 

21  The  last  clause  of  this  sentence  cannot  be  considered  yet  as  entirely  settled, 
though  I  have  other  curves  than  those  shown  here  which  show  it  well.     [This  note 
was  added  to  the  original  paper  by  Professor  Rowland.] 

4 


50  HEJSTRY  A.  ROWLAND 

in  which  A,  H,  D,  and  a  are  constants  depending  upon  the  kind  and 
quality  of  the  metal  used.  A  is  the  maximum  value  of  X,  and  gives 
the  height  of  the  curve  E  D,  Plate  III;  a  establishes  the  inclination  of 
the  diameter;  H  is  the  line  A  0;  and  D  depends  upon  the  line  A  0. 
The  following  equation,  adapted  to  degrees  and  fractions  of  a  degree, 
is  the  equation  from  which  the  values  of  ^  were  found,  as  given  in 
Table  I: 

A  =  81-100  sin 


The  large  curve  in  Plate  III  was  also  drawn  from  this,  and  the  dots 
added  to  show  the  coincidence  with  observation;  it  is  seen  that  this  is 
almost  perfect.  As  X  enters  both  sides  of  the  equation,  the  calculation 
can  only  be  made  by  successive  approximations.  We  might  indeed  solve 
with  reference  to  Q  ;  but  in  this  case  some  values  of  ^  as  obtained  from 
experiment  may  be  accidentally  greater  than  A,  and  so  give  an  imagi- 
nary value  to  Q. 

By  plotting  any  Table  in  this  way  and  measuring  the  distance  0  C, 
we  have  the  maximum  of  magnetism. 

I  have  given  in  the  same  Plate  the  curve  drawn  from  the  observations 
on  the  nickel  ring  with  Q  on  the  same  scale,  but  ^  on  a  scale  four  times 
as  large  as  the  other.  The  curve  of  nickel  satisfies  the  equation 


quite  well,  but  not  so  exactly  as  in  the  case  of  iron.  This  ring,  when 
closely  examined,  was  found  to  be  slightly  porous,  which  must  have 
changed  the  curve  slightly,  and  perhaps  made  it  depart  from  the 
equation. 

In  Table  VIII,  I  have  collected  some  of  the  values  of  the  constants 
in  the  formula  when  it  is  applied  to  the  different  rings  and  bars,  and 
have  also  given  some  columns  showing  the  maximum  of  magnetism. 
When  any  blank  occurs,  it  is  caused  by  the  fact  that  for  some  reason 
or  other  the  observations  were  not  sufficient  to  determine  it.  The 
values  of  a,  H,  D,  and  the  value  of  X,  when  Q  =  0,  can  in  most  cases 
only  be  considered  approximate  ;  for  as  they  all  vary  so  much,  I  did  not 
think  it  necessary  to  calculate  them  exactly.  For  comparison,  I  have 
plotted  Dr.  Stoletow's  curve  and  deduced  the  results  given  in  the  Table, 
of  course  reducing  them  to  the  same  units  as  mine. 

It  will  be  observed  that  the  columns  headed  "maximum  of  mag- 
netism "  contain,  besides  the  maximum  magnetic  field,  two  columns 


MAGNETIC  PERMEABILITY  OF  IRON,  STEEL  AND  NICKEL        51 


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Normal. 
Magnetic. 
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52  HENRY  A.  EOWLAND 

giving  the  tension  of  the  lines  of  force  per  square  centimetre  and  square 
inch  of  section  of  the  lines.     These  have  been  deduced  from  the  formula 

given  by  Maxwell  '3  for  the  tension  per  square  metre,  which  is     2C 

&~ 

absolute  units  of  force. 
This  becomes 

24655^00000  kil°grammes  Per  S(luare  centim  >   I 

}•  ,  (12) 

173240000  Ibs.  per  square  inch, 

from  which  the  quantities  in  the  Table  were  calculated. 

It  is  seen  that  the  maximum  of  magnetism  of  ordinary  bar  iron  is 
about  175,000  times  the  unit  field,  or  177  Ibs.  on  the  square  inch,  and 
for  nickel  63,000  times,  or  22-9  Ibs.  on  the  square  inch.  For  pure  iron, 
however,  I  think  it  may  reach  180,000,  or  go  even  above  that.  It  is 
seen  that  one  of  the  Norway  rings  gave  a  very  high  result;  this  is 
explained  by  the  following  considerations.  All  the  iron  rings  were 
welded  except  this  one,  which  was  forged  solid  from  a  bar  2  inches 
wide  and  then  turned.  Even  the  purest  bar  iron  is  somewhat  fibrous; 
and  between  the  fibres  we  often  find  streaks  of  scale  lying  lengthwise 
in  the  bar  and  so  diminishing  the  section  somewhat  if  the  ring  be 
welded  from  the  bar;  when,  however,  it  is  forged  solid,  these  streaks 
are  thoroughly  disintegrated;  and  hence  we  find  a  higher  maximum 
of  magnetism  for  a  ring  of  this  kind,  and  one  approaching  to  that  of 
pure  iron.  But  a  ring  made  in  this  way  has  to  be  exposed  to  so  much 
heating  and  pounding  that  the  iron  is  rendered  unhomogeneous,  and  a 
tail  appears  to  the  curve  like  that  in  Table  III.  It  is  evident  that  this 
tail  must  always  show  itself  whenever  the  section  of  the  ring  is  not 
homogeneous  throughout. 

Hence  we  may  conclude  that  the  greatest  weight  which  can  be  sus- 
tained by  an  electromagnet  with  an  infinite  current  is,  for  good  but  not 
pure  iron,  354  Ibs.  per  square  inch  of  section,  and  for  nickel  46  Ibs. 

Joule 2*  has  made  many  experiments  on  the  maximum  sustaining- 
power  of  magnets,  and  has  collected  the  following  Table,  which  I  give 
complete,  except  that  I  have  replaced  the  result  with  his  large  magnet 
by  one  obtained  later. 

It  is  seen  that  these  are  all  below  my  estimate,  as  they  should  be. 

23 Treatise  on  Electricity  and  Magnetism,  vol.  ii,  p.  256. 
2*  Phil.  Mag.,  1851. 


MAGNETIC  PERMEABILITY  OF  IRON,  STEEL  AND  NICKEL         53 


For  comparison,  I  have  added  a  column  giving  the  values  of  Q  which 
would  give  the  sustaining-power  observed;  some  of  these  are  as  high 
as  any  I  have  actually  obtained,  thus  giving  an  experimental  proof  that 
my  estimate  of  354  Ibs.  cannot  be  far  from  correct,  and  illustrating 
the  beauty  of  the  absolute  system  of  electrical  measurement  by  which, 
from  the  simple  deflection  of  a  galvanometer-needle,  we  are  able  to 
predict  how  much  an  electromagnet  will  sustain  without  actually  trying 
the  experiment. 

TABLE  IX. 


Magnet  belonging  to 

Least  area  of 
section,  square 
inch. 

Weight 
sustained. 

Weight  sus- 
tained -r 
least  area. 

Q. 

f  1.  . 

10. 

2775 

277 

154700 

I  2.  . 

•196 

49 

250 

147000 

Mr.  Joule.  ^  * 

•0436 

12 

275 

154100 

j  4  

•0012 

•202 

162 

118300 

Mr.  Nesbit  

4-5 

1428 

317 

165500 

Prof.  Henry  

3-94 

750 

190 

128200 

Mr.  Sturgeon  

•196 

50 

255 

148500 

In  looking  over  the  columns  of  Table  VIII,  which  contain  the  values 
of  the  constants  in  the  formula,  we  see  how  futile  it  is  to  attempt  to 
give  any  fixed  value  to  the  permeability  of  iron  or  nickel;  and  we  also 
see  of  how  little  value  experiments  on  any  one  kind  of  iron  are.  Iron 
differs  as  much  in  magnetic  permeability  as  copper  does  in  electric 
conductivity. 

It  is  seen  that  in  the  three  cases  when  iron  bars  have  been  used,  the 
value  of  a  is  negative;  we  might  consider  this  to  be  a  general  law,  if  I 
did  not  possess  a  ring  which  also  gives  this  negative.  All  these  bars 
had  a  length  of  at  least  120  times  their  diameter. 

The  mathematical  theory  of  magnetism  has  always  been  considered 
one  of  the  most  difficult  of  subjects,  even  when,  as  heretofore,  fj.  is 
considered  to  be  a  constant;  but  now,  when  it  must  be  taken  as  a  func- 
tion of  the  magnetism,  the  difficulty  is  increased  many  fold.  There  are 
certain  cases,  however,  where  the  magnetism  of  the  body  is  uniform, 
which  will  not  be  affected. 

Troy,  June  2,  1873. 


(54) 


ON  THE  MAGNETIC  PEEMEABILITY  AND  MAXIMUM  OF 
MAGNETISM  OF  NICKEL  AND  COBALT 

[Philosophical  Magazine  [4],  XL  VIII,  321-340,  1874J 

Some  time  ago  a  paper  of  mine  on  the  magnetic  permeability  of  iron, 
steel,  and  nickel  was  published  in  the  Philosophical  Magazine  (August, 
1873);  and  the  present  paper  is  to  be  considered  as  a  continuation  of 
that  one.  But  before  proceeding  to  the  experimental  results,  I  should 
like  to  make  a  few  remarks  on  the  theory  of  the  subject.  The  mathe- 
matical theory  of  magnetism  and  electricity  is  at  present  developed  in 
two  radically  different  manners,  although  the  results  of  both  methods  of 
treatment  are  in  entire  agreement  with  experiment  as  far  as  we  can 
at  present  see.  The  first  is  the  German  method;  and  the  second  is 
Faraday's,  or  the  English  method.  When  two  magnets  are  placed  near 
each  other,  we  observe  that  there  is  a  mutual  force  of  attraction  or 
repulsion  between  them.  Now,  according  to  the  German  philosophers, 
this  action  takes  place  at  a  distance  without  the  aid  of  any  intervening 
medium:  they  know  that  the  action  takes  place,  and  they  know  the 
laws  of  that  action;  but  there  they  rest  content,  and  seek  not  to  find 
how  the  force  traverses  the  space  between  the  bodies.  The  English 
philosophers,  however,  led  by  Newton,  and  preeminently  by  Faraday, 
have  seen  the  absurdity  of  the  proposition  that  two  bodies  can  act  upon 
each  other  across  a  perfectly  vacant  space,  and  have  attempted  to  ex- 
plain the  action  by  some  medium  through  which  the  force  can  be  trans- 
mitted along  what  Faraday  has  called  "  lines  of  force." 

These  differences  have  given  rise  to  two  different  ways  of  looking 
upon  magnetic  induction.  Thus  if  we  place  an  electromagnet  neat"  a 
compass-needle,  the  Germans  would  say  that  the  action  was  due  in  part 
to  two  causes — the  attraction  of  the  coil,  and  the  magnetism  induced  in 
the  iron  by  the  coil.  Those  who  hold  Faraday's  theory,  on  the  other 
hand,  would  consider  the  substance  in  the  helix  as  merely  "  conduct- 
ing "  the  lines  of  force,  so  that  no  action  would  be  exerted  directly  on 
the  compass-needle  by  the  coil,  but  the  latter  would  only  affect  it  in 
virtue  of  the  lines  of  force  passing  along  its  interior,  and  so  there  could 
be  no  attraction  in  a  perfectly  vacant  space. 


MAGNETIC  PEEMEABILITY  OF  NICKEL  AND  COBALT  57 

According  to  the  first  theory,  the  magnetization  of  the  iron  is  repre- 
sented by  the  excess  of  the  action  of  the  electromagnet  over  that  of  the 
coil  alone;  while  by  the  second,  when  the  coil  ia  very  close  around  the 
iron,  the  whole  action  is  due  to  the  magnetization  of  the  iron.  The 
natural  unit  of  magnetism  to  be  used  in  the  first  theory  is  that  quantity 
which  will  repel  an  equal  quantity  at  a  unit's  distance  with  a  unit  of 
force;  on  the  second  it  is  the  number  of  lines  of  force  which  pass 
through  a  unit  of  surface  when  that  surface  is  placed  in  a  unit  field 
perpendicular  to  the  lines  of  force.  The  first  unit  is  4?r  times  the 
second.  Now  when  a  magnetic  force  of  intensity  &1  acts  upon  a  mag- 
netic substance,  we  shall  have  33  =  £+4-$,  in  which  33  is  the  mag- 
netization of  the  substance  according  to  Faraday's  theory,  and  is  what 
I  formerly  called  the  magnetic  field,  but  which  I  shall  hereafter  call, 
after  Professor  Maxwell,  the  magnetic  induction.  %  is  the  intensity 
of  magnetization  according  to  the  German  theory,  expressed  in  terms 
of  the  magnetic  moment  of  the  unit  of  volume.  Now,  when  the  sub- 
stance is  in  the  shape  of  an  infinitely  long  rod  placed  in  a  magnetic  field 

01 

parallel  to  the  lines  of  force,  the  ratio  2  ==//  is  called  the  magnetic 

0 

permeability  of  the  substance,  and  the  ratio  £  =  K  is  Neumann's  co- 
efficient of  magnetization  by  induction.  Now  experiment  shows  that 
for  large  values  of  Q  the  values  of  both  n  and  K  decrease,  so  that 
we  may  expect  either  $  or  both  33  and  %  to  attain  a  maximum  value. 
In  my  former  paper  I  assumed  that  33  as  well  as  $  attain  a  maxi- 
mum; but  on  further  considering  the  subject  I  see  that  we  have  no  data 
for  determining  which  it  is  at  present.  If  it  were  possible  for  53  to 
attain  a  maximum  value  so  that  //  should  approach  to  0,  K  would  be 
negative,  and  the  substance  would  then  become  diamagnetic  for  very 
high  magnetizing  forces.2  This  is  not  contrary  to  observation;  for  at 
present  we  lack  the  means  of  producing  a  sufficiently  intense  magnetic 
field  to  test  this  experimentally,  at  least  in  the  case  of  iron.  To  pro- 
duce this  effect  at  ordinary  temperatures,  we  must  have  a  magnetic  field 
greater  than  the  following — for  iron  175,000,  for  nickel  63,500,  and  for 

1 1  shall  hereafter  in  all  my  papers  use  the  notation  as  given  in  Professor  Maxwell's 
'  Treatise  on  Electricity  and  Magnetism ;'  for  comparison  with  my  former  paper  I 
give  the  following: 

33  in  this  paper  =  Q  in  former  one. 

6  "  =  4;rM  " 

3  "  =£-M      « 

'See  Maxwell's  'Treatise  on  Electricity  and  Magnetism,'  art.  844. — J.  C.  M. 


58  HENEY  A.  ROWLAND 

cobalt  about  100,000  (?).  These  quantities  are  entirely  beyond  our 
reach  at  present,  at  least  with  any  arrangement  of  solenoids.  Thus, 
if  we  had  a  helix  6  inches  in  diameter  and  3  feet  long  with  an  aperture 
of  1  inch  diameter  in  the  centre,  a  rough  calculation  shows  that,  with 
a  battery  of  350  large  Bunsen  cells,  the  magnetic  field  in  the  interior 
would  only  be  15,000  or  20,000  when  the  coils  were  arranged  for*the 
best  effect.  We  might  obtain  a  field  of  greater  intensity  by  means  of 
electromagnets,  and  one  which  might  be  sufficient  for  nickel;  but  we 
cannot  be  certain  of  its  amount,  as  I  know  of  no  measurement  of  the 
field  produced  in  this  way.  But  our  principal  hope  lies  in  heating  some 
body  and  then  subjecting  it  to  a  very  intense  magnetizing-f  orce ;  for  I 
have  recently  found,  and  will  show  presently,  that  the  maximum  of 
magnetization  of  nickel  and  iron  decreases  as  the  temperature  rises,  at 
least  for  the  two  temperatures  0°  C.  and  220°  C.  I  am  aware  that  iron 
and  nickel  have  been  proved  to  retain  their  magnetic  properties  at  high 
temperatures,  but  whether  they  were  in  a  field  of  sufficient  intensity  at 
the  time  cannot  be  determined.  The  experiment  is  at  least  worth  try- 
ing by  some  one  who  has  a  magnet  of  great  power,  and  who  will  take 
the  trouble  to  measure  the  magnetic  field  of  the  magnet  at  the  point 
where  the  heated  nickel  is  placed.  This  could  best  be  done  by  a  small 
coil  of  wire,  as  used  by  Verdet. 

But  even  if  it  should  be  proved  that  33  does  not  attain  a  maximum, 
but  only  $,  it  could  still  be  explained  by  Faraday's  theory;  for  we 
should  simply  have  to  suppose  that  the  magnetic  induction  33  was 
composed  of  two  parts — the  first  part,  4 Trig,  being  due  to  the  magnetic 
atoms  alone,  and  the  second,  £>,  to  those  lines  of  force  which  traversed 
the  aether  between  the  atoms.  To  determine  whether  either  of  these 
quantities  has  a  maximum  value  can  probably  never  be  done  by  experi- 
ment; we  may  be  able  to  approach  the  point  very  nearly,  but  can  never 
arrive  at  it,  seeing  that  we  should  need  an  infinite  magnetizing-force  to 
do  so.  Hence  its  existence  and  magnitude  must  always  be  inferred 
from  the  experiments  by  some  such  process  as  was  used  in  my  first 
paper,  where  the  curve  of  permeability  was  continued  beyond  the  point 
to  which  the  experiments  were  carried.  Neither  does  experiment  up 
to  the  present  time  furnish  any  clue  as  to  whether  it  is  33  or  $  which 
attains  a  maximum. 

As  the  matter  is  in  this  undecided  state,  I  shall  hereafter  in  most 
cases  calculate  both  $  and  *  as  well  as  33  and  //,  as  I  am  willing  to  admit 
that  $  may  have  a  physical  significance  as  well  as  33,  even  on  Faraday's 
theory. 


MAGNETIC  PEEMEABILITY  OF  NICKEL  AND  COBALT  59 

There  is  a  difficulty  in  obtaining  a  good  series  of  experiments  on 
nickel  and  cobalt  which  does  not  exist  in  the  case  of  iron.  It  is  prin- 
cipally Giving  to  the  great  change  in  magnetic  permeability  of  these 
substances  by  heat,  and  also  to  their  small  permeability.  To  obtain 
sufficient  magnetizing-force  to  trace  out  the  curve  of  permeability  to  a 
reasonable  distance,  we  require  at  least  two  layers  of  wire  on  the  rings, 
and  have  to  send  through  that  wire  a  very  strong  current.  In  this  way 
great  heat  is  developed;  and  on  account  of  there  being  two  layers  of 
wire  it  cannot  escape;  and  the  ring  being  thus  heated,  its  permeability 
is  changed.  So  much  is  this  the  case,  that  when  the  rings  are  in  the 
air,  and  the  strongest  current  circulating,  the  silk  is  soon  burned  off  the 
wire;  and  to  obviate  this  I  have  in  these  experiments  always  immersed 
the  rings  in  some  non-conducting  liquid,  such  as  alcohol  for  low  tem- 
peratures and  melted  paraffin  for  high  temperatures,  the  rings  being 
suspended  midway  in  the  liquid  to  allow  free  circulation.  But  I  have 
now  reason  to  suspect  the  efficacy  of  this  arrangement,  especially  in  the 
case  of  the  paraffin.  The  experiments  described  in  this  paper  were 
made  at  such  odd  times  as  I  could  command,  and  the  first  ones  were  not 
thoroughly  discussed  until  the  series  was  almost  completed;  hence  1 
have  not  been  so  careful  to  guard  against  this  error  as  I  shall  be  in  the 
future.  This  can  be  done  in  the  following  manner — namely,  by  letting 
the  current  pass  through  the  ring  for  only  a  shirt  time.  But  there  is  a 
difficulty  in  this  method,  because  if  the  current  is  stopped  the  battery 
will  recruit,  and  the  moment  it  is  joined  to  the  ring  a  large  and  rapidly 
decreasing  current  will  pass  which  it  is  impossible  to  measure  accu- 
rately. I  have,  however,  devised  the  following  method,  which  I  will 
apply  in  future  experiments.  It  is  to  introduce  into  the  circuit  between 
the  tangent-galvanometer  and  the  ring  a  current-changer,  by  which  the 
current  can  be  switched  off  from  the  ring  into  another  wire  of  the  same 
resistance,  so  that  the  current  from  the  battery  shall  always  be  con- 
stant. Just  before  making  an  observation  the  current  is  turned  back 
into  the  ring,  a  reading  is  taken  of  the  tangent-galvanometer  by  an 
assistant,  and  immediately  afterward  the  current  is  reversed  and  the 
reading  taken  for  the  induced  current;  the  tangent-galvanometer  is 
then  again  read  with  the  needle  on  the  other  side  of  the  zero-point. 
The  pressure  of  outside  duties  at  present  precludes  me  from  putting  this 
in  practice.  But  the  results  which  I  have  obtained,  though  probably 
influenced  in  the  higher  magnetizing-forces  by  this  heating,  are  still 
so  novel  that  they  must  possess  value  notwithstanding  this  defect;  for 
they  contain  the  only  experiments  yet  made  on  the  permeability  of 


60  HENRY  A.  KOWLAXD 

cobalt  at  ordinary  temperatures,  and  of  iron,  nickel,  and  cobalt  at  high 
temperatures. 

The  rings  of  nickel  and  cobalt  which  I  have  used  in  the  experiments 
of  this  paper  were  all  turned  from  buttons  of  metal  obtained  by  fusing 
under  glass  in  a  French  crucible,  it  having  been  found  that  a  Hessian 
crucible  was  very  much  attacked  by  the  metal.  The  crucibles  were  in 
the  fire  three  or  four  hours,  and  when  taken  out  were  very  soft  from 
the  intense  heat.  As  soon  as  taken  out,  the  outside  of  the  crucible  was 
wet  with  water,  so  as  to  cool  the  metal  rapidly  and  prevent  crystalliza- 
tion; but  even  then  the  cooling  inside  went  on  very  slowly.  As  the 
physical  and  chemical  properties  of  these  metals  exercise  great  influence 
on  their  magnetic  properties,  I  will  give  them  briefly.  A  piece  of  nickel 
before  melting  was  dissolved  in  HC1;  it  gave  no  precipitate  with  H2S , 
and  there  were  no  indications  of  either  iron  or  cobalt.  A  solution  of 
the  cobalt  gave  no  precipitate  with  H2S,  but  contained  small  traces  of 
iron  and  nickel.  After  melting  the  metals  no  tests  have  been  made  up 
to  the  present  time;  but  it  is  to  be  expected  that  the  metals  absorbed 
some  impurities  from  the  crucibles.  They  probably  did  not  contain 
any  carbon.  One  button  of  each  metal  was  obtained,  from  each  of 
which  two  rings  were  turned.  The  cobalt  was  quite  hard,  but  turned 
well  in  the  lathe,  long  shavings  of  metal  coming  off  and  leaving  the 
metal  beautifully  polished.  The  metal  was  slightly  malleable,  but  fin- 
ally broke  with  a  fine  granular  fracture.  The  rings  when  made  were 
slightly  sonorous  when  struck;  and  the  color  was  of  a  brilliant  white 
slightly  inclined  to  steel-color,  but  a  little  more  red  than  steel.  The 
nickel  was  about  as  hard. as  wrought  iron,  and  was  tough  and  difficult 
to  turn  in  the  lathe,  a  constant  application  of  oil  being  necessary,  and 
the  turned  surface  was  left  very  rough;  the  metal  was  quite  malleable, 
but  would  become  hard,  and  finally  fly  apart  when  pounded  down  thin  if 
not  annealed.  When  the  rings  were  struck,  they  gave  a  dead  sound  as 
if  made  of  copper.  In  both  cases  the  specific  gravity  was  considerably 
higher  than  that  generally  given  for  cast  metal ;  but  it  may  be  that  the 
metal  to  which  they  refer  contained  carbon,  in  which  case  it  would  be 
more  easily  melted.  There  is  great  liability  to  error  in  taking  the 
specific  gravity  of  these  metals,  because  they  contract  so  much  on  cool- 
ing, and  unless  this  is  carried  on  rapidly  crystals  may  form,  between 
which,  as  the  metal  contracts,  vacant  spaces  may  be  left.  As  the 
specific  gravity  of  my  rings  approaches  to  that  of  the  pure  metals  pre- 
cipitated by  hydrogen,  I  consider  it  evidence  of  their  purity.  The 
dimensions  of  the  rings  and  their  other  constants  are  as  follows:  — 


VNI\ 


MAGNETIC  PERMEABILITY  OF  XICKEL  AND  COBALT 


61 


King. 

Weight  in 
vacuo,  in 
grammes. 

Loss  in  water 
at  4°  C.,in 
grammes. 

Specific 
gravity. 

Mean  dia- 
meter, in 
centimetres. 

Nickel   No   I  

21-823 

2-4560 

8-886 

3-28 

Nickel   No   II      

8-887 

Cobalt   No   I        

10-011 

1  •  1435 

8-7553 

2-48 

Cobalt   No.  II  

4-681 

•5346 

8  •  7550 

1-81 

Ring. 

Mean  circum- 
ference, in 
centimetres. 

Number  of 
coils  of  wire 
on  ring. 

Coils  per 
metre  of  cir- 
cumference. 

Area  of  sec- 
tion, in  square 
centimetres. 

Nickel   No   I        

10  •  304 

318 

3086 

•2384 

Nickel'  No.  II. 

Cobalt,  No.  I  

7-791 

243 

3119 

•1467 

Cobalt   No.  II  

5-686 

158 

2779 

•09403 

Up  to  the  present  time  cnly  the  rings  whose  dimensions  are  given 
have  been  used. 

The  following  Tables  from  the  nickel  ring  No.  I  leave  little  to  be 
desired  in  point  of  regularity,  and  confirm  the  fact  proved  in  my  first 
paper,  that  the  laws  deduced  for  iron  hold  also  for  nickel,  and  also 
confirm  the  value  given  in  my  other  paper  for  the  maximum  value  of 
magnetization  of  nickel.  But  the  most  important  thing  that  they  show 
is  the  effect  of  heat  upon  the  magnetization  of  nickel;  and  Table  III 
contains  the  first  numerical  data  yet  obtained  on  the  effect  of  heat  on 
the  magnetic  properties  of  any  substance. 

As  all  the  rings  were  wound  with  two  layers  of  wire,  a  slight  correc- 
tion was  made  in  the  value  of  S)  for  the  lines  of  inductive  force  which 
passed  through  the  air  and  not  through  the  metal.  In  all  the  experi- 
ments of  this  paper  greater  care  was  used  to  obtain  T  than  in  the  first 
paper.  Each  value  of  £>,  33,  and  T  is  the  mean  of  four  readings.  In 
all  the  Tables  I  have  left  the  order  of  the  observations  the  same  as  that 
in  which  they  were  made,  and  have  also  put  down  the  date,  as  I  now 
have  reason  to  suspect  that  the  leaving  of  a  ring  in  the  magnetized  state 
in  which  it  is  after  an  experiment  will  in  time  affect  its  properties  to  a 
small  extent.  Let  me  here  remark  that  the  time  necessary  to  simply 
make  the  observations  is  only  a  Very  small  fraction  of  that  required  to 
prepare  for  them  and  to  afterwards  discuss  them.  And  this,  with  the 
small  amount  of  time  at  my  disposal,  will  account  for  the  late  day  at 
which  I  publish  my  results. 

The  following  is  the  notation  used,  the  measurements  being  made  on 
that  absolute  system  in  which  the  metre,  gramme,  and  second  are  the 
fundamental  units. 


62 


HENRY  A.  ROWLAND 


$  is  the  magnetizing-force  acting  on  the  metal. 

23  is  the  magnetic  induction  within  the  metal  (see  Maxwell's  '  Trea- 
tise on  Electricity  and  Magnetism/  arts.  400,  592,  and  604). 

«i 
fj.  is  the  magnetic  permeability  of  the  metal  s=_=4*«-H. 

s? 
T  is  the  portion  of  23  which  disappears  when  the  current  is  broken. 

P  is  the  portion  of  33  which  remains  when  the  current  is  broken. 

qa a 

$  is  the  intensity  of  magnetization  =  — - — «• 

ow 

ic  is  Neumann's  coefficient  of  induced  magnetization  =  ^. 

*Q 

TABLE  I. 

CAST  NICKEL,  NOKMAL,  AT  15°  C. 
Experiments  made  November  29,  1873. 


a 

S3 

Ob- 
served. 

Calcu- 
lated. 

Error. 

T. 

P. 

3. 

K. 

Ob- 
served. 

K. 

Calcu- 
lated. 

Error. 

12-84 

675 

52-6 

46-4 

—6-2 

52-7 

4-10 

3  •  65 

—  -45 

26-85 

2169 

80-8 

80-6 

.3 

1263 

906 

170-5 

6-35 

6-27 

08 

45  •  14 

7451 

165-1 

166-8 

1-7 

2894 

4557 

589-3 

13-06 

13-08 

•02 

56-12 

11140 

198-5 

199-1 

•6 

3788 

7352 

882-0 

15-72 

15-70 

—  •02 

70-78 

15410 

217-8 

217-5 

—    -3 

5018 

10392 

1221 

17-25 

17-21 

04 

77-52 

17100 

220-6 

220-6 

•0 

5454 

11646 

1355 

17-47 

17-47 

0 

90-76 

20180 

222-3 

222-0 

-   -3 

6483 

13697 

1599 

17-61 

17-60 

—  •01 

115-4 

25170 

218-2 

214-3 

—3-9 

8313 

16857 

1994 

17-28 

16-98 

—  •30 

139-4 

28540 

204-7 

204-3 

—   -4 

10100 

18440 

2260 

16-21 

16-18 

—  .03 

172-9 

32460 

187-8 

186-6 

—1-2 

12530 

19930 

2569 

14-86 

14-93 

•07 

195-3 

34630 

177-3 

179-1 

1-8 

13320 

21310 

2740 

14-03 

14-12 

•09 

229-5 

37340 

162-8 

165-5 

2-7 

15720 

21620 

2953 

12-87 

13-02 

•15 

275-9 

40860 

148-1 

146-3 

—1-8 

17960 

22900 

3230 

11-71 

11-46 

—  •25 

415-2 

46470 

111-9 

112-8 

•9 

22560 

23910 

3665 

8-82 

8-77 

05 

727-0 

52690 

72-5 

72-8 

•3 

28020 

24670 

4135 

5-69 

5-64 

—  •05 

1042 

55680 

53-4 

52-8 

—   -6 

30680 

25000 

4344 

4-17 

4-17 

0 

63420 

0 

4940 

0 

ooo    • 

=  222  sin 


/"= 


359 


«=17  6  sin 


28 


TABLE  II. 

CAST  NICKEL,  MAGNETIC,  AT  12°  C. 
Experiments  made  December  6,  1873. 


6. 

to. 

M. 

T. 

P. 

3- 

K. 

23-25 

1245 

53-55 

97-2 

4-18 

47-69 

7786 

163-3 

3095 

4691 

615-8 

12-91 

57-78 

11460 

198-3 

3740 

7720 

907-3 

15-70 

73-43 

16040 

218-5 

5032 

11008 

1270-6 

17-30 

88-23 

19790 

224-3 

6554 

13236 

1568 

17-77 

107-3 

23530 

219-2 

7620 

15910 

1864 

17-36 

153-8 

30160 

196-1 

10940 

19220 

2388 

15-52 

206-3 

35880 

174-0 

14030 

21850 

2839 

13-76 

296-4 

41310 

139-4 

18390 

22920 

3264 

11-01 

421-8 

46520 

110-3 

22520 

24000 

3668 

8-70 

MAGNETIC  PERMEABILITY  OF  NICKEL  AND  COBALT 


63 


TABLE  III. 

CAST  NICKEL,  MAGNETIC,  AT  220°  C. 
Experiments  made  December  6,  1873. 


«. 

as. 

n- 

T. 

P. 

3- 

K. 

22-60 

4502 

199-2 

2671 

1831 

356-4 

15-77 

45-06 

14000 

310-8 

5470 

8530 

1111 

24-65 

52-96 

16660 

314-6 

6350 

10310 

1322 

24-96 

67-42 

20300 

301-1 

7722 

12578 

1602 

23-88 

80-69 

22540 

279-3 

8914 

13626 

1787 

22-15 

106-4 

26420 

248-3 

11140 

15280 

2094 

19-68 

150-8 

30740 

203-8 

14040 

16700 

2434 

16-14 

191-0 

33530 

175-6 

15940 

17590 

2653 

13-89 

294-8 

38300 

129-9 

20240 

18060     !     3024 

10-26 

553-6 

42630 

77-0 

24360 

18270         3348              6-05 

789-8 

43900 

55-6 

26060 

17840 

3431 

4-345 

Experiments  made  December  10,  1873. 

13-00 

1537 

118-2 

109-2 

9-33 

22-37 

4262 

190-5 

337-4 

15-08 

25-15 

5337 

212-2 

422-7 

16-81 

33-19 

94S6 

285-8 

4055 

5431 

752-3 

22-15 

43-28 

13570 

313-6 

5357 

8213 

1076 

24-88 

In  Table  I  are  given  the  results  for  nickel  at  about  15°  C.,  together 
with  the  values  of  //  and  <  calculated  from  the  formulae  given  below  the 
Table.  We  see  that  the  coincidence  is  almost  perfect  in  both  cases, 
which  thus  shows  that  the  formula  which  we  have  hitherto  used  for  X 
and  ;j.  can  also  be  applied  to  «,  at  least  within  the  limit  of  experiments 
hitherto  made,  although  it  must  at  last  depart  from  one  or  the  other 
of  the  curves.  The  greatest  relative  error  is  seen  to  be  in  the  first 
line,  where  £)  is  small:  this  does  not  indicate  any  departure  from  the 
curve,  but  is  only  due  to  the  too  small  deflections  Of  the  galvanometer; 
and  the  error  indicates  that  of  only  a  small  fraction  of  a  division  at  the 
galvanometer. 

In  the  calculation  of  /J-  and  K  a  method  was  used  which  may  be  of 
use  to  others  in  like  circumstances,  who  have  to  calculate  a  large  num- 
ber of  values  of  one  variable  from  a  function  which  cannot  be  solved 
with  reference  to  that  variable,  but  can  be  solved  with  reference  to  the 
other.  Thus  we  have 


which  can  be  solved  with  reference  to  S3  but  not  to  //;  for  we  have 


(1) 


(2) 


64  HENEY  A.  ROWLAND 

Suppose  we  have  values  of  33,  and  wish  to  find  the  corresponding  values 
of  .//.  We  first  calculate  a  few  values  of  33  from  (2)  so  that  we  can  plot 
the  curve  connecting  33  and  [JL.  We  then  from  the  plot  select  a  value 
of  p  which  we  shall  call  //,  as  near  the  proper  value  as  possible,  and 
calculate  the  corresponding  value  of  33,  which  we  shall  call  33'.  Our 
problem  then  is,  knowing  33'  and  //,  to  find  the  value  of  /JL  corresponding 
to  33  when  this  is  nearly  equal  to  33'.  Let  33'  receive  a  small  increment 
J33',  so  that  33  =  33'  +  J33'  ;  then  we  have,  from  Taylor's  theorem,  since 
'  +  J33')  and  fjf= 


Remembering  that  the  constants  in  (1)  refer  to  degrees  of  arc  and 
not  to  the  absolute  value  of  the  arc,  we  have 


&c, 


which  is  in  the  most  convenient  form  for  calculation  by  means  of 
Barlow's  Tables  of  squares,  &c.,  and  is  very  easy  to  apply,  being  far 
easier  than  the  method  of  successive  approximation. 

On  comparing  the  magnetic  curve  Table  II  with  the  normal  curve 
Table  I,  we  see  that  the  magnetic  curve  of  nickel  bears  the  same  rela- 
tion to  the  normal  curve  as  we  have  already  found  for  iron;  that  is, 
the  magnetic  curve  falls  below  the  normal  curve  for  all  points  before 
the  vertex,  but  afterwards  the  two  coincide. 

Hence  we  see  that  at  ordinary  temperatures  the  magnetic  properties 
of  nickel  are  a  complete  reproduction  of  those  of  iron  on  a  smaller  scale. 
But  when  we  come  to  study  the  effect  of  temperature  we  shall  find  a 
remarkable  difference,  and  shall  find  nickel  to  be  much  more  susceptible 
than  iron  to  the  influence  of  heat. 

In  Table  III  we  have  experiments  on  the  permeability  of  nickel  at 
a  high  temperature,  the  ring  being  maintained  at  220°  C.  by  being 
placed  in  a  bath  of  melted  paraffin:  in  this  bath  the  silk  covering  of 
the  wire  remained  quite  perfect,  but  after  many  hours  became  some- 
what weak.  After  completing  the  experiments  on  this  and  the  cobalt 
rings,  on  unwinding  some  of  them  I  found  the  outside  layer  quite  per- 
fect; but,  especially  in  the  smallest  ring,  the  silk  on  the  inside  layer 
was  much  weaker,  although  the  insulation  was  still  perfect  when  the 
wire  was  in  place.  I  can  only  account  for  this  by  the  electric  current 
generating  heat  in  the  wire,  which  was  unable  to  pass  outward  because 


MAGNETIC  PERMEABILITY  OF  NICKEL  AND  COBALT 


65 


of  the  outside  layer  and  also  of  the  pieces  of  paper  which  were  used  to 
separate  the  layers  of  wire;  hence  the  ring  at  high  magnetizing-powers 
must  have  been  at  a  somewhat  higher  temperature  than  the  bath,  to  an 
amount  which  it  is  impossible  to  estimate.  It  is  probable  that  it  was 
not  very  great,  however;  for  at  this  high  temperature  continued  for 
hours  it  requires  but  little  increase  of  heat  to  finally  destroy  the  silk. 
We  can,  however,  tell  the  direction  of  the  error. 

We  see,  on  comparing  Tables  I  and  II  with  Table  III,  the  great 
effect  of  heat  on  the  magnetic  properties  of  nickel.  We  see  that  for 
low  magnetization  the  permeability  is  greatly  increased,  which  is  just 
opposite  to  what  we  might  expect;  but  on  plotting  the  curve  we  also 
notice  the  equally  remarkable  fact,  that  the  maximum  of  magnetization 


ZO.OOO  40.000 


eo.ooo 


1.  Curve  at  15°  C. 


2.  Curve  at  220°  C. 


is  decreased  from  33=  63,400  or  3  =  4940  to  33=  49,000  or  $  =  3800. 
This  curious  result  is  shown  in  the  annexed  figure,  where  we  see  that 
for  low  magnetizing-f orces  p  is  increased  to  about  three  or  four  times 
its  value  at  15°  C.,  and  the  maximum  value  of  //  is  increased  from  222 
to  315.  When  33  has  a  value  of  32,000,  p  is  not  affected  by  this  change 
of  temperature,  seeing  that  the  two  curves  coincide;  but  above  that 
point  fji  is  less  at  220°  C.  than  at  15°  C.  In  other  words,  if  nickel  is 
heated  from  15°  C.  to  220°  C.,  the  magnetization  of  nickel  will  increase  if 
the  magnetizing-f orce  is  small,  but  will  decrease  if  it  is  large.  It  is  impos- 
sible to  say  at  present  whether  increase  of  temperature  above  220°  will 
always  produce  effects  in  the  same  direction  as  below  it  or  not. 

These  remarkable  effects  of  heat,  it  seems  to  me,  will,  when  followed 

out,  lead  to  the  discovery  of  most  important  connections  between  heat 

and  magnetism,  and  will  finally  result  in  giving  us  much  more  light 

upon  the  nature  of  heat  and  magnetism,  and  that  equally  important 

5 


66  HENRY  A.  EOWLAND 

question  of  what  is  a  molecule.  To  accomplish  this  we  must  obtain  a 
series  of  curves  for  the  same  ring  between  as  wide  limits  of  temperature 
as  possible.  We  must  then  plot  our  results  in  a  suitable  manner;  and 
from  the  curves  thus  formed  we  can  find  what  would  probably  happen 
if  the  temperature  were  lowered  to  the  absolute  zero,  or  were  increased 
to  the  point  at  which  nickel  is  said  to  lose  its  magnetism.  In  such 
inquiries  as  these  the  graphical  method  is  almost  invaluable,  and  little 
can  be  expected  without  its  aid. 

In  applying  the  formula  to  this  curve,  we  do  not  find  so  good  an 
agreement  as  at  the  lower  temperature.  I  do  not  consider  this  conclu- 
sive that  the  formula  will  not  agree  with  observation  at  this  tempera- 
ture; for  I  have  noticed  that  the  curves  of  different  specimens  of  iron 
and  nickel  seem  to  vary  within  a  minute  range,  not  only  in  their 
elements  but  also  in  their  form.  This  might  perhaps  be  accounted  for 
by  some  small  want  of  homogeneity,  as  in  the  case  of  burning  in  iron 
and  nickel;  but  at  present  the  fact  remains  without  an  explanation. 
But  the  amount  of  the  deviation  is  in  all  cases  very  small  when  all  the 
precautions  are  taken  to  insure  good  results.  The  nature  of  the  devia- 
tion is  in  this  case  as  follows:  when  the  constants  in  the  formula  are 
chosen  to  agree  with  the  observed  curve  at  the  vertex  and  at  the  two 
ends,  then  the  observed  curve  falls  slightly  below  the  curve  of  the 
formula  at  nearly  all  other  points.  In  a  curve  plotted  about  5  inches 
high  and  broad,  the  greatest  distance  between  the  two  curves  is  only 
about  -^  of  an  inch,  and  could  be  much  reduced  by  changing  the  con- 
stants. For  the  benefit  of  those  who  wish  to  study  this  deviation,  I 
have  calculated  the  following  values,  which  will  give  the  curve  touching 
the  vertex  and  the  two  ends  of  the  observed  curve  of  Table  III.  They 
are  to  be  used  by  plotting  in  connection  with  that  Table. 


K. 

3. 

0 

—140 

3802 

12.75 

205 

2833 

18-75 

455 

2269 

22-5 

703 

1835 

25 

1206 

3  +  25/C  +  140 


I  have  not  as  yet  obtained  a  complete  curve  of  iron  at  a  high  temper- 
ature; but  as  far  as  I  have  tried,  it  does  not  seem  to  be  affected  much, 
at  least  for  high  magnetizing-powers.  I  have,  however,  found  that  the 
maximum  of  magnetization  of  iron  decreases  about  2  per  cent  by  a 


MAGNETIC  PEEMEABILITY  OF  NICKEL  AND  COBALT 


67 


rise  of  temperature  from  15°  C.  to  222°  C.,  while  that  of  nickel  de- 
creases 22-7  per  cent. 

The  experiments  which  1  have  made  with  cobalt  do  not  seem  to  be 
so  satisfactory  as  those  made  with  nickel  and  iron.  There  are  some 
things  about  them  which  I  cannot  yet  explain;  but  as  they  are  the  only 
exact  experiments  yet  made  on  cobalt,  they  must  possess  at  least  a 
transient  value.  The  difficulties  of  getting  a  good  cobalt-curve  are. 
manifold,  and  are  due  to  the  following  properties — (1)  its  small  permea- 
bility, (2)  its  sensitiveness  to  temperature,  and  (3)  its  property  of  having 
its  permeability  increased  by  rise  of  temperature  at  all  magnetizing- 
powers  within  the  limits  of  experiment.  The  following  are  the  results 

with  No.  I : — 

TABLE  IV. 

CAST  COBALT,  NORMAL,  AT  5°  C. 
Experiments  made  November  27,  1873. 


fi. 

8. 

M. 

T. 

P. 

3- 

K. 

Ob- 
served. 

K. 

Calcu- 
lated. 

Error. 

49-33 

4303 

87-24 

3702 

601 

338-5 

6-86 

6-75 

—  •11 

58-83 

5608 

95-32 

4526 

1082 

441-6 

7-51 

7-44 

—  07 

76-47 

8409 

109-95 

6175 

2234 

663-1 

8-67 

8-79 

•12 

93-15 

11623 

124-8 

7826 

3797 

917-5 

9-85 

9-81 

04 

113-0 

14993 

132-7 

9805 

5188 

1193-1 

10-48 

10-44 

04 

129-3 

17439 

134-9 

10580 

6859 

1387-8 

10-66 

10-72 

•06 

159-4 

22309 

140-0 

14090 

8219 

1775-3 

11-06 

11-00 

06 

189-0 

26769 

141-6 

16260 

10509 

2130-3 

11-19 

10-97 

22 

219-6 

30580 

139-3 

18200 

12380 

2433-5 

11-01 

10-83 

—  •18 

264-7 

35525 

134-2 

21120 

14405 

2827-0 

10-60 

10-50 

—  •10 

351-1 

43421 

123-7 

25670 

17751 

3455-0 

9-76 

9-73 

—  •03 

400-0 

46640 

116-6 

27830 

18810 

3711-5 

9-20 

9-34 

•14 

552-1 

55410 

100-4 

34090 

21320 

4409-0 

7-91 

8-16 

•25 

732-1 

63400 

86-6 

39850 

23550 

5045-0 

6-81 

6-93 

•12 

999-8 

71800 

71-8 

47310 

24490 

5714-0 

5-63 

5-55 

08 

1471 

80770 

54-9 

55870 

24900 

6430-0 

4-29 

3-98 

—  •31 

8160 

0 

c* +190* +  120 

... — -|i  ain  *y « 

46 

TABLE  V. 

CAST  COBALT,  MAGNETIC,  AT  — 5°  C. 
Experiments  made  November  28,  1873. 


«. 

93. 

M. 

T. 

P. 

3- 

K. 

48-47 

3702 

76-37 

3287 

415 

290-8 

6-00 

76-74 

7254 

94-54 

5760 

1494 

571-1 

7-44 

112-8 

14370 

127-5 

9388 

4982 

1134-5 

10-06 

167-6 

24130 

144-0     14490     9640   1907 

11-38 

264-2 

35860 

135  •  7 

20420 

15440   2833 

10-72 

539-9 

53940 

99-91 

33010 

20930   4249 

7-87 

1473      80760 

54-84 

55920 

24840 

6310 

4-28 

i 

G8 


HENRY  A.  ROWLAND 


TABLE  VI. 

CAST  COBALT,  MAGNETIC,  AT  230°  C. 
Experiments  made  February  3,  1874. 


ft. 

S3. 

M. 

T. 

P. 

3- 

K. 

13-34 

1357 

101-8 

1165 

192 

107 

8-02 

25-67 

2916 

113-6 

2662 

254 

230 

8-96 

38-55 

4940 

128-2 

4397 

543 

390 

10-12 

55-56 

9400 

169-1 

7440 

I960 

743-5 

13-38 

75-16 

15800 

210-2 

10050 

5750 

1143 

16-65 

101-4 

23920 

235-9 

14260 

9660 

1895 

18-70 

132-7 

31260 

235-5 

17710 

13550 

2475 

18-66 

172-9 

38060 

220-2 

21820 

16240 

3015 

17-44 

281-8 

52520 

186-4 

31160 

21360 

4174 

14-76 

393-6 

63430 

161-2 

39070 

24360 

5039 

12-75 

702-9 

82070 

117-0 

54920 

27150 

6515 

9-27 

989-3 

95600 

96-63 

66750 

28850 

7584 

7-67 

1282 

106200 

82-87 

75820 

30380 

8422 

6-57 

From  Table  IV  we  see  that  at  ordinary  temperatures  cobalt  does  not 
offer  any  exception  to  the  general  law  for  the  other  magnetic  metals — 
that  as  the  magnetization  increases,  the  magnetic  permeability  first 
increases  and  then  decreases.  We  also  see  that  the  results  satisfy  to  a 
considerable  degree  of  accuracy  the  equation  which  I  have  used  for  the 
other  magnetic  metals.  The  departure  from  the  equation  is  of  exactly 
the  nature  that  can  be  accounted  for  in  either  of  two  ways — either  by 
the  heating  of  the  ring  by  the  current  for  the  higher  magnetizing- 
forces,  or  by  some  want  of  homogeneity  in  the  ring.  According  to  the 
first  explanation,  the  maximum  of  magnetization  at  0°  C.  will  be  some- 
what lower  than  the  curve  indicates;  but  by  the  second  it  must  be 
higher.  I,  however,  incline  to  the  first,  that  it  is  due  to  heating,  for 
two  reasons:  first,  it  is  sufficient;  and  secondly,  the  smaller  cobalt  ring 
gives  about  the  same  maximum  as  this.  Hence  we  may  take  as  the 
provisional  value  of  the  maximum  of  magnetization  of  cobalt  in  round 
numbers  3=  8000,  or  SB  =  100,000. 

We  also  see  from  Table  IV  that,  at  least  in  this  case,  the  permeability 
of  cobalt  is  less  than  that  of  nickel,  though  we  could  without  doubt 
select  specimens  of  cobalt  which  should  have  this  quality  higher  than  a 
given  specimen  of  nickel.  The  formula  at  the  foot  of  the  Table  also 
shows,  by  the  increased  value  of  the  coefficient  of  K  in  the  right-hand 
member,  that  the  diameter  of  the  curve  is  much  less  inclined  to  the 
axis  of  $  in  this  case  than  in  the  case  of  nickel  or  iron.  In  this  re- 
spect the  three  metals  at  present  stand  in  the  following  order — cobalt, 
nickel,  iron.  This  is  the  inverse  order  also  of  their  permeability;  but 


MAGNETIC  PERMEABILITY  OF  NICKEL  AND  COBALT 


69 


at  present  I  have  not  found  any  law  connecting  these  two,  and  doubt 
if  any  exact  relation  exists,  though  as  a  general  rule  the  value  of  the 
constant  is  greater  in  those  curves  where  the  permeability  is  least. 

In  a  short  abstract  in  the  '  Telegraphic  Journal/  April  1,  1874,  of  a 
memoir  by  M.  Stefan,  it  is  stated  "  that  the  resistance  of  iron  and 
nickel  to  magnetization  is  at  first  very  great,  then  decreases  to  a  mini- 
mum value,  which  is  reached  when  the  induced  magnetic  moment  is 
become  a  third  of  its  maximum."  This  will  do  for  a  very  rough  approx- 
imation, but  is  not  accurate,  as  will  be  seen  from  the  following  Table 
of  this  ratio  from  my  own  experiments : — 


Experiments  published  in  Augnst,  1873. 

Iron. 
Tables  I 
and  II. 

Iron. 
Table  III. 

Bessemer          Iron 
Tabfe'iv.   j     TableV" 

Nickel. 
Table  VI. 

Steel. 
Table  VII. 

1 
3-02 

1 
2-64 

1                      1 

1 
3-15 

1 
2-46 

2-65               2-68 

Experiments  of  present  paper. 

Nickel. 
Tables  I  and  II. 

Nickel. 
Table  III. 

Cobalt. 
Tables  IV  and  V. 

1 
3-23 

1 
3-14 

1 
4-2 

The  average  of  these  is,  if  we  include  Bessemer  steel  with  the  iron,  as 
it  is  more  iron  than  steel:  — 


Hence  the  place  of  greatest  permeability  will  vary  with  the  kind  of 
metal.  From  these,  however,  we  can  approximate  to  the  value  of  6  in 
the  formula;  for  we  have 

27,000      f     AT-  i    i   ^      11,000 
for  Iron,  b  =  -      —  ;    for  Nickel,  *  =  —±=—  ; 
p  " 

for  Cobalt,  b  =  26,000. 

In  Table  V  we  have  the  results  for  cobalt  in  the  magnetic  state. 
We  here  find  the  same  effect  of  magnetization  as  we  have  before  found 
for  iron  and  nickel. 


70  HENRY  A.  KOWLAND 

In  Table  VI  we  have  results  for  cobalt  at  a  high  temperature,  and 
see  how  greatly  the  permeability  is  increased  by  rise  of  temperature, 
this  being  for  the  vertex  of  the  curve  about  70  per  cent.  But  on  plot- 
ting the  curve  I  was  much  surprised  to  find  an  entire  departure  from 
that  regularity  which  I  had  before  found  in  all  curves  taken  from  iron 
and  nickel  when  the  metal  was  homogeneous.  At  present  I  am  not  able 
to  account  for  this,  and  especially  for  the  fact  that  one  of  the  measure- 
ments of  33  is  higher  than  that  which  we  have  taken  for  the  maximum 
of  magnetization,  at,  however,  a  lower  temperature.  The  curve  is 
exactly  of  the  same  nature  as  that  which  I  have  before  found  for  a 
piece  of  nickel  which  had  been  rendered  unhomogeneous  by  heating 
red-hot,  and  thus  burning  the  outside.  The  smaller  cobalt  ring  gives 
a  curve  of  the  same  general  shape  as  this,  but  has  the  top  more  rounded. 
I  will  not  attempt  without  fresh  experiments  to  explain  these  facts,  but 
will  simply  offer  the  following  explanations,  some  one  of  which  may  be 
true.  First,  it  may  be  due  to  want  of  homogeneity  in  the  ring;  but  it 
seems  as  if  this  should  have  affected  the  curve  of  Table  IV  more. 
Secondly,  it  may  be  at  least  partly  due  to  the  rise  in  temperature  of  the 
ring  at  high  magnetizing-powers ;  and  indeed  we  know  that  this  must 
be  greater  in  paraffin  than  in  alcohol  for  several  reasons :  there  is  about 
twice  as  much  heat  generated  in  copper  wire  at  230°  C.  as  at  0°  with 
the  same  current;  and  this  heat  will  not  be  conducted  off  so  fast  in 
paraffin  as  in  alcohol,  on  account  of  its  circulating  with  less  freedom; 
it  probably  has  less  specific  heat  also.  Thirdly,  it  may  be  due  to  some 
property  of  cobalt,  by  which  its  permeability  and  maximum  of  magneti- 
zation are  increased  by  heat  and  the  curve  changed. 

The  experiments  made  with  the  small  ring  confirm  those  made  with 
the  large  one  as  far  as  they  go;  but  as  it  was  so  small,  they  do  not 
possess  the  weight  due  to  those  with  the  larger  one.  But,  curious  as 
it  may  seem,  although  they  were  turned  from  the  same  button  side  by 
side,  yet  the  permeability  of  the  larger  is  about  45  per  cent  greater  than 
that  of  the  smaller.  I  have  satisfied  myself  that  this  is  due  to  no  error 
in  experiment,  but  illustrates  what  extremely  small  changes  will  affect 
the  permeability  of  any  metal. 

We  have  now  completed  the  discussion  of  the  results  as  far  as  they 
refer  to  the  magnetic  permeability,  leaving  the  discussion  of  the  tem- 
porary and  permanent  or  residual  magnetism  to  the  future,  although 
these  latter,  when  discussed,  will  throw  great  light  upon  the  nature 
of  the  coercive  force  in  steel  and  other  metals.  The  whole  subject 
seems  to  be  a  most  fruitful  one,  and  I  can  hardly  understand  why  it  has 


MAGNETIC  PERMEABILITY  OF  NICKEL  AND  COBALT  71 

been  so  much  neglected.  It  may  have  been  that  a  simple  method  of 
experiment  was  not  known;  but  if  so,  I  believe  that  my  method  will  be 
found  both  accurate  and  simple,  though  it  may  be  modified  to  suit  the 
circumstances.  Professor  Maxwell  has  suggested  to  me  that  it  would 
be  better  to  use  rods  of  great  length  than  rings,  because  that  in  a  ring 
we  can  never  determine  its  actual  magnetization,  but  must  always  con- 
tent ourselves  with  measuring  the  change  on  reversing  or  breaking  the 
current.  This  is  an  important  remark,  because  it  has  been  found  by 
MM.  Marianini  and  Jamin,  and  was  noticed  independently  by  myself 
in  some  unpublished  experiments  of  1870,  that  a  bar  of  steel  which  has 
lain  for  some  time  magnetized  in  one  direction  will  afterwards  be  more 
easily  magnetized  in  that  direction  than  in  the  other.  This  fact  could 
not  have  been  discovered  from  a  ring;  and  indeed  if  a  ring  got  a  one- 
sided magnetism  in  any  way  we  might  never  know  it,  and  yet  it  might 
affect  our  results,  as  indeed  we  have  already  seen  in  the  case  of  the 
magnetic  curve.  But  at  the  same  time  I  think  that  greater  errors 
would  result  from  using  long  bars.  I  have  tried  one  of  iron  3  feet 
long  and  £  inch  diameter;  and  the  effect  of  the  length  was  still  appar- 
ent, although  the  ratio  of  length  to  diameter  was  144.  To  get  exact 
results  it  would  probably  have  to  be  several  times  this  for  the  given 
specimen  of  iron,  and  would  of  course  have  to  be  greater  for  a  piece 
of  iron  having  greater  permeability.  This  rod  must  be  turned  and 
must  be  homogeneous  throughout — conditions  which  it  would  be  very 
difficult  to  fulfil,  and  which  would  be  impossible  in  the  case  of  nickel 
and  cobalt.  We  might  indeed  use  ellipsoids  of  very  elongated  form; 
and  this  would  probably  be  the  best  of  all,  as  the  mathematical  theory 
of  this  case  is  complete,  and  it  is  one  of  the  few  where  the  magnetization 
is  uniform,  and  which  consequently  will  still  hold,  although  the  permea- 
bility may  vary  with  the  amount  of  magnetization.  This  form  will,  of 
course,  satisfy  Professor  Maxwell's  objection. 

The  method  of  the  ring  introduces  a  small  error  which  has  never 
yet  been  considered,  and  which  will  affect  Dr.  Stoletow's  results  as  well 
as  mine.  The  number  of  lines  of  induction  passing  across  the  circular 
section  of  a  ring-magnet  we  have  seen  to  be 

/»+  «         J  ~Jp y* 

J—n        a, — x 

in  which  a  is  the  mean  radius  of  the  ring,  E  the  radius  of  the  section, 
n'  the  number  of  coils  in  the  helix,  and  i  the  intensity  of  the  current. 
Xow  in  integrating  this  before,  I  assumed  that  ft  was  a  constant 
throughout  the  section  of  the  ring:  now  we  have  found  that  11  is  a 


72  HENET  A.  EOWLAND 

function  of  the  magnetization,  and  hence  a  function  of  the  magnetizing- 
force;  but  the  latter  varies  in  different  parts  of  the  section,  and  hence 
n  must  vary.  But  the  correction  will  be  small,  because  the  average 
value  will  be  nearly  the  same  as  if  it  were  a  constant.  We  may  estimate 
the  correction  in  the  following  manner.  Let  //  and  §  be  the  values  of 
those  quantities  at  any  point  in  the  section  of  the  ring,  //  and  §'  the 
values  at  the  centre  of  the  section,  and  fjtt  and  §,  the  observed  values. 
Then,  by  Taylor's  theorem, 


But  £  =  2n'1    and  ft'  =  — ,  and  so  we  have 
a  —  x  a 

\  4     a*  2//    dJQr  \  a2 

Jp'2    dz>j.  I  R*    ,   q  K 

But  in  my  Tables  I  have  already  calculated 

Q1 

A*J  = 


a 

&c.     . 


t  —  /  i         T53  \  J 

,lfV  (l  +  i  ^  +  fto.) 

and  as  ftl  is  very  nearly  equal  to  fjf,  and  $,  to  ^)',  we  have  approximately 
6,    din.  I  IP        3     If       . 

-- 


. 

2          4      a4 

which  will  give  the  value  of  //  corresponding  to  Q'  and  £>'.     Hence  the 
correct  values  of  the  quantities  will  be  //,  §',  and  S3'  =  ^V. 

The  quantities   -^-  and  ^/-  can  be  obtained  either  by  measuring  a 

"§/  **§/ 

plot  of  the  curve,  or  from  the  empirical  equation 


=      sn 


when  we  know  the  values  of  the  constants.     In  this  case 

dp  _     ,  ft, 
*$/  " 
^V/ 
d£? 
in  which 


MAGNETIC  PERMEABILITY  OF  NICKEL  AND  COBALT  73 

In  all  these  the  upper  signs  are  to  be  taken  for  all  values  of  £>,  less  than 

—  ,  and  the  lower  signs  for  greater  values. 
t> 

On  applying  these  formulas  to  the  observations,  I  have  found  that  the 
corrections  will  in  no  way  influence  my  conclusions,  being  always  very 
small;  but  at  the  same  time  the  calculation  shows  that  it  would  be  well 

R 

to  diminish  the  ratio  —  as  much  as  possible.     In  all  my  rings  this  ratio 
a 

did  not  depart  very  much  from  —  -  ;  but  I  would  advise  future  experi- 

o'o 

menters  to  take  it  at  least  as  small  as   ^:  the  amount  of  correction 

R 

will  be  very  nearly  proportional  to  the  square  of   —  . 

ct 

Summary. 

The  following  laws  have  been  established  entirely  by  my  own  experi- 
ments, though  in  that  part  of  (2)  which  refers  to  iron  I  have  been 
anticipated  in  the  publication  by  Dr.  Stoletow  (Phil.  Mag.  Jan.  1873). 
When  any  measurements  are  given,  they  are  on  the  metre,  gramme, 
second  system. 

(1)  Iron,  nickel,  and  cobalt,  in  their  magnetic  properties  at  ordinary 
temperatures,  differ  from  each  other  only  in  the  quantity  of  those 
properties  and  not  in  the  quality. 

(2)  As  the  magnetizing-force  is  increased  from  0  upwards,  the  resist- 
ance of  iron,  nickel,  and  cobalt  to  magnetization  decreases  until  a 
minimum  is  reached,  and  after  that  increases  indefinitely.     This  mini- 
mum is  reached  when  the  metal  has  attained  a  magnetization  of  from 
•24  to  -38  of  the  maximum  of  magnetization  of  the  given  metal. 

(3)  The  curve  showing  the  relation  between  the  magnetization  and 
the  magnetic  permeability,  or  Neumann's  coefficient,  is  of  such  a  form 
that  a  diameter  can  be  drawn  bisecting  chords  parallel  to  the  axis  of  33, 
and  is  of  very  nearly  the  form  given  by  the  equation 


where  B,  &,  and  D  are  constants,  jut  is  the  ratio  of  the  magnetization  to 
the  magnetizing-force  in  an  infinitely  long  bar,  and  33  is  the  amount 
of  magnetization. 

(4)  If  a  metal  is  permanently  magnetized,  its  resistance  to  change  of 
magnetism  is  greater  for  low  magnetizing-powers  than  when  it  is  in  the 
normal  state,  but  is  the  same  for  high  magnetizing-powers.  This 


74  HENRY  A.  EOWLAND 

applies  to  the  permanent  state  finally  attained  after  several  reversals  of 
magnetizing-f  orce ;  but  if  we  strongly  magnetize  a  bar  in  one  direction 
and  then  afterwards  apply  a  weak  magnetizing-force  in  the  opposite 
direction,  the  change  of  magnetization  will  be  very  great. 

(5)  The  resistances  of  nickel  and  cobalt  to  magnetization  vary  with 
the  temperature;  but  whether  it  is  increased  or  not  in  nickel  depends 
upon  the  amount  of  magnetization :  for  a  moderate  amount  of  magneti- 
zation it  decreases  with  rise  of  temperature  very  rapidly;  but  if  the 
magnetization  is  high  the  resistance  is  increased.     In  cobalt  it  appar- 
ently always  decreased,  whatever  the  magnetization.     The  resistance 
of  iron  to  magnetization  is  not  much  affected  by  the  temperature. 

(6)  The  resistance  of  any  specimen  of  metal  to  magnetization  de- 
pends on  the  kind  of  metal,  on  the  quality  of  the  metal,  on  the  amount 
of  permanent  magnetization,  on  the  temperature,  and  on  the  total 
amount  of  magnetization,  and,  in  at  least  iron  and  nickel,  decreases 
very  much   on  careful   annealing.     The   maximum   of   magnetization 
depends  on  the  kind  of  metal  and  on  the  temperature. 

(7)  Iron,  nickel,  and  cobalt  all  probably  have  a  maximum  of  magneti- 
zation, though  its  existence  can  never  be  entirely  established  by  experi- 
ment, and  must  always  be  a  matter  of  inference;  but  if  one  exists,  the 
values  must  be  nearly  as  follows  at  ordinary  temperatures.     Iron  when 
33  =  175,000  or  when  3  =  13,900;  nickel  when  33  =63,000  or  when 
3  =  4940;  cobalt  when  33  =  100,000(  ?)  or  when  3  =  8000  (?). 

(8)  The  maximum  of  magnetization  of  iron  and  nickel  decreases  with 
rise  of  temperature,  at  least  between  10°  C.  and  220°  C.,  the  first  very 
slowly  and  the  second  very  rapidly.     At  220°  C.  the  maximum  for  iron 
is  when  33  =  172,000  and  3  =  13,600,  and  for  nickel  when  33  =  49,000 
and  3  =  3800. 

The  laws  which  govern  temporary  and  residual  magnetism,  except  so 
far  as  they  have  been  hitherto  given,  I  leave  for  the  future,  when  I 
shall  have  time  for  further  experiment  on  the  subject  to  develop  some 
points  which  are  not  yet  quite  clear. 

Troy,  New  York,   U.  S.  A.,  April,  1874. 


ON  A  NEW  DIAMAGNETIC  ATTACHMENT  TO  THE  LANTERN, 
WITH  A  NOTE  ON  THE  THEOEY  OF  THE  OSCILLATIONS 
OF  INDUCTIVELY  MAGNETIZED  BODIES 

[American  Journal  of  Science  [8],  IX,  357-361,  1875] 

1.  DESCRIPTION  OF  APPARATUS 

Some  time  ago,  in  thinking  of  the  theory  of  diamagnetism,  I  came 
to  the  conclusion  that  apparatus  of  large  size  was  by  no  means  neces- 
sary in  diamagnetic  experiments,  and  on  testing  my  conjectures  experi- 
mentally, I  was  much  pleased  to  find  that  they  were  true.  So  that  for 
more  than  a  year  I  have  been  in  the  habit  of  illustrating  this  subject 
to  my  classes  by  means  of  a  small  apparatus  weighing  only  about  a 
pound  or  two,  which  I  place  in  my  lantern  and  magnify  to  a  large  size 
on  the  screen. 

The  effects  obtained  in  this  way  are  very  fine  and  are  not  surpassed 
by  those  with  the  largest  magnets;  and  we  are  by  no  means  confined, 
to  strongly  diamagnetic  substances,  but,  with  proper  care,  can  use  any- 
thing, even  the  most  feeble.  The  apparatus  which  I  used  consisted  of 
a  horseshoe  electro-magnet,  made  of  an  iron  bar  half  an  inch  in  diam- 
eter and  about  ten  inches  long,  bent  into  the  proper  form,  and  sur- 
rounded with  four  or  five  layers  of  No.  16  wire.  But  the  following 
apparatus  will,  without  doubt,  be  found  much  more  convenient.  It  can 
be  made  of  any  size,  though  the  dimensions  given  will  probably  be 
found  convenient. 

d  d 


r—  j  3  <d 

=3 

a 

a. 
e 

i 

FIGURE  1. 


The  apparatus  is  represented  in  Fig.  1.  To  a  straight  bar  of  iron  h, 
7  in.  long,  £  in.  thick,  and  f  in.  wide,  are  attached  two  pieces  e  e  of 
the  same  kind  of  iron  by  two  set  screws  g  g,  which  move  in  slots  in  the 


76  HENRY  A.  EOWLAND 

piece  h.  Into  these  pieces  are  screwed  two  tubes  c  made  of  iron  and 
having  an  internal  diameter  of  about  T7T  in.  and  a  thickness  not  to 
exceed  ^  in.  Through  these  tubes  the  iron  rods  a  I  slide  and  are 
held  at  any  point  by  the  screws  d.  One  end  b  of  this  rod  is  rounded 
off  for  diamagnetic  experiments  and  the  other  enlarged  and  flattened 
at  the  end  for  magnecrystallic  experiments.  On  the  tube  c  a  helix  of 
N~o.  16  or  No.  18  wire  is  wound  so  as  to  make  up  a  thickness  of  -4  or  -5 
of  an  inch  and  having  a  length  of  2£  in.  The  object  of  the  screws  g  is 
principally  to  allow  the  rods  a  &  to  be  reversed  quickly  and  to  adjust  the 
position  of  the  helices.  When  the  apparatus  is  to  be  used  for  only  one 
kind  of  work  it  can  be  much  simplified  by  doing  away  with  many  of  the 
moving  parts. 

This  instrument  can  be  used  either  with  the  ordinary  magic  lantern, 
or  better,  with  one  having,  a  vertical  attachment.  In  the  latter  case 
the  plane  of  the  instrument  is  horizontal  and  the  substances  are  sus- 
pended from  a  wire  made  quite  small,  so  as  not  to  cut  off  too  much 
light. 

The  suspending  thread  in  the  case  of  bismuth  can  be  quite  large 
but  for  other  bodies  a  single  fibre  of  silk  is  best;  these  in  the  shape  of 
bars  half  an  inch  long  can  be  each  attached  to  a  fibre  having  a  little 
wire  hook  at  its  upper  end  and  hung  in  a  cabinet  until  required. 

The  theory  of  feebly  magnetic  or  diamagnetic  bodies  oscillating  in 
a  magnetic  field  is  very  simple  and  yet  the  results  are  of  the  greatest 
interest,  especially  the  effect  of  the  size  of  the  apparatus,  which  is 
here  given  for  the  first  time. 

2.  THEORY 

Let  a  very  small  particle  of  a  body  whose  coefficient  of  magnetization 
AC  is  very  small,  and  either  positive  or  negative,  be  placed  in  a  magnetic 
field  of  intensity  R;  it  will  then  have  an  induced  magnetic  moment  of 
<vR,  where  v  is  the  volume  of  the  element.  The  force  acting  on  this 
particle  to  cause  it  to  go  in  any  given  direction  will  be  equal  to  the 
product  of  the  magnetic  moment  into  the  rate  of  variation  of  R  in  that 

direction,1  and  hence  is  KvR  ~r  in  the  direction  of  x.     The  total  force 

ax 

acting  on  the  body  in  the  direction  of  x  is  therefore 


1  Thomson,  Reprint  of  Papers,  art.  679,  Prob.  vii. 


NEW   DlAMAGNETIC    ATTACHMENT   TO    THE    LANTERN  77 

and  the  other  components  of  the  force  are 


and 


•- 


Let,  now,  the  axis  of  z  be  vertical,  the  axis  of  x  in  the  line  of  the 
magnetic  poles  of  the  magnet,  and  y  at  right  angles  to  both.  Then 
the  moment  of  the  forces  acting  on  the  body  to  turn  it  about  the  axis 

of  z  is 


where  the  integration  extends  throughout  the  volume  of  the  body. 

If  the  body  is  suspended  so  as  to  turn  freely  about  the  axis  of  z  it 
will  vibrate  about  the  position  for  which  M  is  a  minimum  or  else  will 
remain  at  rest  at  that  point.  The  number  of  single  oscillations  made 
when  the  angular  elongation  &  is  very  small,  is 


1      /  M 

'      T.      V      tfj' 


in  which  M  and  $  must  be  measured  simultaneously,  and  I  is  the 
moment  of  inertia  of  the  body. 


I  r  r  r 

A/   I     l/f 
\  J  J  J 


i  Jw     d(i^)\,  ^  ^ 

y      ,      —  3—  -,  —  \dxdydz. 
\J     dx  dy   j 


Xow  let  us  suppose  that  the  whole  apparatus  changes  size,  the  relation 
between  the  parts  remaining  constant,  so  that  the  apparatus  becomes 
m  times  as  great  as  before.  Then  x,  y,  dx,  dy,  and  dz  will  increase  ra 

times  and  /,  m5  times.     To  determine  the  changes  in     ^     ^  and  -X—  * 

aye?  ^y 

we  make  use  of  the  theorem  of  Sir  Win.  Thomson,  that  "  similar  bars 
of  different  dimensions,  similarly  rolled,  with  lengths  of  wire  propor- 
tional to  the  squares  of  their  linear  dimensions,  and  carrying  equal 
currents,  cause  equal  forces  at  points  similarly  situated  with  reference 
to  them."  But  as  the  above  only  applies  to  equal  currents,  I  have 
generalized  it  in  the  following:  In  any  two  magnetic  systems  whatever, 
similar  in  all  their  parts  and  composed  of  any  number  of  permanent  or 
electro-magnets,  wires  carrying  currents,  or  bodies  under  magnetic  induc- 
tion, the  magnetic  force  at  similar  points  of  each  will  be  the  same  when  the 
following  conditions  are  complied  with:  1st,  the  magnetic  materials  at 
similar  prints  in  the  two  systems  must  be  exactly  the  same  in  quality  and 


78  HENRY  A.  KOWLAND 

temper;  2d,  the  permanent  magnets  must  be  magnetized  to  the  same  degree 
at  similar  points  of  the  systems;  3d,  the  coils  of  the  electro-magnets  and 
other  wires  or  bundles  of  wires  carrying  the  current  must  have  similar 
external  dimensions  in  the  two  systems  and  must  have  the  product  of  the 
current  by  the  number  of  wires  passing  through  similar  sections  of  the  two 
systems  proportional  to  the  linear  dimensions  of  the  systems. 

This  will  apply  to  the  case  we  are  considering  when  the  product  of 
the  current  by  the  number  of  the  turns  of  wire  varies  in  direct  propor- 
tion to  the  size  of  the  apparatus.  Hence  in  this  case  \  and  !-i — f 

dx  ay 

will  vary  inversely  as  m.  Hence  we  see  that  n  will  be  inversely  pro- 
portional to  the  size  of  the  apparatus;  and  although  we  have  only 
proved  this  for  the  case  when  *  is  small,  it  is  easy  to  see  that  it  is 
perfectly  general.  The  advantage  of  small  diamagnetic  apparatus  is 
thus  apparent,  for  the  smaller  we  make  it  the  more  vibrations  the  bar 
will  make  in  a  given  time  and  the  more  promptly  will  the  results  be 
shown. 

It  might  be  thought  that  by  hanging  a  very  small  bar  in  the  field  oi' 
a  large  magnet,  we  might  obtain  just  as  many  vibrations  as  by  the  use 
of  a  small  apparatus;  but  this  is  not  so,  for  Sir  Wm.  Thomson  has 
shown 2  that  the  number  of  oscillations  of  a  feebly  magnetic  or  diamag- 
netic body  of  elongated  form  in  a  magnetic  field  is  nearly  independent 
of  the  length  when  that  is  short.  So  that  the  only  way  of  increasing 
the  number  of  vibrations  is  to  decrease  the  size  of  the  whole  apparatus, 
or  to  increase  the  power  of  the  magnets;  the  latter  has  a  limit  and 
hence  we  become  dependent  on  the  former. 

The  theory  of  the  effect  of  the  size  of  the  body  is  very  simple,  and  we 
may  proceed  as  follows.  Let  the  body  be  in  the  form  of  a  small  bar 
whose  sectional  area,  a,  is  very  small  compared  with  its  length,  and  let 
f  be  the  angle  of  the  axis  of  the  bar  with  the  line  joining  the  poles,  and 
r  the  radius  vector  from  the  origin.  Developing  R2  as  a  function  of 
x  and  y  by  Taylor's  theorem,  and  noting  that  as  R  is  symmetrical  with 
reference  to  the  planes  XZ  and  YZ,  only  the  even  powers  of  x  and  y 
can  enter  into  the  development,  we  have,  calling  R0  the  value  of  R 
at  the  origin, 


2  \    dy?  dy 

r#(/2n 


2.3.4V    dtf  dtfdf  dy* 

2  Reprint  of  Papers,  art.  670.       Remarques  sur  les  oscillations  d'aiguilles  non  crys- 
tallisees. 


NEW   DlAMAGNETIC    ATTACHMENT   TO   THE    LANTERN  79 

When  the  vibrating  body  is  very  small  the  first  two  terms  will  suffice: 
hence  we  have 

M=  i  a 

in  which  I  is  the  length  of  the  bar.     If  d  is  the  density  of  the  body 
(weight  of  a  unit  of  volume),  I  =  —^  and  n  becomes 


in  which,  however,  it  is  to  be  noted  that      ^  .7    is  essentially  negative 

and  so  the  sign  of  the  term  containing  it  will  be  positive  in  the  actual 
development. 

This  equation  is  independent  of  the  dimensions  of  the  body,  and 
hence  we  conclude  that  when  the  body  is  small  and  very  long  as  com- 
pared with  its  other  dimensions,  the  number  of  vibrations  which  it  will 
make  in  a  given  field  is  dependent  merely  on  its  coefficient  of  magneti- 
zation and  on  its  density;  a  result  first  given  by  Sir  Wm.  Thomson,  in 
the  paper  referred  to.  I  have  given  it  once  more  and  put  it  in  its 
present  form  merely  to  call  attention  to  the  facility  with  which  «  can 
be  obtained  from  it  when  we  have  measured  R  in  different  parts  of  the 
field  by  known  methods.  This  could  be  done  by  means  of  a  rotating 
coil  as  used  by  Verdet,  or  by  my  magnetic  proof  plane  which  I  will 
soon  describe,  combined  with  my  method  of  using  the  earth  inductor. 
This  will  give  the  best  method  that  I  know  of  for  obtaining  K  for 
diamagnetic  or  weak  paramagnetic  substances. 

Troy,  January  15,  1875. 


8 
NOTES  ON  MAGNETIC  DISTKIBUTION 

[Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  XI,  191,  19^,  187(i.     Pre- 
sented June  9,  1  875] 

In  two  papers  which  have  recently  appeared  on  this  subject,  by  Mr. 
Sears  (Amer.  Jour,  of  Science,  July,  1874),  and  Mr.  Jacques  (Proc. 
Amer.  Acad.  of  Sciences,  1875,  p.  445),  a  method  is  used  for  determining 
magnetic  distribution,  founded  on  induced  currents,  in  which  results 
contrary  to  those  published  by  M.  Jamin  have  been  found.  It  does  not 
seem  to  have  been  noticed  that  the  method  then  used  does  not  give 
what  we  ordinarily  mean  by  magnetic  distribution.  In  mathematical 
language,  they  have  measured  the  surface  integral  of  magnetic  induc- 
tion across  the  section  of  the  bar  instead  of  along  a  given  length  of  its 
surface.1  M.  Jamin's  method  gives  a  result  depending  on  the  so-called 
surface  density  of  the  magnetism,  which  is  nearly  proportional  to  the 
surface  integral  of  the  magnetic  induction  along  a  given  length  of  the 
bar.  Hence  the  discrepancy  between  the  different  results.  Had  the 
experiments  of  Mr.  Sears  and  Mr.  Jacques  been  made  by  sliding  the 
helix  inch  by  inch  along  the  bars,  their  results  would  have  confirmed 
those  of  M.  Jamin.  Four  or  five  years  ago,  I  made  a  large  number  of 
experiments  in  this  way,  which  I  am  now  rewriting  for  publication,  and 
where  the  whole  matter  will  be  made  clear.  At  present,  I  will  give  the 
following  method  of  converting  one  into  the  other.  Let  Q  be  the  sur- 
face integral  of  magnetic  induction  across  the  section  of  the  rod,  and 

let  Qe  be  that  along  one  inch  of  the  rod:  then  Qe  <x  — ^.x  beinar  the 

(IX 

distance  along  the  rod.  Hence,  M.  Jamin's  results  depend  on  the  rate 
of  variation  of  the  magnetization  of  the  rod,  while  those  of  Mr.  Sears 
and  Mr.  Jacques  depend  on  the  magnetization.  In  conclusion,  let  me 
heartily  agree  with  Mr.  Jacques's  remarks  about  M.  Jamin's  conclusions 
from  his  experiments.  Such  experiments  as  those  give  no  data  what- 
ever for  a  physical  theory  of  magnetism,  and  can  all  be  deduced  from 
the  ordinary  mathematical  theory,  which  is  independent  of  physical 

1  Maxwell's  Electricity  and  Magnetism,  art.  402. 


NOTES  ON  MAGNETIC  DISTRIBUTION  81 

hypothesis,  combined  with  what  is  known  with  regard  to  the  magnetiz- 
ing function  of  iron.  This  will  be  shown  in  the  paper  I  am  rewriting. 
It  seems  to  me  that  M.  Jamin's  method  is  very  defective;  and  I  know 
of  no  method  of  experimenting,  which  is  theoretically  without  objection 
except  that  of  induced  currents,  and  this  I  have  used  in  all  my  experi- 
ments on  magnetic  distribution  for  the  last  four  or  five  years,  and  have 
developed  into  a  system  capable  of  giving  results  in  absolute  measure. 
Mr.  Jacques  is  to  be  congratulated  on  pointing  out  these  errors  in 
M.  Jamin's  conclusions. 

Troy,  June  7,  1875. 


9 

NOTE  ON  KOHLKAUSCJFS  DETERMINATION  OF  THE  ABSO- 
LUTE VALUE  OF  THE  SIEMENS  MERCURY  UNIT  OF 
ELECTRICAL  RESISTANCE 

[Philosophical  Magazine  [4],  L,  161-163,  1875] 

In  looking  over  Kohlrausch's  paper1  upon  the  determination  of  a 
resistance  in  absolute  measure,  with  a  view  to  undertaking  something 
of  the  kind  myself,  and  also,  if  possible,  to  discover  the  reason  of  the 
difference  from  the  results  of  the  Committee  of  the  British  Association, 
I  think  I  have  come  across  an  error  of  sufficient  magnitude  and  in  the 
proper  direction  to  account  for  the  2  per  cent  difference.  Kohlrausch's 
experiments  were  made  with  such  great  care  and  by  so  experienced  a 
person  that  it  is  only  after  due  thought  and  careful  consideration  that 
I  take  it  upon  me  to  offer  a  few  critical  remarks. 

We  observe,  then,  first  of  all,  that  the  principal  peculiarity  of  his 
method  consists  in  doing  away  with  all  measurements  of  the  coils  of 
the  galvanometer,  and  in  its  place  making  accurate  determinations  of 
the  logarithmic  decrement  both  with  the  circuit  closed  and  open,  to- 
gether with  various  absolute  determinations  rendered  necessary  by  this 
change.  In  this  way  the  logarithmic  decrement  is  raised  from  being  a 
small  correction  to  a  most  important  factor  in  the  equation.  Hence 
it  is  that  we  should  carefully  scrutinize  the  theory  and  see  whether  it 
be  correct  enough  for  this  purpose ;  for  only  an  approximation  is  needed 
for  the  first  method. 

The  resistances  to  a  bar  magnet  swinging  within  a  coil  may  be  divided 
into  two  principal  parts — first,  that  due  to  the  resistance  of  air  and 
viscosity  of  suspending  fibre,  and,  second,  that  due  to  the  induced  cur- 
rent in  the  coils.  The  first  resistance  is  usually  taken  as  proportional 
to  the  velocity,  and  thus  assumes  the  viscosity  of  the  air  to  be  the  most 
important  element.  This  is  proba,bly  true  in  most  cases  where  the 
motion  is  slow.  This  factor  is  quite  small  compared  with  the  second 
when  the  magnet  is  large  and  heavy  and  the  coils  wound  close  to  it,  as 

^oggendorff's  Annalen,  Erganzungsband  vi,  p.  1;  translated  in  Phil.  Mag.,  S.  4, 
vol.  xlvii,  pp.  294,  342. 


NOTE  ox  KOHLRAUSCH'S  DETERMINATION  83 

in  Kohlrausch's  instrument.  Kohlrausch's  principal  error  lies  in  the 
omission  of  the  coefficient  of  self-induction  from  his  equations. 

For  the  sake  of  clearness,  and  because  the  subject  is  quite  often 
misapprehended,  I  shall  commence  at  the  beginning  and  deduce  nearly 
all  equations. 

Let  us  proceed  at  first  in  the  method  of  Helmholtz,  using  the  nota- 
tion of  Maxwell's  '  Electricity.' 

Let  a  current  of  strength  /  be  passing  in  a  circuit  whose  resistance 
is  7?,  and  coefficient  of  self-induction  L.  Also  let  a  magnet  be  near  the 
circuit  whose  potential  energy  with  respect  to  the  circuit  is  IV.  Let  A 
be  the  electromotive  force  of  the  battery  in  the  circuit. 

The  work  done  by  the  battery  in  the  time  dt  is  equal  to  the  sum  of 
the  work  done  in  heating  the  wire,  in  moving  the  magnet,  and  in 
increasing  the  mutual  potential  of  the  circuit  on  itself.2  Hence  we  have 

AUt  =  PRdt  +  l~dt  +  -L  j 
dt  2 

and  if  A  is  equal  to  zero,  we  find 

/=_.±7£r  +  L*L\ 


If  we  apply  this  to  the  case  of  a  magnet  swinging  within  a  coil  the 
angle  of  the  magnet  from  a  fixed  position  being  x,  we  have  since   -j- 

&3s 

is  the  moment  of  the  force  acting  on  the  magnet  with  unit  current  and 
may  be  denoted  by  q, 

dx    ,     r 


where  my  R  is  Kohlrausch's  w. 

This  expression  differs  from  that  used  by  Kohlrausch  in  the  addition 
of  the  last  term,  which  is  the  correction  due  to  self-induction.  The 
last  term  vanishes  whenever  the  magnet  moves  with  such  velocity  as 
to  keep  the  induced  current  constant  ;  but  in  the  swinging  of  a  galvano- 
meter-needle it  has  a  value. 

To  form  the  equation  of  motion  of  the  needle,  we  can  proceed  the 
rest  of  the  way  as  Maxwell  has  done  (Electricity,  art.  762).  Assuming 
that  all  frictional  resistances  to  the  needle  are  proportional  to  the 
velocity  of  the  needle,  we  have 

B<S  +  cw  +  l)x  =  «r'  .......  ^ 

where  B,  C,  and  D  are  constants. 

2  See  remarks  in  Maxwell's  '  Electricity,'  art.  544,  near  bottom  of  page. 


84  HENRY  A.  ROWLAND 

Eliminating  /  between  this  equation  and  (1),  we  find 


At  first  sight  this  equation  will  appear  to  be  the  same  as  that  of  Max- 
well; but  on  further  examination  we  see  that  it  is  more  general  in  the 
value  of  q. 

Equation  (3)  is  the  correct  equation  to  use  in  this  case,  and  reduces 
to  that  of  Kohlrausch  when  L  =  0. 

To  see  how  this  error  will  affect  Kohlrausch's  results,  we  must  re- 
member that  he  uses  this  equation  to  find  the  constant  of  his  galvano- 
meter, on  which  his  whole  experiment  depends;  and  the  error  is  so 
interwoven  with  all  his  results  .that  an  entire  recomputation  is  neces- 
sary, provided  the  data  for  calculating  the  coefficient  of  self-induction 
of  the  galvanometer  coils  and  earth  inductor  can  be  obtained. 

The  equation 

t*  tl 

*2  +  /2       -2  +  /S 

does  not  hold  when  self-induction  is  considered  ;  and  so  his  fundamental 
equation  (1)  is  not  correct,  containing  a  twofold  error. 

The  linear  differential  equation  (3)  is  easily  solved;  but  as  the  results 
are  complicated,  it  is  hardly  worth  while  at  present,  until  a  recalcula- 
tion can  be  made.  I  prefer  to  solve  it  on  the  supposition  that  L  is 
small,  and  thus  merely  obtain  a  correction  to  Kohlrausch's  equation 
connecting  t  and  t0,  after  which  equation  (15)  or  (17)  (Maxwell's  '  Elec- 
tricity/ art.  762)  can  be  used  when  made  more  general  by  substituting 
q  for  Om. 

As  far  as  I  have  had  time  to  go  at  present,  the  correction  seems  to 
be  in  the  direction  of  making  Kohlrausch's  determination  more  nearly 
coincide  with  that  of  the  Committee  on  Electrical  Standards  of  the 
British  Association.  Other  engagements  occupy  my  attention  at  pres- 
ent ;  but  I  hope  to  see  these  corrections  made  to  an  otherwise  excellent 
determination  of  this  most  important  unit. 

London,  August  4,  1875. 


10 

PKELIMINAEY  NOTE  ON  A  MAGNETIC  PEOOF  PLANE 

[American  Journal  of  Science  [3],  X,  14-17,  1875] 

About  four  years  ago  I  made  a  large  number  of  experiments  on  the 
distribution  of  magnetism  on  iron  and  steel  bars  by  means  of  a  coil  of 
wire  sliding  along  the  bar;  the  induced  current  in  the  coil  as  measured 
by  a  galvanometer  was  a  measure  of  the  number  of  lines  of  force  cut  by 
the  coil  and  can  be  found  in  absolute  measure  by  my  method  of  using 
the  earth  inductor.  These  researches  have  never  yet  been  published 
owing  to  circumstances  beyond  my  control,  but  are  known  to  quite  a 
number  of  persons  in  this  country,  and  will  soon  be  published.  The 
method  there  used  is  the  only  correct  one  that  I  know  of  for  experi- 
menting on  magnetic  distribution,  and  my  purpose  in  this  note  is  to 
extend  it  to  bodies  of  all  shapes,  so  that  experiments  on  magnetic  dis- 
tribution may  become  as  simple  and  easy  to  perform  as  those  on  elec- 
trical distribution.  And  so  well  has  my  magnetic  proof  plane  accom- 
plished this  that  I  can  illustrate  the  subject  to  my  classes  with  the 
greatest  ease. 

The  apparatus  required  is  merely  a  small  coil  of  wire  i  to  ^  inch  in 
diameter,  containing  from  10  to  50  turns,  and  a  Thomson  galvanometer. 
When  we  require  to  reduce  to  absolute  measure,  another  coil  about  a 
foot  in  diameter  and  containing  20  or  30  turns  is  required.  Having 
attached  the  small  coil  (or,  as  I  call  it,  the  magnetic  proof  plane)  to 
the  galvanometer,  we  have  merely  to  lay  it  on  the  required  spot,  and 
when  everything  is  ready,  to  pull  it  away  suddenly  and  carry  it  to  a 
distance,  and  the  momentary  deflection  of  the  galvanometer  needle  will 
be  proportional  to  that  component  of  the  lines  of  force  at  that  point 
which  is  perpendicular  to  the  plane  of  the  coil.  And  if  we  apply  it  to 
the  surface  of  a  permanent  magnet  the  so-called  surface  density  of  the 
magnetism  at  that  point  will  be  nearly  proportional  to  the  deflection. 
In  the  case  of  an  electro-magnet  the  surface  density  will  be  nearly  pro- 
portional to  the  deflection  minus  the  deflection  which  would  be  pro- 
duced by  the  helix  alone,  though  the  last  is  generally  small  and  may  be 
neglected.  I  use  the  words  nearly  proportional  in  the  above  statement 
because  thev  are  only  exactly  true  in  the  cases  where  the  lines  of  force 


8G  HENKY  A.  KOWLAND 

proceed  from  the  surface  in  a  perpendicular  direction;  otherwise  the 
deflections  must  be  multiplied  by  the  secant  of  the  angle  made  by  the 
lines  of  force  with  the  surface  of  the  magnet.  In  the  case  of  an  electro- 
magnet made  of  very  soft  iron,  theory  shows  that  the  lines  pass  out 
nearly  perpendicular  to  the  surface  and  so  no  correction  is  needed. 

We  can  also,  by  a  coil  of  this  kind,  determine  the  intensity  of  the 
magnetic  field  at  any  point  and  thus  be  able  to  make  a  complete  map 
of  it.  Having  done  this,  we  have  all  the  data  necessary  to  substitute 
in  the  formula  which  I  have  given  in  this  Journal,1  and  by  a  simple 
experiment  can  thus  determine  the  coefficient  of  magnetization  of  any 
diamagnetic  or  weak  paramagnetic  body  probably  in  a  more  accurate 
manner  than  any  Weber  used.  Only  the  largest-sized  magnets  could  of 
course  be  used  for  this  purpose  with  any  accuracy,  and  indeed  they  are 
always  to  be  preferred  in  obtaining  the  distribution  by  this  method. 

Having  obtained  the  distribution  for  any  given  magnet,  the  distribu- 
tion for  any  similar  magnet  of  the  same  material  but  of  different  size 
becomes  known  by  a  well-known  law  of  Sir  William  Thomson. 

As,  in  the  present  state  of  our  knowledge,  magnetic  measurements 
are  of  small  value  unless  made  on  the  absolute  scale,  we  require  to 
reduce  our  results  to  this  system.  There  are  several  methods  of  doing 
this,  but  the  simplest  is  that  which  I  have  used  in  my  experiments  on 
magnetic  permeability,  and  consists  in  including  an  earth  inductor  in 
the  circuit.  A  coil  laid  on  a  perfectly  level  surface  is  sufficient  for 
this :  when  this  is  turned  over,  the  induced  current  will  be  equal  to  C  = 

%n  ~VA 

where  n  is  the  number  of  turns  in  the  coil,  A  its  mean  area,  V 
-Ti- 
the vertical  component  of  the  earth's  magnetism,  and  R  the  resistance 
of  the  circuit.     When  the  small  coil  is  pulled  suddenly  away  the  current 

will  be  C"  =  *-&?,  and  so  we  have  Q  =  2V^£,  in  which  when  a 
li  an  6 

Thomson  galvanometer  is  used  C'  and  C  can  be  replaced  by  the  cor- 
responding deflections:  hence  0  =  2V—~-,  in  which  a  and  n'  are  the 

an  D 

area  and  number  of  turns  in  the  small  coil  and  Q  is  that  component  of 
the  magnetic  field  we  are  measuring  in  the  direction  of  the  axis  of  the 
small  coil. 

As  an  illustration  of  this  method  I  will  give  a  few  experiments  made 
with  the  magnets  of  a  Euhmkorff  diamagnetic  apparatus,  which  was 
altogether  about  2  ft.  long  and  had  its  magnets  2  in.  in  diameter,  with 

'On  a  new  diamagnetic  attachment  to  the  lantern,  &c.,  this  Journal,  May,  1875. 


PRELIMINARY  NOTE  ON  A  MAGNETIC  PROOF  PLANE  8? 

a  hole  £  in.  in  diameter  through  them  for  experiments  on  the  rotation 
of  the  plane  of  polarization  of  light,  but  which  in  these  experiments 
were  closed  by  the  solid  poles  which  were  screwed  on.  The  first  experi- 
ments were  with  two  discs  of  iron,  4*6  in.  in  diameter  and  If  in.  thick, 
screwed  on  to  the  poles.  In  the  first  place  the  poles  were  turned  away 
from  one  another,  the  current  being  sent  through  only  one  magnet, 
and  the  values  of  the  magnetic  field  obtained  at  different  points  close  to 
the  surface  of  the  disc.  These  may  be  numbered  as  follows :  No.  1,  at 
centre  of  face  of  disc;  No.  2,  on  face  of  disc  half  an  inch  from  the  edge; 
No.  3,  on  centre  of  edge  of  disc.  The  measures  are  on  the  metre,  gram, 
second  system. 

1st.  Strength  of  current,  4-4  farads  per  second. 

1.  2220.          2.  3550.          3.  4440. 

2nd.  Strength  of  current  8-3  farads  per  second. 

1.  3600.         2.  5300.         3.  7500. 

Next  the  poles  were  turned  toward  each  other  and  the  current  sent 
through  both  magnets,  so  as  to  make  the  poles  of  the  same  name. 
Current  4 '6  farads  per  second. 

1st.  Distance  of  poles,  3  in. 

1.     1300.  3.     3800. 

2nd.  Distance  of  poles,  1^  in. 

1.       600.  3.     4000. 

Here  we  see  an  approach  to  one  of  Faraday's  places  of  no  magnetic 
action. 

After  this  the  current  in  one  of  the  magnets  was  reversed  so  as  to 
make  the  poles  opposite.  Current  the  same. 

1st.  Distance  of  poles,  3  in. 

1.  5800.         2.  8200.         3.  6700. 

2nd.  Distance  of  poles,  1£  in. 

1.     9800.  2.     7500.  3.     5800. 

It  is  curious  to  note  how  the  distribution  changes  with  the  distance  of 
the  discs;  thus,  on  one  disc  free  from  the  other,  the  edge  of  the  disc 
has  the  greatest  magnetic  surface  density,  but  when  the  two  discs  form 
opposite  poles  and  are  3  in.  apart,  position  2  gives  the  greatest  effect, 
while,  when  they  are  1£  in.  apart,  the  field  is  greatest  at  the  centre. 
This  entirely  agrees  with  theory. 

The  conical  poles  for  diamagnetic  experiments  were  then  screwed  on. 
These  were  portions  of  cones  with  an  angle  at  vertex  of  about  60°,  with 
the  vertex  considerably  rounded  off.  They  were  one  inch  apart  and 
the  poles  were  opposite.  Current  4-4  farads  per  second. 


88  HENRY  A.  KOWLAND 

At  centre  of  field  between  the  poles 12500 

On  the  axis  near  one  pole 32100 

On  cone  one  inch  from  vertex 11000 

On  cylindrical  portion  of  magnet  2f  inches  from  the 

vertex  of  the  cone 5800 

These  poles  were  now  replaced  by  frustums  of  cones  with  flat  ends, 
the  original  diameter  of  the  iron,  2  inches,  being  reduced  at  the  end  to 
If  inches,  and  they  were  placed  \  inch  apart.  The  field  in  this  case 
between  them  was  61000,  or  nearly  up  to  the  maximum  of  magnetiza- 
tion of  nickel  at  common  temperatures,  and  above  that  at  high  tem- 
peratures. 

Troy,  April  1,  1875. 


11 

STUDIES  ON  MAGNETIC  DISTK1BUTION 

[Philosophical  Magazine  [4],  L,  257-277,  348-367,  1875] 
[American  Journal  of  Science  [3],  X,  325-335,  451-459,  1875;  XI,   17-29, 103-108,  1876] 

PART  I. — LINEAR  DISTRIBUTION 

CONTENTS 

I.  Preliminary  remarks. 
II.  Mathematical  theory. 

III.  Experimental  methods  for  measuring  linear  distribution. 

IV.  Iron  rods  magnetized  by  induction. 

V.  Straight  electro-magnets  and  permanent  steel  magnets. 
VI.   Miscellaneous  applications. 

I. 

In  a  paper  of  mine  published  about  two  years  ago,  I  alluded  to  some 
investigations  which  I  had  made  in  1870  and  1871  on  the  distribution 
of  magnetism.  It  is  with  diffidence  that  I  approach  this  subject,  being 
aware  of  the  great  mathematical  difficulties  with  which  it  is  surrounded. 
But  as  the  facts  are  still  in  advance  of  what  is  known  on  the  subject, 
and  as  I  see  that  other  investigators  *  are  following  hard  upon  my  foot- 
steps, I  thought  it  would  be  well  to  publish  them,  particularly  as  it  is 
no  fault  of  mine  that  they  did  not  appear  some  years  ago.2  The  mathe- 
matical theory  which  I  give,  although  not  particularly  elegant,  will  at 
least  be  found  to  present  the  matter  in  a  new  and  more  simple  light, 
and  may  be  considered  simply  as  a  development  of  Faraday's  idea  of 
the  analogy  between  a  magnet  and  a  voltaic  battery  immersed  in  water. 
I  shall  throughout  speak  of  the  conduction  of,  and  resistance  to,  lines 
of  magnetic  force,  and  shall  otherwise  treat  them  as  similar  to  lines  of 
conducted  electricity  or  heat,  it  now  being  well  established  from  the 
researches  of  Professor  Maxwell  and  others  that  this  method  gives 
exactly  the  same  results  as  the  other  method  of  considering  the  action 
to  take  place  at  a  distance. 

In  arranging  this  paper  I  have  thought  best  to  give  the  theory  of 

1  Particularly  M.  Jamin. 

2  All  the  experiments  referred  to  in  this  paper  were  made  in  the  winter  of  1870-71. 


90  HENRY  A.  BOWLAND 

the  distribution  first,  and  then  afterwards  to  see  how  the  results  agree 
with  experiment;  in  this  way  we  can  find  out  the  defects  of  the  theory, 
and  what  changes  should  be  made  in  it  to  adapt  it  to  experiment. 

At  present  I  am  acquainted  with  two  formulae  giving  the  distribu- 
tion of  magnetism  on  bar  magnets:  the  first  was  given  by  Biot,  in  his 
Traite  de  Physique  Experimentale  et  Mathematique,  vol.  iii,  p.  77,  and 
was  obtained  by  him  from  the  analogy  of  the  magnet  to  a  dry  electric 
pile,  or  to  a  crystal  of  tourmaline  electrified  by  heat.  He  compared 
his  formula  with  Coulomb's  observations,  and  showed  it  to  represent 
the  distribution  with  considerable  accuracy.  Green,  in  his  '  Essay/ 
has  obtained  a  formula  which  gives  the  same  distribution;  but  he  ob- 
tains it  by  a  series  of  mathematical  approximations  whi^h  it  is  almost 
impossible  to  interpret  physically.  M.  Jamin  has  recently  used  a 
formula  of  the  same  form;  but  I  have  as  yet  been  unable  to  find  how 
he  obtained  it.  My  own  formulae  are  also  quite  similar  to  these,  but 
have  the  advantage  of  being  obtained  in  a  more  simple  manner  than 
Green's ;  and,  what  is  of  more  consequence,  all  the  limitations  are  made 
at  once,  after  which  the  solution  is  exact;  so  that  although  they  are 
only  approximate,  yet  we  know  just  where  they  should  differ  from 
experiment. 

II. 

If  we  take  an  iron  bar  and  magnetize  one  end  of  it  either  by  a  magnet 
or  helix,  we  cause  lines  of  magnetic  induction  s  to  enter  that  end  of  the 
bar,  and,  after  passing  down  it  to  a  certain  distance,  to  pass  out  into 
the  air  and  so  round  to  the  bar  again  to  complete  their  circuit.  At 
every  part  of  their  circuit  they  encounter  some  resistance,  and  always 
tend  to  pass  in  that  direction  where  it  is  the  least:  throughout  their 
whole  course  they  obey  a  law  similar  to  Ohm's  law;  and  the  number 
of  lines  passing  in  any  direction  between  two  points  is  equal  to  the 
difference  of  magnetic  potential  of  those  points  divided  by  the  resist- 
ance to  the  lines. 

The  complete  solution  of  the  problem  before  us  being  impossible,  let 
us  limit  it  by  two  hypotheses.  First,  let  us  assume  that  the  permea- 
bility of  the  bar  is  a  constant  quantity;  and  secondly,  that  the  resist- 
ance to  the  lines  of  induction  is  composed  of  two  parts,  the  first  being 
that  of  the  bar,  and  the  second  that  of  escaping  from  the  bar  into  the 

3  For  difference  between  lines  of  magnetic  force  and  lines  of  magnetic  induction 
see  Maxwell's  'Treatise  on  Electricity  and  Magnetism,'  arts.  400,  592,  and  604. 


STUDIES  ON  MAGNETIC  DISTRIBUTION  91 

medium  -  and  that  the  latter  is  the  same  at  every  part  of  the  bar.  The 
first  of  these  assumptions  is  the  one  usually  made  in  the  mathematical 
theory  of  magnetic  induction;  but,  as  has  been  shown  by  the  experi- 
ments of  Miiller,  and  more  recently  by  those  of  Dr.  Stoletow  and  my- 
self, this  is  not  true;  and  we  shall  see  this  when  we  come  to  compare 
the  formula  with  experiment.  The  second  assumption  is  more  exact 
than  the  first  for  all  portions  of  the  bar  except  the  ends. 

Let  us  first  take  the  case  of  a  rod  of  iron  with  a  short  helix  placed  on 
any  portion  of  it,  through  which  a  current  of  electricity  is  sent.  The 
lines  of  magnetic  induction  stream  down  the  bar  on  either  side:  at 
every  point  of  the  bar  two  paths  are  open  to  them,  either  to  pass  further 
down  the  rod,  or  to  pass  out  into  the  air.  We  can  then  apply  the 
ordinary  equations  for  a  derived  circuit  in  electricity  to  this  case. 
Let  n  be  the  magnetic  permeability  of  the  iron, 

R  be  the  resistance  of  unit  of  length  of  the  rod, 

R'  be  the  resistance  of  medium  along  unit  of  length  of  rod, 

/>  be  the  resistance  at  a  given  point  to  passing  down  the  rod, 

s  be  the  resistance  at  the  end  of  the  rod, 

Q' 4  be  the  number  of  lines  of  induction  passing  along  the  rod 

at  a  given  point, 
$'.5  be  the  number  of  lines  of  induction  passing  from  the  rod 

into  the  medium  along  a  small  length  of  the  rod  JL, 
L  be  the  distance  from  the  end  of  the  rod  to  a  given  point, 

R  ' 


A  _  V  RR'  +  s 


,  dL 

+  dp=    ,57 


To  find  ft,  the  ordinary  equation  for  the  resistance  of  a  derived  cir- 
cuit gives 


whence 


4  These  are  the  surf  ace-integrals  of  magnetic  induction  (see  Maxwell's  '  Electricity,' 

art.  402) the  first  across  the  section  of  the  bar,  and  the  second  along  a  length  AZ, 

of  the  surface  of  the  bar. 

5  It  is  to  be  noted  that  Q',  when  A£  is  constant,  is  nearly  proportional    to  the  so- 
called  surface-density  of  magnetism  at  the  given  point. 


92  HENRY  A.  EOWLAND 

and 

To  find  Q',  we  have 

whence 


and 

fV^AT  HAT 

^  _«-").       .     .     (3) 


When  L  is  very  large,  or  s  =*/RR' ,  we  have 

Q'  =  CfL>  and  C: 
in  which  L/  is  reckoned  from  an  origin  at  any  point  of  the  rod. 

These  equations  give  the  distribution  on  the  part  outside  the  helix; 
and  we  have  now  to  consider  the  part  covered  by  the  helix.     Let  us 


A:  c:    E 


FIG.  1. 


limit  ourselves  to  the  case  where  the  helix  is  long  and  thin,  so  that  the 
field  in  its  interior  is  nearly  uniform. 

As  we  pass  along  the  helix,  the  change  of  magnetic  potential  due  to 
the  helix  is  equal  to  the  product  of  the  intensity  of  the  field  multiplied 
by  the  distance  passed  over  ;  so  that  in  passing  over  an  elementary  dis- 
tance dy  the  difference  of  potential  will  be  &dy.  The  number  of  lines 
of  force  which  this  difference  of  potential  causes  in  the  rod  will  be  equal 
to  Qdy  divided  by  the  sum  of  the  resistances  of  the  rod  in  both  direc- 
tions from  the  given  point.  These  lines  of  force  stream  down  the  rod 
on  either  side  of  the  point,  creating  everywhere  a  magnetic  potential 
which  can  be  calculated  by  equation  (2),  and  which  is  represented  by 
the  curves  in  Fig.  1.  In  that  figure  A  B  is  the  rod,  C  D  the  helix,  and 

cPQ' 
«  This  could  have  been  obtained  directly  from  the  equation    ,?9  =Q/ry,  and  Q/e  from 

Cl-Li' 

dQ' 
the  equation  Qfe  =  -V  A  L. 


STUDIES  ON  MAGNETIC  DISTEIBUTION  93 

E  the  element  of  length  dy.  Now,  if  we  take  all  the  elements  of  the 
rod  in  the  same  way  and  consider  the  effect  at  H  F,  the  total  magnetic 
potential  at  this  point  will,  by  hypothesis  No.  1,  be  equal  to  the  sum 
of  the  potentials  due  to  all  the  elements  dy. 

Let  4Q'  be  the  number  of  lines  of  force  produced  in  the  bar  at  the 
point  E  due  to  the  elementary  difference  of  potential  at 
that  point,  Qdy, 
AQ"  be  the  number  o*  lines  of  force  arriving  at  the  point  F  due 

to  the  same  element, 

Q"  be  the  number  of  lines  passing  from  bar  along  length  JL, 
/>„  be  the  sum  of  the  resistances  of  the  bar  in  both  directions 

from  E, 

/>zbe  resistance  at  F  in  direction  of  D, 
y  be  the  distance  D  E, 
x  be  the  distance  D  F, 
6  be  the  distance  C  D, 
s"  and  s'  be  the  resistance  of  the  bar,  &c.,  respectively  at  C  in 

the  direction  of  A,  and  at  D  in  direction  of  B, 
§  be  the  magnetizing-force  of  helix  in  its  interior. 
Let 


At y  jt^t   -r  *  AH  *v  jm,    T  *  

•**•        ~—  * — ^  »    9  •"•  ' j---,^    ^>^  7i    9 

f>*  = 


ft 


4-  e 


_ 

~  2R'r  A'A"£™-1 

This  gives  the  positive  part  of  Q"-  To  find  the  negative  part, 
change  x  into  &  —  a;,  A'  into  A",  and  A"  into  A',  and  then  change  the 
sign  of  the  whole. 

When  the  helix  is  symmetrically  placed  on  the  bar,  we  have  s'  =  s", 
A'=A";  whence,  adding  the  positive  and  negative  parts  together,  we 
have 


94  HENRY  A.  ROWLAND 

0 "  =    £J-/y      *  ~  A'     (er  (»-*>  —  £rx>)  (5^) 

ZVTU?  A'?b—  1  v 

which  gives  the  number  of  lines  of  induction  passing  out  from  the  rod 
along  the  length  AL  when  the  helix  is  symmetrically  placed  on  the  rod. 
To  get  the  number  of  lines  of  induction  passing  along  the  rod  at  a 
given  point,  we  have 

f\Z  (L  1     A  I 

where 

crt  —  1 


When  the  bar  extends  a  distance  L'  out  of  both  ends  of  the  helix,  so 
that 


if  =  */RW  and  A'  = 

we  have 


It  may  be  well,  before  proceeding,  to  define  what  is  meant  by  mag- 
netic resistance,  and  the  units  in  which  it  is  measured.  If  ft  is  the 
magnetic  permeability  of  the  rod,  we  can  get  an  idea  of  the  meaning 
of  magnetic  resistance  in  the  following  manner.  Suppose  we  have  a 
rod  infinitely  long  placed  in  a  magnetic  field  of  intensity  £  parallel  to 
the  lines  of  force.  Let  Q'  be  the  number  of  lines  of  inductive  force 
passing  through  the  rod,  or  the  surface-integral  of  the  magnetic  induc- 
tion across  its  section;  also  let  a  be  the  area  of  the  rod.  Then  by 

definition  n  =  -sL.     If  L  is  the  length  of  the  rod,  the  difference  of 

flEty 

potential  at  the  ends  will  be  LS&  ;  hence 

0'  -   L§  and  fl    -  -    L®  -   L 

^     X          '  ~  IT  ~^' 

and  R  in  the  formula?  becomes 

R  _  R,  _  .  1 

-ft  —  -jL  —  . 

L*          a/j. 

It  is  almost  impossible  to  estimate  R'  theoretically,  seeing  that  it 
will  vary  with  the  circumstances.  We  can  get  some  idea  of  its  nature, 
however,  by  considering  that  the  principal  part  of  it  is  due  to  the 
cylindric  envelope  of  medium  immediately  surrounding  the  rod.  The 
resistance  of  such  an  envelope  per  unit  of  length  of  rod  is 


STUDIES  ox  MAGNETIC  DISTRIBUTION  95 


where  D  is  the  diameter  of  the  envelope,  d  of  the  rod,  and  /JL}  the  permea- 
bility of  the  medium.  But  we  are  not  able  to  estimate  D.  If,  however, 
we  have  two  magnetic  systems  similar  in  all  their  parts,  it  is  evident 
that  beyond  a  certain  point  similarly  situated  in  each  system  we  may 

neglect  the  resistance  of  the  medium,  and  -r  will  be  the  same  for  the 

two  systems.  Hence  R'  is  approximately  constant  for  rods  of  all  diam- 
eters in  the  same  medium,  and  r  takes  the  form 

r  =  ^ 

It  is  evident  that  the  reasoning  would  apply  to  rods  of  any  section  as 
well  as  circular. 

In  Green's  splendid  essay  (Eeprint,  p.  Ill,  or  Maxwell's  '  Treatise 
on  Electricity  and  Magnetism,'  art.  439)  we  find  a  formula  similar  to 
equation  (5),  but  obtained  in  an  entirely  different  manner,  and  applying 
only  to  rods  not  extending  beyond  the  helix.  In  the  '  Keprint,'  ft 
corresponds  to  my  r;  and  its  value,  using  my  notation,  is  obtained  from 
the  equation 

•231863  —  2  hyp.  log  p  +  2p  =       _4       , ,  ....    (8) 

rd 
where  p  =  -=-. 

rd 
If  we  make  p  a  constant  in  this  formula,  we  must  have  p  ==  -^  = 

constant;  hence 


which  is  the  same  result  for  this  case  as  from  equation  (7). 

When  fj.  in  the  two  formula  is  made  to  vary,  the  results  are  not 
exactly  the  same;  but  still  they  give  approximately  the  same  results  for 
the  cases  we  shall  consider;  and  since  the  formula  is  at  the  best  only 
approximate,  we  shall  not  spend  time  in  discussing  the  merits  of  the 
two. 

III. 

Among  the  various  methods  of  measuring  linear  magnetic  distribu- 
tion, we  find  few  up  to  the  present  time  that  are  satisfactory.  Coulomb 
used  the  method  of  counting  the  number  of  vibrations  made  by  a 
magnetic  needle  when  near  various  points  of  the  magnet.  Thus,  in 


96  HENRY  A.  KOWLAND 

the  curve  of  distribution  most  often  reproduced  from  his  work,  he  used 
a  magnetized  steel  bar  27  French  inches  long  and  2  lines  in  diameter 
placed  vertically;  opposite  to  it,  and  at  a  distance  of  8  lines,  he  hung 
a  magnetic  needle  3  lines  in  diameter  and  6  lines  long,  tempered  very 
hard;  and  the  number  of  oscillations  made  by  it  was  determined.  The 
square  of  this  number  is  proportional  to  the  magnetic  field  at  that  point, 
supposing  the  magnetism  of  the  needle  to  be  unchanged;  and  this, 
corrected  for  the  magnetism  of  the  earth,  gives  the  magnetic  field  due 
to  the  magnet  alone.  This  for  points  near  the  magnet  and  distant  from 
the  ends  is  nearly  proportional  to  the  so-called  magnetic  surface-density 
opposite  the  point.  At  the  end  Coulomb  doubled  the  quantity  thus 
found,  seeing  that  the  bar  extended  only  on  one  side  of  the  needle. 

It  will  be  seen  that  this  method  is  only  approximate,  and  almost 
incapable  of  giving  results  in  absolute  measure.  The  effect  on  the 
needle  depends  not  only  on  that  part  of  the  bar  opposite  the  needle, 
but  on  portions  to  either  side,  and  gives,  as  it  were,  the  average  value 
for  some  distance;  in  the  next  place,  the  correction  at  the  end,  by 
multiplying  by  2,  seems  to  be  inadequate,  and  gives  too  small  a  result 
compared  with  other  parts.  For  at  points  distant  from  the  end  the 
average  surface-density  at  any  point  will  be  nearly  equal  to  the  average 
for  a  short  distance  on  both  sides,  while  at  the  end  it  will  be  greater 
than  the  average  of  a  short  distance  measured  back  from  the  end.  To 
these  errors  must  be  added  those  due  to  the  mutual  induction  of  the 
two  magnets. 

The  next  method  we  come  to  is  that  which  has  been  recently  used 
by  M.  Jamin,  and  consists  in  measuring  the  attraction  of  a  piece  of 
soft  iron  applied  at  different  points  of  the  magnet.  In  this  case  it 
does  not  seem  to  have  been  considered  that  the  attraction  depends  not 
only  on  the  magnetic  density  at  the  given  point,  but  also  on  that  around 
it,  and  that  a  piece  of  soft  iron  applied  to  a  magnet  changes  the  distri- 
bution immediately  at  all  points,  but  especially  at  that  where  the  iron  is 
applied.  The  change  is  of  course  less  when  the  magnet  is  of  very  hard 
steel  and  the  piece  of  soft  iron  small.  Where,  however,  we  wish  to 
get  the  distribution  on  soft  iron,  it  becomes  a  quite  serious  difficulty. 
Another  source  of  error  arises  from  the  fact  that  the  coefficient  of 
magnetization  of  soft  iron  is  a  function  of  the  magnetization:  this 
source  of  error  is  greatest  when  the  contact-piece  is  long  and  thin,  and 
is  a  minimum  when  it  is  short  and  thick  and  not  in  contact  with  the 
magnet.  Hence  this  method  will  give  the  best  results  when  the  con- 
tact-piece is  small  and  in  the  shape  of  a  sphere  and  not  in  contact  with 


STUDIES  ON  MAGNETIC  DISTRIBUTION  97 

the  magnet,  and  when  the  method  is  applied  to  steel  magnets.  But 
after  taking  all  these  precautions,  the  question  next  arises  as  to  how 
to  obtain  the  magnetic  surface-density  from  the  experiments.  Theory 
indicates,  and  M.  Jamin  has  assumed,  that  the  attractive  force  is  nearly 
proportional  to  the  square  of  the  surface-density.  But  experiment 
does  not  seem  to  confirm  this,  except  where  there  is  some  distance 
between  the  two  bodies,  at  least  in  the  case  of  a  sphere  and  a  plane 
surface,  as  in  Tyndall's  experiments  (Phil.  Mag.,  April,  1851).  It  is 
not  necessary  at  present  to  consider  the  cause  of  this  apparent  dis- 
crepancy between  theory  ar>d  experiment;  suffice  it  to  say  that  the 
explanation  of  the  phenomenon  is  without  doubt  to  be  sought  for  in 
the  variable  character  of  the  magnetizing-function  of  iron.  All  I  wish 
to  show  is  that  the  attraction  of  iron  to  a  magnet,  especially  when  the 
two  are  in  contact,  is  a  very  complicated  phenomenon,  whose  laws  in 
general  are  unknown,  and  hence  is  entirely  unsuitable  for  experiments 
on  magnetic  distribution. 

A  third  method  is  that  used  in  determining  the  correction  for  the 
distribution  on  the  magnets  in  finding  the  intensity  of  the  earth's 
magnetism.  Usually  the  distribution  is  not  explicitly  found  in  this 
case;  but  it  is  easy  to  see  how  it  might  be.  Thus,  one  way  would  be  as 
follows: — Take  the  origin  of  coordinates  at  the  centre  of  the  magnet. 
Develop  the  distribution  in  an  ascending  series  of  powers  of  x  with 
unknown  constant  coefficients.  Calculate  the  magnetic  force  due  to 
this  distribution  for  any  points  along  the  axis,  or  else  on  a  line  perpen- 
dicular to  the  magnet  at  its  centre.  Determine  the  force  at  a  series  of 
points  extending  through  as  great  a  range  and  as  near  the  magnet  as 
possible.  These  experiments  give  a  series  of  equations  from  which  the 
coefficients  in  the  expansion  can  be  determined.  Other  and  better 
methods  of  expansion  might  be  found,  except  for  short  magnets,  where 
the  method  suggested  is  very  good. 

The  similarity  of  this  method  to  that  used  by  Gauss  in  determining 
the  distribution  on  the  earth  is  apparent. 

A  fourth  method  is  similar  to  the  above,  except  that  the  lines  of 
force  around  the  magnet  are  measured  and  calculated  instead  of  the 
force. 

The  last  two  methods  are  very  exact,  but  are  also  very  laborious,  and 
therefore  only  adapted  to  special  investigations.  Thus,  by  the  change 
in  direction  of  the  lines  of  force  around  the  magnet,  we  have  a  delicate 
means  of  showing  the  change  in  distribution,  as,  for  instance,  when  the 
current  around  an  electro-magnet  varies. 


98  HENEY  A.  EOWLAND 

The  fifth  method  is  that  used  lately  in  some  experiments  of  Mr. 
Sears  (American  Journal  of  Science,  July,  1874),  but  only  adapted  to 
temporary  magnetization.  At  a  given  point  on  the  bar  a  small  coil  of 
wire  is  placed,  and  the  current  induced  in  it  measured  by  the  swing  of 
the  galvanometer-needle  when  the  bar  is  demagnetized.  It  does  not 
seem  to  have  been  noticed  that  what  we  ordinarily  consider  the  mag- 
netic distribution  is  not  directly  measured  in  this  way;  and  indeed,  to 
get  correct  results,  the  magnetization  should  have  been  reversed,  seeing 
that  a  large  portion  of  the  magnetization  will  not  disappear,  on  taking 
away  the  magnetizing-force,  where  the  bar  is  long.  The  quantity  which 
is  directly  measured  is  the  surface-integral  of  the  temporary  magnetic 
induction  across  the  section  of  the  bar,  while  the  magnetic  surface- 
density  is  proportional  to  the  surface-integral  of  magnetic  induction 
along  a  given  portion  of  the  Itar.  In  other  words,  the  quantity  measured 

is  Q  instead  of  -^L.  We  can,  however,  derive  one  from  the  other  very 
easily. 

The  sixth  and  last  method  is  that  which  I  used  first  in  1870,  and  by 
which  most  of  my  experiments  have  been  performed.  This  consists  in 
sliding  a  small  coil  of  wire,  which  just  fits  the  bar  and  is  also  very 
narrow,  along  the  bar  inch  by  inch,  and  noting  the  induced  current 
over  each  inch  by  the  deflection  of  a  galvanometer-needle.  This  meas- 
ures Q  f ,  except  for  some  corrections  which  I  now  wish  to  note.  In  the 
first  case,  to  give  exact  results,  the  lines  of  force  should  pass  out  per- 
pendicular to  the  bar,  or  the  coil  must  be  very  small.  But  even  when 
the  last  condition  is  fulfilled  errors  will  be  introduced  at  certain  por- 
tions of  the  bar.  The  error  is  vanishingly  small  in  most  cases,  except 
near  the  ends;  and  even  there  it  is  not  large,  except  in  special  cases; 
for  at  this  part  the  lines  of  force  pass  forward  toward  the  end  of  the 
bar,  and  so  the  observation  next  to  the  end  may  be  too  small,  while 
that  at  the  end  is  too  large.  The  correction  can  be  made  by  finding 
where  the  lines  of  force  through  the  centre  of  the  section  of  the  coil 
in  its  two  positions  meet  the  bar.  The  error  from  this  source  is  not 
large,  and  may  be  avoided  to  a  great  extent. 

One  very  great  advantage  in  the  method  of  induced  currents  is  the 
facility  with  which  the  results  can  be  reduced  to  absolute  measure  by 
including  an  earth-inductor  in  the  circuit  as  I  have  before  described 
(Phil.  Mag.,  August,  1873).  There  is  also  no  reaction  (except  a  tem- 
porary one)  between  the  magnet  and  current;  so  that  the  distribution 
remains  unchanged.  Hence  it  seems  to  me  that  this  method  is  the 
only  one  capable  of  giving  exact  results  directly. 


STUDIES  ON  MAGNETIC  DISTRIBUTION  99 

The  coils  of  wire  which  I  used  consisted  of  from  twenty  to  one 
hundred  turns  of  fine  wire  wound  on  thin  paper  tubes  which  just  fitted 
the  bar  and  extended  considerably  beyond  the  coils.  The  coils  were 
mostly  from  -1  to  -25  of  an  inch  wide  and  from  -1  to  -2  inch  thick.  A 
measure  being  laid  by  the  side  of  the  given  bar  under  experiment,  the 
coil  was  moved  from  one  division  of  the  rule  to  the  next  very  quickly, 
and  the  deflection  produced  on  an  ordinary  astatic  galvanometer  noted. 
After  experience  this  could  be  done  with  great  accuracy.  It  might  be 
better  in  some  cases  to  have  the  coil  slide  over  a  limited  distance  on 
the  tube,  though  for  the  use  to  which  I  intend  to  put  the  results  the 
other  is  best. 

Up  to  35°  Q  f  is  nearly  proportional  to  the  deflection;  and  when  any 
larger  value  is  put  down  in  the  Tables,  it  is  the  sum  of  two  or  more 
deflections.  I  have  not  the  data  in  most  cases  to  reduce  my  results 
to  absolute  measure,  but  took  pains  to  ensure  that  certain  series  of  ex- 
periments should  be  comparable  among  themselves. 

Having  measured  Qe  at  all  points  of  a  rod,  we  may  find  Q  by  adding 
up  the  values  of  Qf  from  the  end  of  the  rod. 

The  magnetizing  force  to  which  the  bar  was  subjected  was  in  all 
cases  a  helix  placed  at  some  part  of  the  bar.  The  iron  bars  were  of 
course  demagnetized  thoroughly  before  use  by  placing  them  in  the 
proper  position  with  reference  to  the  magnetic  meridian  and  striking 
them. 

In  the  Tables  L  is  the  distance  in  inches  from  the  zero-point,  Qf  is 
the  deflection  of  the  galvanometer  when  the  helix  is  passed  between  the 
points  indicated  in  the  first  column.  Thus,  in  Table  II,  34-7  is  the 
deflection  on  the  galvanometer  when  the  helix  was  moved  from  the 
tenth  to  the  eleventh  inch  from  the  zero-point;  and  so  we  may  con- 
sider it  as  the  value  of  Qf  at  10£  inches;  so  that  the  values  of  Q(  refer 
to  the  half  inches,  but  Q  to  the  even  inches. 

In  all  the  calculations  the  constants  in  the  formulae  were  taken  to 
represent  Q  most  nearly,  and  then  the  corresponding  formulae  for  Qe 
taken  with  the  same  constants. 

For  ease  in  calculating  by  ordinary  logarithmic  Tables,  we  may  put 

-rL 1  /ymSrt 

IV. 

Table  I  is  from  a  bar  17£  inches  long  with  a  magnetizing  helix  1£ 
inch  long  at  one  end,  the  zero-point  being  at  the  other.  Table  II  is 
from  a  bar  9  feet  long  with  a  helix  4$  inches  long  quite  near  one  end, 
the  zero-point  being  at  1  inch  from  the  helix  toward  the  long  end. 


100 


HENRY  A.  EOWLAND 


Table  III  is  from  a  bar  2  feet  long  with  a  helix  4r|  inches  long  near 
one  end,  so  that  its  centre  was  19f  inches  from  the  end  on  which  the 
experiments  were  made,  the  zero-point  being  at  the  end. 

In  adapting  the  formula  to  apply  to  the  case  of  Table  I,  we  may 
assume  that  at  the  end  of  the  bar  s  =o>  and  (7  =  0,  which  is  equivalent 
to  assuming  that  the  number  of  lines  of  induction  which  pass  out  at 
the  end  of  the  rod  are  too  small  to  be  appreciated. 

TABLE  I. 

BAR   -18  INCH  DIAMETER.     0  AT  END  OF  BAR. 


L. 

0<£ 

Q'. 
Calcu- 

Error of 

at 

Q'. 
Calcu- 

Error of 

served. 

lated. 

Q,. 

served. 

lated. 

0 

0 

0 

0 

3 

.... 

2-7 

3-5 

+    -8 

5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

2-0 
2-5 
3-2 
3-7 
4-3 
5-3 
6-5 
7-7 
9-5 

2-0 
2-4 
2-8 
3-5 
4-3 
5-2 
6-5 
8-0 
9-9 

0 
—  -1 
—  -4 
—  -2 
0 
—   -1 
0 
+    -3 
+    -4 

5-9 

7-9 
10-4 
13-6 
17-3 
21-6 
26-9 
33-4 
41-1 
50-6 

6-6 
8-6 
11-0 
13-8 
17-3 
21-6 
26-8 
33-3 
41-3 
51-2 

+    -7 
+    -7 
+    -6 
+    -2 
0 
0 
—   -1 
—   -1 
+    -2 
+    -6 

n^iCi,=,54(e™+e-™, 

In  Table  II  observations  were  not  made  over  the  whole  length  of 
the  rod,  and  the  zero-point  was  not  at  the  end  of  the  bar.  It  is  evident, 
however,  that  by  giving  a  proper  value  to  s  we  may  suppose  the  bar  to 
end  at  any  point.  As  the  rod  is  very  long,  expressions  of  the  form 

Q'—C"  =  0'^L—C"  and  Q't  =  rC'e-*L 
will  apply. 

In  Table  II  the  observations  were  near  the  end  of  the  rod,  and  were 
repeated  several  times.  Neglecting  the  end  of  the  rod,  we  have  s=oo . 

In  these  Tables  we  see  quite  a  good  agreement  between  theory  and 
observation;  but  on  more  careful  examination  we  observe  a  certain  law 
in  the  distribution  of  errors.  Thus  in  Table  I  the  errors  of  Q'  are  all 
positive  between  0  and  8  inches;  and  this  has  always  been  found  to  be 
the  case  at  this  part  of  the  bar  in  all  my  experiments. 

The  explanation  of  this  is  very  simple.  In  obtaining  the  formulae,, 
we  assumed  that  the  magnetic  permeability  of  the  bar  fj.  was  a  constant 


STUDIES  ON  MAGNETIC  DISTRIBUTION 


101 


TABLE  II. 
BAR  -39  INCH  DIAMETER.     0  AT  1  INCH  FROM  HELIX. 


L. 

served. 

Calcu- 
lated. 

Error  of 
Q^- 

Q'-C". 
Ob- 
served. 

Q'-C". 
Calcu- 
lated. 

Error  of 
Q'- 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
21 
23 
25 
27 
29 
31 

825-2 
753-5 
688-3 
628-8 
575-3 
524-1 
477-4 
434-2 
394-2 
357-0 
322-3 
290-6 
261-1 
235-4 
209-9 
187-9 
166-4 
146-4 
127-3 
94-8 
67-3 
44-3 
25-8 
11-3 
0 

902-5 
825-9 
755-1 
689-8 
629-5 
574-3 
523-1 
476-0 
432-5 
392-5 
355-6 
321-5 
290-1 
261-2 
234-5 
210-0 
187-3 
166-4 
147-1 
129-4 
97-8 
71-1 
48-6 
29-0 
12-6 
—1-2 

+    -7 
+  1-6 
+  1-5 
+    -7 
—1-0 
—1-0 
—1-4 
—1-7 
—1-7 
—1-4 
—   -8 
—   -5 
+    -1 
—    -9 
+    -1 
—    -6 
0 
+    -7 
+  2-1 
+  3-0 
+  3-8 
+  4-3 
+  3-2 
+  1-3 
—1-2 

71-7 
65-2 
59-5 
53-5 
51-2 
46-7 
43-2 
40-0 
37-2 
34-7 
31-7 
29-5 
25-7 
25-5 
22-0 
21-5 
20-0 
19-1 
32-5 
27-5 
23-0 
18-5 
14-5 
11-3 

70-8 
65-3 
60-2 
55-5 
51-2 
47-2 
43-5 
40-1 
37-0 
34-1 
31-4 
28-9 
26-6 
24-6 
22-7 
20-9 
19-3 
17-8 
31-5 
26-7 
22-8 
19-4 
16-5 
14-0 

—    -9 
+    -1 
+    -7 
+  2-0 
0 
+    -5 
+    -3 
+    -1 
—   -2 
—   -6 
—   -3 
—   -6 
+    -9 
—   -9 
+    -7 
—   -6 
.7 

—1-3 
—1-0 

—   -8 
—   -2 
+    -9 
+  2-0 

+  2-7 

Qf  _C'//=983r-o8i35z;_80-5=983-(10)--o<«tfA_80-5. 

quantity;  but  it  has  been  shown  by  Dr.  Stoletow  and  myself,  independ- 
ently of  each  other,  that  JJL  increases  as  the  magnetism  of  the  bar  in- 
creases when  the  latter  is  not  great.  Hence  between  0  and  8  inches 
the  resistance  of  the  bar,  R,  is  greater  than  at  succeeding  points,  and 
hence  a  less  number  of  lines  of  induction  pass  down  the  bar  from  8 
towards  0  than  would  be  given  by  the  formula,  which  has  been  adapted 
to  the  average  value  of  E  at  from  9  to  14  inches.  In  Table  II  this 
same  fact  shows  itself  towards  the  end  of  the  Table,  and  would  prob- 
ably be  more  prominent  had  the  Table  been  carried  further.  However, 
in  this  Table  all  things  have  combined  to  satisfy  the  formula  with  great 
accuracy. 

In  Table  III  we  come  across  a  fact  of  an  entirely  different  nature 
from  the  above.  Fig.  2  is  the  plot  of  this  Table,  and  gives  the  values 
of  Q'(  at  different  parts  of  the  rod. 


102 


HENRY  A.  EOWLAND 


TABLE  III. 
BAB  -39  INCH  DIAMETER.     0  AT  END  OF  BAR. 


L. 

served. 

Qe. 

Calcu- 
lated. 

Error  of 

served. 

Q'- 
Calcu- 
lated. 

Error  of 
Q'- 

o 

0- 

o 

0 

1 
2 
3 

19-7 
16-3 
16-0 

15-2 
15-3 
15-5 

—4-5 
—1-0 
—   -5 

19-7 
36-0 
52-0 

15-2 
30-5 
46-0 

—4-5 
—5-5 
—6-0 

4 
5 
6 

15-8 
16-5 
17-0 

15-9 
16-3 
16-9 

+    -1 
—   -2 
—   -1 

67-8 
84-3 
101-3 

61-8 
78-1 
95-0 

—6-0 
—6-2 
—6-3 

7 
8 
9 
10 
11 
12 
13 
14 
15 
16 

17-6 
18-4 
19-2 
20-3 
21-8 
22-8 
84-8 
26-8 
28-8 
31-8 

17-6 
18-4 
19-4 
20-5 
21-7 
23-1 
24-7 
26-5 
28-4 
30-5 

0 
0 
+    -2 
+    -2 
—   -1 
+    -3 
—   -1 
—   -3 
—   -4 
—1-3 

118-9 
137-3 
156.5 
176-8 
198-6 
221-4 
246-2 
273-0 
301-8 
333-6 

112-6 
130-9 
150-3 
170-7 
192-2 
215-3 
239-9 
266-4 
294-6 
325-1 

—6-3 
—6-4 
—  6-2 
—6-1 
—6-4 
—6-1 
—6-3 
—6-6 
—7-2 
—8-5 

Q't  =7-6(10  os7t-)-io-'OS7L);    Q'=89(10  «37i  10-°37t). 

The  horizontal  line  in  the  figure  represents  values  of  L,  and  the  verti- 
cal ordinates  are  values  of  Q'g.  The  full  line  gives  the  observed  dis- 
tribution, and  the  dotted  line  that  according  to  the  formula. 


15  10  5  O 

FIG.  2. — Distribution  at  end  of  bar. 

The  formula  gives  the  distribution  very  nearly  for  all  points  except 
those  near  the  end.  The  formula  indicates  that  Q'f  decreases  contin- 
ually toward  the  end;  but  by  experiment  we  see  that  it  increases  near 
this  point.  On  first  seeing  this,  I  thought  that  it  was  due  to  some 
residual  magnetism  in  the  bar;  but  after  repeating  the  experiment 
several  times  with  proper  care,  I  soon  found  that  this  was  always  the 
case.  I  give  the  following  explanation  of  it : — In  the  f ormulse  we  have 
assumed  R',  the  resistance  of  the  medium,  to  be  a  constant;  now  this 
resistance  includes  that  of  the  lines  of  force  as  they  pass  from  the  rod 
through  the  medium  and  thus  back  to  the  other  end  of  the  rod ;  and  of 


STUDIES  ON  MAGNETIC  DISTRIBUTION  103 

this  whole  quantity  the  part  which  affects  the  relative  distribution  at 
any  part  of  the  rod  most  is  that  of  the  medium  immediately  surrounding 
that  part;  and  so  the  parts  near  the  end  have  the  advantage  over  those 
further  back,  inasmuch  as  the  lines  can  pass  forward  as  well  as  outward 
into  the  medium.  The  same  thing  takes  place  in  the  case  of  the  dis- 
tribution of  electricity,  where  the  "density"  is  inversely  proportional 
to  the  resistance  which  the  lines  of  inductive  force  experience  from 
the  medium;  and  here  we  find  that  the  "density"  is  greatest  on  the 
projections  of  the  body,  showing  that  the  resistance  to  the  lines  of  in- 
duction is  less  in  such  situations,  and  by  analogy  showing  that  this 
must  also  be  the  case  for  lines  of  magnetic  force.  But  this  effect  is 
not  very  great  in  cylinders  until  quite  near  the  end;  for  Coulomb,  in  a 
long  electrified  cylinder,  has  found  the  density  at  one  diameter  back 
from  the  end  only  1-25  times  that  at  the  centre;  and  so  there  is  prob- 
ably a  long  distance  in  the  centre  where  the  density  is  sensibly  constant. 
Hence  we  may  suppose  that  our  second  hypothesis,  that  R'  is  a  con- 
stant, will  be  approximately  correct  for  all  parts  of  a  bar  except  the 
ends,  though  of  course  this  will  vary  to  some  extent  with  the  distribu- 
tion of  the  lines  in  the  medium;  at  least  the  change  in  E'  will  be 
gradual  except  near  the  end,  and  so  may  be  partially  allowed  for  by 
giving  a  mean  value  to  r. 

Hence  we  see  that  could  the  formula  be  so  changed  as  to  include 
both  the  variation  of  R  and  of  R',  it  would  probably  agree  with  the 
three  Tables  given. 

To  study  the  effect  of  variation  in  the  permeability  more  carefully, 
we  can  proceed  in  another  manner,  and  use  the  formulae  only  to  get 
the  value  of  r  at  different  parts  of  the  rods. 

No  matter  how  r  may  vary,  equations  (2)  and  (3)  will  apply  to  a  very 
small  distance  Z  along  the  rod;  and  as  the  orgin  of  coordinates  may  be 
at  any  point  on  the  rod,  if  Qr  and  Q'f  are  taken  at  one  point  and  Q  and 
Qt  at  another  point  whose  distance  from  the  first  is  Z,  we  shall  have  the 
four  equations 


Calling  "•  =H  and  ?  =  G,  we  shall  find,  on  eliminating  C  and  A 
and  developing  £r'  and  ?~rt, 


104 


HENRY  A.  EOWLAND 


?m»1**±*-i), 

f    \  (jf  +  ti  / 


or,  to  a  greater  degree  of  approximation, 


r"  — 


+  1-6 


(9ft) 


Before  applying  these  formulae  to  any  series  of  observations,  the 
latter  should  be  freed  from  most  of  the  irregularities  due  to  accidental 
causes.  For  this  purpose  the  following  Tables  have  been  plotted  and  a 
regular  curve  drawn  to  represent  as  nearly  as  possible  the  observations; 
in  other  cases  a  column  of  differences  was  formed  and  plotted.  In 
either  case  the  ordinates  of  the  curves  were  accepted  as  the  true  quan- 
tities. But,  for  fear  that  some  might  accuse  me  of  tampering  with  my 
observations,  I  have  in  all  cases  added  these  as  they  were  obtained. 

TABLE  IV. 
BAR  -19  INCH  DIAMETER.     0  AT  CENTRE  OF  BAR. 


L. 

Qe- 

Observed. 

Qi. 

Corrected. 

Q'. 
Corrected. 

r"     IT 

1       K' 
r2~  K 

1 

2 
3 
4 
5 

24-0 
17-0 
13-7 
11.  6 

10-2 

24-0 
17-0 
13-7 
11-65 
10-15 

151-7 
127-7 
110-7 
97.0 
85-4 

•041 
•0256 
•0192 
•0168 

24.4 
39-1 
52-1 
59-5 

9-0 

9-0 

•0150 

66-7 

7 
8 

8-0 
7-1 

8.0 
7-15 

66-2 

58-2 

•0142 
•0150 

70-4 
66-7 

9 
10 
11 
12 
13 
14 
15 
28^ 

6-4 
5-7 
4-9 
4-4 
3-6 
3-3 
22-4 

6-35 
5-65 
5-0 
4-4 
3.9 
3-4 
22-4 

51-1 
44-7 
39-1 
34-1 
29-7 
25-8 
22-4 

•0159 
•0160 
•0167 
•0180 
•0184 
•0184 

62-9 
52-5 
59-9 
55-6 
54-3 
54-3 

The  correction  is  necessary,  because  small  irregularities  in  the  obser- 
vations will  produce  immense  changes  in  r2. 

Table  IV  contains  some  of  the  best  observations  I  have  obtained. 
It  is  from  a  bar  57  inches  long  with  a  helix  1|  inch  long  in  the  centre 
to  magnetize  it.  Each  quantity  is  the  mean  of  six  observations,  these 
being  made  on  both  ends  of  the  bar  and  with  the  current  in  opposite 
directions. 

In  this  Table  a  source  of  error  was  guarded  against  which  I  have  not 


STUDIES  ON  MAGNETIC  DISTRIBUTION  105 

seen  mentioned  elsewhere.  When  a  bar  of  iron  is  magnetized  at  any 
part  and  the  distribution  over  the  rest  quickly  measured,  on  being  then 
allowed  to  stand  some  time  and  the  distribution  again  taken,  it  will  have 
changed  somewhat,  the  magnetism  having,  as  it  were,  crept  down  the 
bar  further.  Hence  in  this  Table  time  was  allowed  for  the  bar  to  reach 
its  permanent  state. 

1      Rr 
On  looking  over  column  6,  which  contains  the  values  of  -^  —  -^  =  R'a/i 

(equation  7),  we  observe  that  as  Q'  decreases,  the  value  of  R'ap.  first 
increases  and  then  decreases.  Now  it  is  not  probable  that  R'  undergoes 
any  sudden  change  of  this  sort;  and  so  it  is  probably  due  to  change  in 
the  permeability  of  the  rod.  Hence  by  this  method  we  arrive  at  the 
same  results  as  by  a  more  direct  and  exact  method.7  But  by  this  means 
we  are  able  to  prove  in  the  most  unequivocal  manner  that  magnetic 
permeability  is  a  function  of  the  magnetization  of  the  iron  and  not  of  the 
magnetizing  force.  Hence  it  is  that  I  have  preferred,  in  my  papers  on 
Magnetic  Permeability,  to  consider  it  in  this  way  in  the  formulae  and 
also  in  the  plots,  while  Dr.  Stoletow  (in  his  paper,  Phil.  Mag.,  January, 
1873)  plots  the  magnetizing-function  as  a  function  of  the  magnetizing 
force. 

When  we  plot  the  results  in  this  Table  with  reference  to  Q'  and  R'a^, 
the  effect  of  the  variation  of  R'  is  apparent;  and  we  see,  on  comparing 
the  curve  with  those  given  in  my  paper  above  referred  to,  that  R'  in- 
creases as  L  increases,  at  least  between  L  =  2  and  L  =  8,  which  is  as 
we  should  suppose  from  the  arrangement  of  the  apparatus.  For  this 
Table  I  happen  to  have  data  for  determining  Q  in  absolute  measure; 
and  these  show  that  the  maximum  value  of  n  should  be  about  where 
the  Table  shows  it  to  be. 

This  method  of  finding  the  variation  of  p  is  analogous  to  that  of 
finding  conductivity  for  heat  by  raising  the  temperature  of  one  end 
of  a  bar  and  noting  the  distribution  of  heat  over  the  bar;  indeed  the 
curves  of  distribution  are  nearly  the  same  in  the  two  cases. 

If  it  were  thought  worth  while,  it  would  be  very  easy  to  obtain  a 
curve  of  magnetic  distribution  for  a  rod  and  then  enclose  the  whole 
rod  in  a  helix  and  determine  its  curve  of  permeability.  This  would 
give  data  for  determining  R'  in  absolute  measure  at  every  point  of  the 
rod. 

To  complete  the  argument  that  the  variation  of  rz  is  in  great  measure 
due  to  that  of  //,  I  have  caused  the  magnetizing  force  on  a  bar  to  vary. 

7  Phil.  Mag.,  August,  1873. 


106 


HENRY  A.  EOWLAND 


Tables  V,  VI,  and  VII  are  from  a  bar  9  feet  long  and  -25  inch  in 
diameter.  At  the  centre  a  single  layer  of  fine  wire  was  wound  for  a 
distance  of  1  foot;  and  the  current  for  magnetizing  the  bar  was  sent 
through  this.  The  zero-point  was  at  the  centre  of  this  helix  and  at  the 
centre  of  the  bar;  so  that  the  observations  on  the  first  6  inches  include 
the  part  of  the  bar  covered  by  the  helix. 

The  values  of  Q'f  are  the  sum  of  four  observations  on  each  end  of 
the  bar  and  with  the  current  reversed.  The  three  Tables  are  compar- 
able with  each  other,  the  same  arbitrary  unit  being  used  for  all. 

TABLE  V. 
MAGNETIZING  CURRENT  -176. 


L. 

fe 

served. 

Qe- 

Cor- 
rected. 

Cor- 
rected. 

•** 

1    R' 

F'=R~- 

Qe". 

Calcu- 
lated. 

0 

2-7 

2-40 

1 

6-9 

7-32 

2 

12-7 

12-54 

3 

18-2 

18-31 

4 

24-4 

24-87 

5 
6 
•  7 
8 
9 
10 
11 
12 
13 
14 
15  . 
16 
17  j. 
18  ' 
End. 

32-4 
31-5 
28-2 
24-9 
21-4 
18-6 
16-8 
14  2 
12-0 

17-7 

11-6 
22-4 

31-7 
32-0 
28-2 
24-7 
21-7 
19-0 
16-4 
14-2 
12-0 
10-0 
8-2 
6-6 
5-1 
22-4 

220-5 
188-5 
160-3 
135-6 
113-9 
94-9 
78-5 
64-3 
52-3 
42-3 
34-1 
27-5 
22-4 

•0190 
•0212 
•0218 
•0236 
•0252 
•0278 
•0311 
•0367 
•0404 
•0440 
•0445 
•0570 

52-4 

47-2 
45-9 
42-4 
39-7 
36-0 
32-2 
27-2 
24-8 
22-7 
22-5 
17-5 

32-38 
£ 

A    ^ 

II 

OS 
00 

f 

t-L 

o 

3 

r 

o 

o 

H 

Here  we  see  an  excellent  confirmation  of  the  results  deduced  from 
Table  IV.  In  Table  V,  where  the  magnetizing  force  is  very  small,  and 
where,  consequently,  no  part  of  the  iron  has  yet  reached  its  minimum 

1      R' 
resistance,  the  value  of  —t  ~  ^  —  R'ap.  decreases  continually  as  the  value 

of  Q'  decreases,  as  it  should  do.     In  Table  VI,  with  a  higher  magnetiz- 
ing power,  which  was  sufficient  to  bring  a  portion  of  the  bar  to  about 

the  minimum  resistance,  we  see  that  -5  remains  nearly  stationary  for  a 

short  distance  from  the  helix  and  then  decreases  in  value.     In  Table 
VII,  where  the  bar  is  highly  magnetized  and  the  portion  near  the  zero- 


STUDIES  ON  MAGNETIC  DISTRIBUTION 


107 


TABLE  VI. 
MAGNETIZING  CURRENT  -31. 


L. 

Si 

served. 

CoV- 
rected. 

Cor- 
rected. 

t-2. 

r* 

9''- 
Calcu- 
lated. 

0 

16-3 

17-3 

2 

22-0 

22-3 

3 

32-4 

32-28 

4 

43-8 

43-34 

5 
6 

7 
8 
9  I 

11  i 

8 
gj 

16  ( 
17  f 

1ft    I 

55-9 
55-2 
46-8 

81-3 
61-8 
46-4 
35-4 
22-0 

55-1 
48-1 
42-3 
37-4 
33  0 
29-0 
25-3 
21-9 
18-7 
15-6 
12-7 
9-8 

391-9 
336-8 
288-7 
246-4 
209  0 
176-0 
147-0 
121-7 
99-8 
81-1 
65-5 
52-8 

•0204 
•0201 
•0202 
•0220 
•0243 
•0262 
•0300 
•0352 
•0405 
•0479 

49-0 
49-7 
49-5 
45-5 
41-2 
38-2 
33-3 
28-4 
24-7 
20-9 

55-90 

#3 

V 

p 

I 

r 

o 

End. 

43-0 

_ 

TABLE  VII. 
MAGNETIZING  CURRENT  1-12. 


L. 

served. 

& 

Cor- 
rected. 

Cor- 
rected. 

r2. 

1 
r* 

Qi'. 
Calcu- 
lated. 

0 

762-4 

1 

3-5 

758  •  9 

.... 

.... 

2-58 

2 

9-4 

.... 

749-5 

.... 

.... 

8-29 

3 

15-4 

734-  1 

.... 

15-78 

4 
5 

6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18  ^ 
19} 
20  * 

27-5 
44-3 
66-6 
71-2 
59-5 
51-0 
45-2 
40-3 
36-3 
33-3 
30-6 
28-1 
25-6 
23-4 
20-0 

34-0 

71-2 
59-7 
51-2 
45-2 
40-3 
36-8 
33-5 
30-5 
28-0 
25-4 
22-7 
20-3 
18-1 
16-0 

706-6 
662-3 
595-7 
524-5 
464'-  8 
413-6 
368-4 
328-1 
291-3 
257-8 
227-3 
199-3 
173-9 
151-2 
130-2 
112-8 
96-8 

•0239 
•0200 
•0162 
•0141 
•0120 
•0107 
•0110 
•0116 
•0118 
•0140 
•0147 
•0161 
•0180 

41-8 
50-0 
61-7 
70-9 
83-3 
93-5 
90-9 
86-2 
84-7 
71-4 
68-0 
62-1 
55-6 

26-70 
43-36 
69-37 

if 

0 

it 
I 

r 

o 

J 

End. 

108  HENEY  A.  ROWLAND 

points  approaches  the  maximum  of  magnetization,    a  increases  in  value 

as  we  pass  down  the  bar;  and  having  reached  its  maximum  at  L=  11£ 
nearly,  it  decreases.  These  Tables,  then,  show  in  the  most  striking 
manner  the  effect  of  the  variation  of  the  magnetic  permeability  of  iron 
upon  the  distribution  of  magnetism. 

It  is  evident  that  these  Tables  also  give  the  data  for  obtaining  the 
relative  values  of  R'  at  different  parts  of  the  bar;  but  the  results  thus 
obtained  are  conflicting,  and  will  need  further  experiment  to  obtain 
accurate  results.  Where  such  a  small  magnetizing  force  is  used  as  in 
Table  V  it  is  almost  impossible  to  attain  accuracy ;  and  allowance  should 
be  made  for  this  in  deducing  results  from  it.  The  greatest  liability  to 
error  is  of  course  where  the  magnetization  is  small;  for  any  small  re- 
sidual magnetism  which  the  bar  may  contain  will  be  more  apparent 
here — although  great  care  was  taken  to  remove  all  residual  magnetism 
before  use.  Besides  this  there  are  many  other  disturbances  from  which 
the  higher  magnetizing  powers  are  free. 

If  we  accept  Green's  formula  as  correct,  these  observations  give  us  data 
for  determining  the  magnetizing-f unction  of  iron  in  a  unique  manner,  for 
nearly  all  other  methods  depend  on  absolute  measurements  of  some 
kind.  Thus  the  least  value  of  rz  in  Table  IV  for  a  rod  -19  inch  diam- 
eter is  -0142,  which  gives  p=  -01132,  which  in  Green's  formula  (equa- 
tion 8)  gives  //=3388  for  the  greatest  permeability  of  this  iron;  and 
this  is  as  nearly  right  as  we  can  judge  for  this  kind  of  iron.  It  is  to  be 
noted  that  Green's  formula  has  been  found  for  the  portion  of  the  bar 
covered  by  the  helix;  but,  as  seen  from  my  formulse,  it  will  approxi- 
mately apply  to  all  portions,  though  it  would  be  better  to  find  a  new 
formula  for  each  case. 

We  shall,  toward  the  last,  resume  this  subject  again;  and  so  will  leave 
it  for  the  present. 

The  results  which  I  have  now  given,  and  indeed  all  the  results  of  this 
paper,  have  been  deduced  not  only  from  the  observations  which  I  pub- 
lish, but  from  very  many  others;  so  that  my  Tables  may  be  considered 
to  represent  the  average  of  a  very  extended  series  of  researches,  though 
they  are  not  really  so. 

V. 

Let  us  now  consider  the  case  of  that  portion  of  the  bar  which  is 
covered  by  the  helix.  First  of  all,  when  the  helix  is  symmetrically 
placed  on  the  rod,  equations  (5)  and  (6)  will  apply.  As  Q"  is  the 


STUDIES  ox  MAGNETIC  DISTRIBUTION 


109 


quantity  which  is  usually  taken  to  represent  the  distribution  of  mag- 
netism, being  nearly  proportional  to  the  "surface-density"  of  mag- 
netism, I  shall  principally  discuss  it. 

In  the  first  place,  then,  this  equation  (5)  shows  that  the  distribution 
of  magnetism  in  a  very  elongated  electromagnet,  and  indeed  in  a  steel 
magnet,  does  not  change  when  pieces  of  soft  iron  bars  of  the  same 
diameter  as  the  magnet  are  placed  against  the  poles,  provided  that  equal 
pieces  are  applied  to  both  ends;  otherwise  there  is  a  change.  This  result 
would  be  modified  by  taking  into  account  the  variation  of  the  permea- 
bility, &c. 

Let  us  first  consider  the  case  where  the  rod  projects  out  of  the  end 
of  the  helix,  as  in  Tables  V,  VI,  and  VII.  By  giving  proper  values  to 
the  constants,  we  obtain  the  results  given  in  the  last  column  of  the 

TABLE  VIII. 


Strength  of  magnetizing  current. 

•108. 

•194. 

•378. 

•600. 

0 

1 

2 

!2-7 
2-4 

3-2 

2-7 

•7 
•9 
•9 

•6 
•6 

•8 

3-3 

3-9 

1-7 

•8 

4-0 

6-0 

4-0 

3-2 

6 

5-7 

8-7 

9-3 

14-7 

Tables.  The  agreement  with  observation  is  in  most  cases  very  perfect. 
We  also  see  the  same  variation  of  r  that  we  before  noticed  in  the  rest  of 
the  curves,  and  we  see  that  it  is  in  just  the  direction  theory  would 
indicate  from  the  change  of  p. 

In  these  Tables  we  come  to  a  very  important  subject,  and  one  to 
which  I  called  attention  some  years  back — namely,  the  change  in  the 
distribution  when  the  magnetizing  force  varies,  and  which  is  due  to  change 
of  permeability.  The  following  Tables  and  figures  show  this  extremely 
well,  and  are  from  very  long  rods  with  a  helix  a  foot  long  at  their 
centre,  as  in  the  last  three  Tables.  The  bar  in  both  these  Tables  was 
•19  inch  in  diameter  and  5  feet  long.  The  zero-point  was  at  the  centre 
of  the  bar  and  of  the  helix.  The  Tables  give  values  of  Q'e  for  the 
magnetizing  forces  which  appear  at  the  head  of  each  column,  and  which 
are  the  tangents  of  the  angles  of  deflection  of  the  needles  of  a  tangent- 
galvanometer.  Table  VIII  only  gives  the  part  covered  by  the  helix. 
Both  Tables  are  from  the  mean  of  both  ends  of  the  bar. 


110 


HENRY  A.  EOWLAND 


These  experiments  show  in  the  most  positive  manner  the  effect  we 
are  considering;  and  we  are  impressed  by  them  with  the  great  compli- 
cation introduced  into  magnetic  distribution  by  the  variable  character 
of  magnetic  permeability. 

In  Fig.  3  I  have  represented  the  distribution  on  half  the  bar,  as  given 
in  Table  IX,  the  other  half  being  of  course  similar.  Here  the  greatest 

TABLE  IX. 


X. 

C. 

•257. 

B. 
•363. 

A. 
1-303. 

I) 

2-5 

3-1 

1-1 
1-3 

ii 

7-2 

4-1 
5-9 

2-1 
4-0 

6-1 

8-2 

9-6 

7-7 

10-9 

18-6 

6 

7-9 

11-5 

21-3 

7 

6-5 

9-0 

16-8 

10 
12 
15 
18 
30 

10-0 
6-2 
5-0 
2-0 
2-0 

15-0 
10-9 
9-8 
4-7 
3-6 

27-4 
20-9 
21-5 
14-8 
16-5 

0  5  10  15  20 

FIG.  3. — Plot  of  Table  IX,  showing  surface-density  for  different  values  of  the 

magnetizing  force. 

change  is  observed  in  the  part  covered  by  the  helix,  though  there  is 
also  a  great  change  in  the  other  part.  These  Tables  show  that,  as 
the  magnetization  of  the  bars  increases,  at  least  beyond  a  certain  point, 
the  curves  on  the  part  covered  by  the  helix  increase  in  steepness;  and 
the  figure  even  shows  that  near  the  middle  of  the  helix  an  increase  of 
magnetizing  force  may  cause  the  surface-density  to  decrease;  and  Table 
VIII  shows  this  even  better.  Should  we  calculate  Q",  however,  we 
should  always  find  it  to  increase  with  the  magnetizing  force  in  all  cases. 
These  effects  can  be  shown  also  in  the  case  where  the  bar  does  not 


STUDIES  ON  MAGNETIC  DISTRIBUTION 


111 


extend  beyond  the  helix,  but  not  nearly  so  well  as  in  this  case,  seeing 
that  here  Q"  can  obtain  a  greater  value. 

Assuming  that  /u  is  variable,  the  formula  indicates  the  same  change 
that  we  observe;  for  as  Q"  increases  from  zero  upwards,  ft  will  first 
increase  and  then  decrease ;  so  that  as  we  increase  the  magnetizing  force 
from  zero  upwards,  the  curve  should  first  decrease  in  steepness  and 
then  increase  indefinitely  in  steepness.  In  these  Tables  the  decrease 
of  steepness  is  not  very  apparent,  because  the  magnetization  is  always 
too  great;  and  indeed  on  this  account  it  is  difficult  to  show  it;  but  in 
Tables  V,  VI,  and  VII  this  action  is  shown  to  some  extent  by  the 

TABLE  x. 


x  and  L. 

A. 
•245. 

B. 
•360. 

C. 

•600. 

D. 
1-09. 

0 

+  17-6 

+  29-4 

+  52-0 

+  108-7 

+    9-6 

+  16-8 

+  31-5 

+    60-1 

+    7-4 

+  13-1 

+  24-3 

+    45-8 

3 

+   5-4 

+    9-8 

+  19-1 

+    34-1 

+    3-4 

+    7-2 

+  14-7 

+    22-8 

5 

+   2-0 

+    4-6 

+   9-9 

+   16-0 

6 

-f   0-6 

+    2-4 

+    5-4 

+      9-6 

7 

—  0-8 

+   0-3 

+    1-2 

+      0-6 

—  1-8 

—  1-6 

—  2-1 

—     0-3 

9 
1  f\ 

—  30 

—  3-6 

—  6-6 

—     8-8 

10 

—  5-0 

—  6-3 

—  8-6 

—  15-6 

11 

—  7-4 

—10-0 

—16-4 

—  27-1 

12 

—  8-4 

—10-0 

—16-9 

—  26-5 

13 

—  6-0 

—  7-9 

—14-5 

—  22-6 

14 

—  5-2 

—  -7-0 

—12-5 

—  21-0 

15 

~i  a 

—  5-3 

—11-9 

—  19-0 

16 

—  9-4 

—19-1 

—  31-2 

18 

OA 

—  5-3 

—15-2 

20 

—  6-5 

—19-3 

24 

Ort 

—  5-6 

—  6-0 

OO 

_  0-7 

—  1-2 

48 

values  of  r  in  the  formulae.  The  change  of  distribution  with  the  helix 
arranged  in  this  way  at  the  centre  of  the  bar  is  greater  than  in  almost 
every  other  case,  because  the  magnetism  of  the  bar,  Q",  can  change 
greatly  throughout  the  whole  length  of  the  helix,  and  thus  the  value 
of  r  be  changed,  and  so  the  distribution  become  different. 

The  next  case  of  distribution  which  I  shall  consider  is  that  of  a  very 
long  rod  having  a  helix  wound  closely  round  it  for  some  distance  at 
one  end. 

Table  X  is  from  a  bar  9  feet  long  with  a  helix  wound  for  one  foot 
along  one  end.  The  bar  was  -25  inch  in  diameter.  All  except  the  first 


112 


HENRY  A.  KOWLAND 


column  is  the  sum  of  two  results  with  the  current  in^  opposite  direc- 
tions, and  after  letting  the  bar  stand  for  some  time,  as  indeed  was  done 
in  nearly  every  case.  The  first  column  contains  twice  the  quantities 
observed,  so  as  to  compare  with  the  others.  The  zero-point  was  at  the 
end  of  the  bar  covered  by  the  helix. 

The  value  of  Q"^  between  0  and  1  includes  the  lines  of  force  passing 
out  at  the  end  of  the  bar,  and  is  therefore  too  large. 

In  Fig.  4  we  have  a  plot  of  the  results  found  for  this  bar.  The 
curves  are  such  as  we  should  expect  from  our  theory,  except  for  the 
variations  introduced  by  the  causes  which  we  have  hitherto  considered. 
Thus  the  sharp  rise  in  the  curve  when  near  the  end  of  the  bar  has 
already  been  explained  in  connection  with  Table  III.  A  small  portion 


FIG.  4.— Plot  of  Table  X. 

of  it,  however,  is  due  to  those  lines  of  induction  which  pass  out  through 
the  end  section  of  the  bar;  and  in  future  experiments  these  should  be 
estimated  and  allowed  for.* 

To  estimate  the  shape  of  the  curve  theoretically  in  this  case,  let  us 
take  equation  (4)  once  more,  and  in  it  make  s'=oo  and  s"  =  \/TZR', 
which  will  make  it  apply  to  this  case.  We  shall  then  have  A'  =  —  1, 
and  A"  =o>,  whence  for  the  positive  part  of  Q'f'  we  have 


2R'rl 
and  for  the  negative  part 

(1  +  e* 


_     -rxN  . 


8  When  considering  surface-density,  we  should  also  allow  for  the  direct  action  of 
the  helix,  though  this  is  always  found  too  small  to  be  worth  taking  into  account 
except  in  very  accurate  experiments. 


STUDIES  ox  MAGNETIC  DISTRIBUTION 
therefore  the  real  value  is 

Q,,  _    &AL    f       (Z_b},         b  _  o\       ,      f-rx\   . 

U<  ~        2R'r  C 
And  if  x  is  reckoned  from  the  end  of  the  rod,  we  have 


113 


(10) 


When  x  =  0,  this  becomes 


and  when  x  =  b,  it  becomes 


the  ratio  of  which  is 


and  this  is  the  ratio  of  the  values  of  Q"  at  the  ends  of  the  helix. 
When  &  is  12  inches,  as  in  this  case,  we  get  the  following  values  of  this 
ratio  :  — 


r— 

•05. 

•1. 

•15. 

•20. 

•30. 

00. 

-*(£-*-!)  = 
—2 

•2256 
4-43 

•3494 
2-86 

•4173 
2-40 

•4546 
2-20 

•4863 
2-06 

•500 
2-00 

e-'-*—  1 

To  compare  this  with  our  experiments,  let  us  plot  Table  X  once  more, 
rejecting,  however,  the  end  observations  and  completing  the  curve  by 
the  eye,  thus  getting  rid  of  the  error  introduced  at  this  point.  We  then 
find  for  this  ratio,  according  to  the  different  curves, 

B.  C.  D. 

2-1  2-3  3-2 

It  is  seen  that  these  are  all  above  the  limit  2,  as  they  should  be — 
though  it  is  possible  that  it  may  fall  below  in  some  cases,  owing  to  the 
variation  of  the  permeability.  As  the  magnetization  increases,  the 
values  of  the  above  ratio  show  that  r  decreases,  as  we  should  expect  it 
to  do  from  the  variation  of  /*. 

To  find  the  neutral  point  in  this  case,  we  must  have  in  formula  (10) 


114 


HENRY  A.  EOWLAND 


where  x  is  the  distance  of  the  neutral  point  from  the  end.     Making 
b  =  12,  we  have  from  this : — 


r= 
x= 

•05. 

•10. 

•15. 

•20. 

•30. 

00  . 

10-1 

8-96 

8-31 

7-89 

7-39 

6-00 

By  experiment  we  find  that  the  neutral  point  is,  in  all  the  cases  we 
have  given  in  Table  X,  between  7-5  and  8-1  inches,  which  are  quite 
near  the  points  indicated  by  theory  for  the  proper  values  of  r,  though 
we  might  expect  curve  D  to  pass  through  the  point  x  =  9,  except  for 
the  disturbing  causes  we  have  all  along  considered. 

Our  formulae,  then,  express  the  general  facts  of  the  distribution  in 
this  case  with  considerable  accuracy. 

These  experiments  and  calculations  show  the  change  in  distribution 
in  an  electromagnet  when  we  place  a  piece  of  iron  against  one  pole  only. 
In  an  ordinary  straight  electromagnet  the  neutral  point  is  at  the 
centre.  When  a  paramagnetic  substance  is  placed  against  or  near  one 
end,  the  neutral  point  moves  toward  it;  but  if  the  substance  is  diamag- 
netic  it  moves  from  it. 

The  same  thing  will  happen,  though  in  a  less  degree,  in  the  case  of  a 
steel  magnet;  so  that  its  neutral  point  depends  on  external  conditions 
as  well  as  on  internal. 

We  now  come  to  practically  the  most  interesting  case  of  distribution, 
namely  that  of  a  straight  bar  magnetized  longitudinally  either  by  a 
helix  around  it,  or  by  placing  it  in  a  magnetic  field  parallel  to  the  lines 
of  force;  we  shall  also  see  that  this  is  the  case  of  a  steel  magnet  mag- 
netized permanently.  This  case  is  the  one  considered  by  Biot  (Traite 
de  PJiys.,  tome  iii,  p.  77)  and  Green  (Mathematical  Papers  of  the  late 
George  Green,  p.  Ill,  or  Maxwell's  '  Treatise/  art.  439),  though  they 
apply  their  formula?  more  particularly  to  the  case  of  steel  magnets. 
Biot  obtained  his  formula  from  the  analogy  of  the  magnet  to  a  Zamboni 
pile  or  a  tourmaline  electrified  by  heat.  Green  obtained  his  for  the 
case  of  a  very  long  rod  placed  in  a  magnetic  field  parallel  to  the  lines 
of  force,  and,  in  obtaining  it,  used  a  series  of  mathematical  approxima- 
tions whose  physical  meaning  it  is  almost  impossible  to  follow.  Prof. 
Maxwell  has  criticised  his  method  in  the  following  terms  ('  Treatise/ 
art.  439) : — "  Though  some  of  the  steps  of  this  investigation  are  not 
rigorous,  it  is  probable  that  the  result  represents  roughly  the  actual 
magnetization  in  this  most  important  case."  From  the  theory  which 


STUDIES  ON  MAGNETIC  DISTKIBUTION  115 

I  have  given  in  the  first  part  of  this  paper  we  can  deduce  the  physical 
meaning  of  Green's  approximations;  and  these  are  included  in  the 
hypotheses  there  given,  seeing  that,  when  my  formula  is  applied  to  the 
special  case  considered  by  Green,  it  agrees  with  it  where  the  permea- 
bility of  the  material  is  great.  My  formula,  however,  is  far  more  gen- 
eral than  Green's. 

It  is  to  Green  that  we  owe  the  important  remark  that  the  distribu- 
tion in  a  steel  magnet  may  be  nearly  represented  by  the  same  formula 
that  applies  to  electromagnets. 

As  Green  uses  what  is  known  as  the  surface-density  of  magnetization, 
let  us  first  see  how  this  quantity  compares  with  those  I  have  used. 

Suppose  that  a  long  thin  steel  wire  is  so  magnetized  in  the  direction 
of  its  length  that  when  broken  up  the  pieces  will  have  the  same  mag- 
netic moment.  While  the  rod  is  together,  if  we  calculate  its  effect  on 
exterior  bodies,  we  shall  see  that  the  ends  are  the  only  portions  which 
seem  to  act.  Hence  we  may  mathematically  consider  the  whole  action 
of  the  rod  to  be  due  to  the  distribution  of  an  imaginary  magnetic  fluid 
over  the  ends  of  the  rod.  As  any  case  of  magnetism  can  be  represented 
by  a  proper  combination  of  these  rods,  we  see  that  all  cases  of  this  sort 
can  be  calculated  on  the  supposition  of  there  being  two  magnetic  fluids 
distributed  over  the  surfaces  of  the  bodies,  a  unit  quantity  of  which 
will  repel  another  unit  of  like  nature  at  a  unit's  distance  with  a  unit  of 
force.  The  surface-density  at  any  point  will  then  be  the  quantity  of 
this  fluid  on  a  unit  surface  at  the  given  point;  and  the  linear  density 
along  a  rod  will  be  the  quantity  along  a  unit  of  length,  supposing  the 
density  the  same  as  at  the  given  point. 

Where  we  use  induced  currents  to  measure  magnetism  we  measure 
the  number  of  lines  of  force,  or  rather  induction,  cut  by  the  wire,  and 
the  natural  unit  used  is  the  number  of  lines  of  a  unit  field  which  will 
pass  through  a  unit  surface  placed  perpendicular  to  the  lines  of  force., 
The  unit  pole  produces  a  unit  field  at  a  unit's  distance;  hence  the  num- 
ber of  lines  of  force  coming  from  the  unit  pole  is  4  x,  and  the  linear 
density  is 

'  =  &•  .......  •  •  <H> 

and  the  surface-density 


These  really  apply  only  to  steel  magnets  ;  but  as  in  the  case  of  electro- 
magnets the  action  of  the  helix  is  very  small  compared  with  that  of  the 


116  HENKY  A.  ROWLAND 

iron,  especially  when  it  is  very  long  and  the  iron  soft,9  we  can  apply 
these  to  the  cases  we  consider. 

Transforming  Green's  formula  into  my  notation,  it  gives 


(13) 


in  which  <  is  Neumann's  coefficient  of  magnetization  by  induction,  and 
is  equal  to 


This  equation  then  gives 

c  f 

£r(/;.-i)£        ~-  ,   ....    (U) 


Equation  (5)  can  be  approximately  adapted  to  this  case  by  making 
s'  —  oo  ,  which  is  equivalent  to  neglecting  those  lines  of  force  which 
pass  out  of  the  end  section  of  the  bar.  This  gives  A'  =  —  1  :  hence 


2      /     1 
Now  we  have  found  (equation  7)  that  r  —  -=-  J  nearly;  and 

this  in  Green's  formula  (equation  14)  gives 


which  is  identical  with  my  own  when  JJL  is  large,  as  it  always  is  in  the 
case  of  iron,  nickel,  or  cobalt  at  ordinary  temperatures. 

When  x  is  measured  from  the  centre  of  the  bar,  my  equation  becomes 


(17) 


The  constant  part  of  Biot's  formula  is  not  the  same  as  this;  but  for  any 
given  case  it  will  give  the  same  distribution. 

Both  Biot  and  Green  have  compared  their  formulae  with  Coulomb's 
experiments,  and  found  them  to  represent  the  distribution  quite  well. 
Hence  it  will  not  be  necessary  to  consider  the  case  of  steel  magnets  very 
extensively,  though  I  will  give  a  few  results  for  these  further  on. 

9I  take  this  occasion  to  correct  an  error  in  Jenkin's  'Textbook  of  Electricity,' 
where  it  is  stated  that  by  the  introduction  of  the  iron  bar  into  the  helix,  the  num- 
ber of  lines  of  force  is  increased  32  times.  The  number  should  have  been  from  a 
quite  small  number  for  a  short  thick  bar  and  hard  iron  to  nearly  6000  for  a  long 
thin  bar  and  softest  iron. 


STUDIES  ON  MAGNETIC  DISTRIBUTION 


117 


At  present  let  us  take  the  case  of  electromagnets. 

For  observing  the  effect  of  the  permeability,  I  took  two  wires  12-8 
inches  long  and  -19  inch  in  diameter,  one  being  of  ordinary  iron  and 
the  other  of  Stubs'  steel  of  the  same  temper  as  when  purchased.  These 
were  wound  uniformly  from  end  to  end  with  one  layer  of  quite  fine 
wire,  making  600  turns  in  that  distance. 

In  finding  /  from  Q"f)  the  latter  was  divided  by  4~JL,  except  at  the 
end,  where  the  end-section  was  included  with  JL  in  the  proper  manner. 
x  was  measured  from  the  end  of  the  bar  in  inches. 

The  observations  in  Table  XI  are  the  mean  of  four  observations 
made  on  both  ends  of  the  bar  and  with  the  current  in  both  directions. 


TABLE  XI. 
IKON  ELECTROMAGNET. 


x  =  distance 
from  end. 

I 

Q«-                          4irA. 

Observed.     .     Observed. 

4irA. 

Computed. 

Error. 

0 

22-5                  41-1 

33-9 

—7-2 

} 

12-6                  25-1 

26-9 

'  +1-8 

1 

19-3                  19-3 

18-9 

—0-4 

12-0                  12-0 

11-7 

—   -3 

6-6                    6-6 

7-1 

+    -5 

4 

3-9                    3-9 

4-0 

+    -1 

5 

6 

2-9                    2-9 

1.7 

—1-2 

4jr2.  =  42 

The  agreement  with  the  formula  in  this  Table  is  quite  good;  but  we 
still  observe  the  excess  of  observation  over  the  formula  at  the  end,  as 
we  have  done  all  along.  Here,  for  the  first  time,  we  see  the  error 
introduced  by  the  method  of  experiment  which  I  have  before  referred 
to  (p.  98)  in  the  apparently  small  value  of  4;rA  at  x=  -75. 

On  trying  the  steel  bar,  I  came  across  a  curious  fact,  which,  how- 
ever. I  have  since  found  has  been  noticed  by  others.  It  is,  that  when 
an  iron  or  steel  bar  has  been  magnetized  for  a  long  time  in  one  direction 
and  is  then  demagnetized,  it  is  easier  to  magnetize  it  again  in  the  same 
direction  than  in  the  opposite  direction.  The  rod  which  I  used  in  this 
experiment  had  been  used  as  a  permanent  magnet  for  about  a  month, 
but  was  demagnetized  before  use.  From  this  rod  five  cases  of  distribu- 
tion were  observed: — first,  when  the  bar  was  used  as  an  electromagnet 
with  the  magnetization  in  the  same  direction  as  the  original  mag- 


118 


HENKY  A.  EOWLAND 


netism;  second,  ditto  with  magnetization  contrary  to  original  mag- 
netism; third,  when  used  as  a  permanent  magnet  with  magnetism  the 
same  as  the  original  magnetism;  fourth,  ditto  with  magnetism  oppo- 
site; and  fifth,  same  as  third,  but  curve  taken  after  several  days.  The 
permanent  magnetism  was  given  by  the  current. 

The  observations  in  Tables  XI  and  XII  can  be  compared  together, 
the  quantities  being  expressed  in  the  same  unknown  arbitrary  unit. 
It  is  to  be  noted  that  the  bars  in  Tables  XI  and  XII  were  subjected  to 
the  same  magnetizing  force. 

TABLE  XII. 

STUBS'  STEEL. 


Electromagnet. 

Permanent  Magnet. 

X. 

Magnetism 
same  as 
original. 

Magnetism 
opp  site  to 
original. 

Magnetism 
same  as 
original. 

Magnetism 
opposite  to 
original. 

Same  as  third, 
after  three  or 
four  days. 

Qe- 

4irA. 

Qe- 

47TA. 

Qe- 

4irA. 

Qe- 

4rrA. 

Qe- 

4irA. 

0 
i 

23-3 
11-5 

42-5 
23-0 

15-9 

7-7 

29-0 
15-4 

I  14-4 

13-7 

4-8 

4-6 

12-8 

12-2 

H 

8-2 
6-1 

16-4 
12-2 

5-9 
4-3 

11-8 
8-6 

I    8-2 

8-2 

4-0 

4-0 

7-3 

7-3 

7-4 

7-4 

5-5 

5-5 

5-3 

5-3 

2-9 

2-9 

4-8 

4-8 

3 

8-6 

3-6 

2-7 

2-5 

3-0 

3-0 

1-6 

1-6 

2-9 

2-9 

4 
6 

1-7 

•8 

1-0 

•5 

2-2 

1-1 

•9 

•4 

2-0 

1-0 

First  of  all,  from  these  Tables  and  figures  (p.  119)  we  notice  the 
change  in  distribution  due  to  the  quality  of  the  substance;  thus  in  Fig.  5 
we  see  that  the  curves  for  steel  are  much  more  steep  than  that  of  iron, 
and  would  thus  give  greater  values  to  r  in  the  formula — a  result  to  be 
expected.  We  also  observe  in  both  figures  the  great  change  in  distri- 
bution due  to  the  direction  of  magnetization.  In  the  case  of  the  elec- 
tromagnet this  amounts  to  little  more  than  a  change  in  scale;  but  in 
the  permanent  magnet  there  is  a  real  change  of  form  in  the  curve.  It 
seems  probable  that  this  change  of  form  would  be  done  away  with  by 
using  a  sufficient  magnetizing  power  or  magnetizing  by  application  of 
permanent  magnets;  for  it  is  probable  that  the  fall  in  the  curve  E  is 
due  to  the  magnetizing  force  having  been  sufficient  to  change  the 
polarity  completely  at  the  centre,  but  only  partially  at  the  ends. 

On  comparing  the  distribution  on  electromagnets  with  that  on  perma- 
nent magnets,  we  perceive  that  the  curve  is  steeper  toward  the  end  in 


STUDIES  ON  MAGNETIC  DISTRIBUTION 


119 


electromagnets  than  in  permanent  magnets.  At  first  I  thought  it 
might  be  due  to  the  direct  action  of  the  helix,  but  on  trial  found  that 
the  latter  was  almost  inappreciable.  I  do  not  at  present  know  the 
explanation  of  it. 

As  before  mentioned,  Coulomb  has  made  many  experiments  on  the 
distribution  of  magnetism  on  permanent  magnets;  and  so  I  shall  only 
consider  this  subject  briefly.  I  have  already  given  one  or  two  results 
in  Table  XII. 


654321 

FIG.  5. — Results  from  electromagnets. 

A.  Iron,  from  Table  XI. 

B.  Steel,  from  Table  XII,  magnetized  same  as  originally. 

C.  Steel,  from  Table  XII,  magnetized  opposite  to  its  original  magnetism. 


6          S          4  3          2  1  O 

FIG.  6. — Results  from  steel  permanent  magnets. 

D.  Magnetized  in  its  original  direction,  Table  XII. 

E.  Magnetized  opposite  to  its  original  direction,  Table  XII. 
Scale  four  times  that  of  Fig.  5. 

The  following  Tables  were  taken  from  two  exactly  similar  Stubs' 
steel  rods  not  hardened,  one  of  which  was  subsequently  used  in  the 
experiments  of  Table  XII.  They  were  12-8  inches  long  and  -19  inch 
in  diameter. 

The  coincidence  of  these  observations  with  the  formula  is  very  re- 


120 


HENRY  A.  ROWLAND 


markable;  but  still  we  see  a  little  tendency  in  the  end  observation  to 
rise  above  the  value  given  by  the  formula. 
In  equation  (7),  and  also  from  Green's  formula,  we  have  seen  that 

*  T 

for  a  given  quality  and  temper  of  steel  p  =  r»-  is  a  constant.     From 

to 

Coulomb's  experiments  on  a  steel  bar  -176  inch  in  diameter  (whose 
quality  and  temper  is  unknown,  though  it  was  probably  hardened)  Green 
has  calculated  the  value  of  this  constant,  and  obtained  -05482,  which 
was  found  from  the  French  inch  as  the  unit  of  length,  but  which  is 
constant  for  all  systems.  From  Tables  XIII  and  XIV  we  find  the  value 

TABLE  XIII. 


X. 

Q<- 

Observed. 

47TA. 

Observed. 

47TA. 

Computed. 

Error. 

0 
1-28 
2-56 
3-84 
5-12 
6-40 

46-6 
23-8 
12-6 
7-2 
2-3 

34-9 
18-6 
9-8 
5-6 

1-8 

34-26 
18-60 
9-88 
4-77 
1-41 

-•6 
0 

+  -1 
—  •8 
—  •4 

47r;i=-117<10'203(&-a:)-10'203!t). 

TABLE  XIV. 


X. 

Qe- 

Observed. 

Observed. 

4irA. 

Computed. 

Error. 

0 

1  .98 

42-6 

31-9 

30-74 

—1-2 

2-56 

21-4 

16-7 

16-72 

0 

3-  84 

10-9 

8-5 

8-86 

+    -4 

5-12 

5-4 

4-2 

4-28 

+    -1 

6-40 

1-7 

1-33 

1-27 

—   -1 

47rA=-105(10'203(6-z)-10'!i031). 

of  r  to  be  -4674,  whence  ^=  -04440  for  steel  not  hardened.     As  the 

steel  becomes  harder  this  quantity  increases,  and  can  probably  reach 
about  twice  this  for  very  hard  steel. 

To  show  the  effect  of  hardening.  I  broke  the  bar  used  in  Table  XIV 
at  the  centre,  thus  producing  two  bars  6-4  inches  long.  One  of  these 
halves  was  hardened  till  it  could  scarcely  be  scratched  by  a  file ;  but  the 
other  half  was  left  unaltered.  The  following  Table  gives  the  distribu- 
tion, using  the  same  unit  as  that  of  Tables  XIII  and  XIV.  The  bars 
were  so  short  that  the  results  can  hardly  be  relied  on ;  but  they  will  at 
least  suffice  to  show  the  change. 


STUDIES  ON  MAGNETIC  DISTKIBUTION 


121 


In  Fig.  7  I  have  attempted  to  give  the  curve  of  distribution  from 
Table  XV,  and  have  made  the  curves  coincide  with  observation  as  nearly 
as  possible,  making  a  small  allowance,  however,  for  the  errors  intro- 
duced by  the  shortness  of  the  bar.  It  is  seen  that  the  effect  of  harden- 
ing in  a  bar  of  these  dimensions  is  to  increase  the  quantity  of  magnetism, 
but  especially  that  near  the  end.  Had  the  bar  been  very  long,  no  increase 

TABLE  XV. 


X. 

Soft  Steel,  A. 

Hard  Steel,  B. 

Or 

4.A. 

Qe- 

47TA. 

0 
•64 

1-28 
1-92 
3-20 

20-4 
9-8 
6-0 

3-8 

29-1 
15-3 
9-4 
3-0 

47-7 
13-9 
7-0 
2-6 

68-1 
21-7 
11-0 
2-0 

-Results  from  permanent  magnets. 

A.  Soft  steel. 

B.  Hard  steel. 

in  the  total  quantity  of  magnetism  would  have  taken  place;  but  the  distri- 
bution would  have  been  changed.  From  this  we  deduce  the  important 
fact  that  hardening  is  most  useful  for  short  magnets.  And  it  would  seem 
that  almost  the  only  use  in  hardening  magnets  at  all  is  to  concentrate  the 
magnetism  and  to  reduce  the  weight.  Indeed  I  have  made  magnets  from 
iron  wire  whose  magnetization  at  the  central  section  was  just  as  intense 
as  in  a  steel  wire  of  the  same  size;  but  to  all  appearance  it  was  less 


122  HENRY  A.  KOWLAND 

strongly  magnetized  than  the  steel,  because  the  magnetism  was  more 
diffused;  and  as  the  magnetism  was  not  distributed  so  nearly  at  the  end 
as  in  the  steel,  its  magnetic  moment  and  time  of  vibration  were  less. 

It  is  for  these  reasons  that  many  makers  of  surveyors'  compasses  find 
it  unnecessary  to  harden  the  needles,  seeing  these  are  long  and  thin. 

We  might  deduce  all  these  facts  from  the  formulae  on  the  assumption 
that  r  is  greater  the  harder  the  iron  or  steel. 

Having  now  considered  briefly  the  distribution  on  electromagnets 
and  steel  magnets,  and  found  that  the  formulae  represent  it  in  a  general 
way,  we  may  now  use  them  for  solving  a  few  questions  that  we  desire 
to  solve,  though  only  in  an  approximate  manner. 

VI. 

M.  Jamin,  in  his  recent  experiments  on  magnetic  distribution,  has 
obtained  some  very  interesting  results,  although  I  have  shown  his 
method  to  be  very  defective.  In  his  experiments  on  iron  bars  mag- 
netized at  one  end,  he  finds  the  formula  srl  to  apply  to  long  ones  as  I 
have  done.  Now  it  might  be  argued  that  as  the  two  methods  apparently 
give  the  same  result,  they  must  be  equally  correct.  But  let  us  assume 
that  the  attraction  of  his  piece  of  soft  iron  F  varied  as  some  unknown 
power  n  of  the  surface-density  d.  Then  we  find 

F=CenrL, 

which  shows  that  the  attractive  force  or  any  power  of  that  force  can 
be  represented  by  a  logarithmic  curve,  though  not  by  the  same  one. 
Hence  the  error  introduced  by  M.  Jamin's  method  is  insidious  and  not 
easily  detected,  though  it  is  none  the  less  hurtful  and  misleading,  but 
rather  the  more  so. 

However,  his  results  with  respect  to  what  he  calls  the  normal  mag- 
net 10  are  to  some  extent  independent  of  these  errors ;  and  we  may  now 
consider  .them. 

Thus,  in  explaining  the  effect  of  placing  hardened  steel  plates  on 
one  another,  he  says,  "  Quand  on  superpose  deux  lames  aimante'es 
pareilles,  les  courbes  qui  represontent  les  valeurs  de  F  [the  attractive 
force  on  the  piece  of  soft  iron]  s'e!6vent,  parce  que  le  magnetisme  quitte 
les  faces  que  1'on  met  en  contact  pour  se  refugier  sur  les  parties  ex- 
te"rieures.  En  meme  temps,  les  deux  courbes  se  rapprochent  1'une  dc 
1'autre  et  du  milieu  de  1'aimant.  Get  effet  augmente  avec  une  troisieme 

10<On  the  Theory  of  the  Normal  Magnets,'  Comptes  Rendus,  March  31,  1873; 
translated  in  Phil.  Mag.,  June,  1873. 


STUDIES  ON  MAGNETIC  DISTRIBUTION  123 

lame  et  avec  une  quatrieme.  Finalement  les  deux  courbes  se  joignent 
au  milieu." 

In  applying  the  formula  to  this  case  of  a  compound  magnet,  we  have 
only  to  remark  that  when  the  bars  lie  closely  together  they  are  theoret- 
ically the  same  as  a  solid  magnet  of  the  same  section,  but  are  practically 
found  to  be  stronger,  because  thin  bars  can  be  tempered  more  uniformly 
hard  than  thick  ones.  The  addition  of  the  bars  to  each  other  is  similar, 
then,  to  an  increase  in  the  area  of  the  rod,  and  should  produce  nearly 
the  same  effect  on  a  rod  of  rectangular  section  as  the  increase  of 

3 

diameter  in  a  rod  of  circular  section.     Now  the  quantity  p  =  ~*  is 

m 

nearly  constant  in  these  rods  for  the  same  quality  of  steel,  whence  r 
decreases  as  d  increases;  and  this  in  equation  (17)  shows  that  as  the 
diameter  is  increased,  the  length  being  constant,  the  curves  become 
less  and  less  steep,  until  they  finally  become  straight  lines.  This  is 
exactly  the  meaning  of  M.  Jamin's  remark. 

Where  the  ratio  of  the  diameter  to  the  length  is  small,  the  curves  of 
distribution  are  apparently  separated  from  each  other  and  are  given  by 
the  equation 


which  is  not  dependent  on  the  length  of  the  rod  This  is  exactly  the 
result  found  by  Coulomb  (Biot's  Physique,  vol.  iii,  pp.  74,  75).  M. 
Jamin  has  also  remarked  this.  He  states  that  as  he  increases  the  num- 
ber of  plates  the  curves  approach  each  other  and  finally  unite;  this  he 
calls  the  "  normal  magnet  ;  "  and  he  supposes  it  to  be  the  magnet  of 
greatest  power  in  proportion  to  its  weight.  "From  this  moment," 
says  he,  "the  combination  is  at  its  maximum."  The  normal  magnet, 
as  thus  defined,  is  very  indefinite,  as  M.  Jamin  himself  admits. 

By  our  equations  we  can  find  the  condition  for  a  maximum,  and  can 
give  the  greatest  values  to  the  following,  supposing  the  weight  of  the 
bar  to  be  a  fixed  quantity  in  the  first  three. 

1st.  The  magnetic  moment. 

2nd.  The  attractive  force  at  the  end. 

3rd.  The  total  number  of  lines  of  magnetic  force  passing  from  the 
bar. 

4th.  The  magnetic  moment,  the  length  being  constant  and  diameter 
variable. 

Either  of  these  may  be  regarded  as  a  measure  of  the  power  of  the 
bar,  according  to  the  view  we  take.  The  magnetic  moment  of  a  bar  is 
easily  found  to  be 


124  HENRY  A.  ROWLAND 


M—  4rr2fl'  1  2~rl4-c-rt  h         (19) 


and  if  ?  is  the  weight  of  a  unit  of  volume  of  the  steel  and  W  is  the 
weight  of  the  magnet,  we  have  finally 

M-  -* 


This  only  attains  a  maximum  when  -  —  oo  ,   or  the  rod  is  infinitely 

long  compared  with  its  diameter. 

•  The  second  case  is  rather  indefinite,  seeing  it  will  depend  upon 
whether  the  body  attracted  is  large  or  small.  When  it  is  small,  we 
require  to  make  the  surface-density  a  maximum,  the  weight  being  con- 
stant. We  find 


which  attains  a  maximum  as  before  when    -,  —  oo  •     When  the  attracted 

CL 

body  is  large,  the  attraction  will  depend  more  nearly  upon  the  linear 
density, 


which  is  a  maximum  when  -7—  -—  . 

a       p 

For  the  third  case  we  have  the  value  of  Q"  at  the  centre  of  the  bar 
from  equation  (6), 


The  condition  for  a  maximum  gives  in  this  case 

5  _  1-65 
d~~    p 

For  the  last  case,  in  which  the  magnetic  moment  for  a  given  length 
is  to  be  made  a  maximum,  we  find 

b_-l 
d~  p' 

This  last  result  is  useful  in  preparing  magnets  for  determining  the 


STUDIES  ON  MAGNETIC  DISTRIBUTION  125 

intensity  of  the  earth's  magnetism,  and  shows  that  the  magnets  should 
be  made  short,  thick,  and  hard  for  the  best  effect.11 

But  for  all  ordinary  purposes  the  results  for  the  second  and  third 
cases  seem  most  important,  and  lead  to  nearly  the  same  result;  taking 
the  mean  we  find  for  the  maximum  magnet 


fCtA\ 

(24) 


We  see  from  all  our  results  that  the  ratio  of  the  length  of  a  magnet 
to  its  diameter  in  all  cases  is  inversely  as  the  constant  p.  This  con- 
stant increases  with  the  hardness  of  the  steel;  and  hence  the  harder  the 
steel  the  shorter  we  can  make  our  magnets.  It  would  seem  from  this 
that  the  temper  of  a  steel  magnet  should  not  be  drawn  at  all,  but  the 
hardest  steel  used,  or  at  least  that  in  which  p  was  greatest.  The  only 
disadvantage  in  using  very  hard  steel  seems  to  be  the  difficulty  in 
imparting  the  magnetism  at  first;  and  this  may  have  led  to  the  practice 
of  drawing  the  temper;  but  now,  when  we  have  such  powerful  electro- 
magnets, it  seems  as  if  magnets  might  be  made  shorter,  thicker,  and 
harder  than  is  the  custom.  With  the  relative  dimensions  of  magnets 
now  used,  however,  hardening  might  be  of  little  value. 

We  can  also  see  from  all  these  facts,  that  if  we  make  a  compound 
magnet  of  hardened  steel  plates  there  will  be  an  advantage  in  filing 
more  of  them  together,  thus  making  a  thicker  magnet  than  when  they 
are  softer.  We  also  observe  that  as  we  pile  them  up  the  distribution 
changes  in  just  the  way  indicated  by  M.  Jamin,  the  curve  becoming 
less  and  less  steep. 

Substituting  in  the  formula  the  value  of  p  which  we  have  found  for 
Stub's  steel  not  hardened,  but  still  so  hard  as  to  rapidly  dull  a  file,  we 
find  the  best  ratio  of  length  to  diameter  to  be  33-8  —  and  for  the  same 
steel  hardened,  about  17,  though  this  last  is  only  a  rough  approxima- 
tion. This  gives  what  M.  Jamin  has  called  the  normal  magnet.  The 
ratio  should  be  less  for  a  U-magnet  than  for  a  straight  one. 

For  all  magnets  of  the  same  kind  of  steel  in  which  the  ratio  of 
length  to  diameter  is  constant  the  relative  distribution  is  the  same; 
and  this  is  not  only  true  for  our  approximate  formula,  but  would  be 
found  so  for  the  exact  one. 

Thus  for  the  "  normal  magnet  "  the  distribution  becomes 


11  Weber  recommends  square  bars  eight  times  as  long  as  they  are  broad,  and  tem- 
pered very  hard.     (Taylor's  Scientific  Memoirs,  vol.  ii,  p.  86.) 


126 


HENEY  A.  ROWLAND 


where  C  is  a  constant,  and  x  is  measured  from  the  centre.     The  distri- 
bution will  then  be  as  follows : — 


X  _ 

0. 

•1. 

•2. 

•3. 

•4. 

•5. 

A 

0 

•609 

1-27 

2-05 

3-02 

4-26 

This  distribution  is  not  the  same  as  that  given  by  M.  Jamin;  but  as 
his  method  is  so  defective,  and  his  "  normal  magnet "  so  indefinite,  the 
agreement  is  sufficiently  near. 

The  surface-density  at  any  point  of  a  magnet  is 


d  = 


(25) 


which,  for  the  same  kind  of  steel,  is  dependent  only  on   ?   and    -3- 
Hence  in  two  similar  magnets  the  surface-density  is  the  same  at  similar 


0  .1  .2  .A  .4  .5 

FIG.  8. — Distribution  on  "normal  magnet." 

points,  the  linear  density  is  proportional  to  the  linear  dimensions,  the 
surface  integral  of  magnetic  induction  over  half  the  magnet  or  across 
the  section  is  proportional  to  the  surface  dimensions  of  the  magnets, 
and  the  magnetic  moments  to  the  volumes  of  the  magnets.  The  forces 
at  similar  points  with  regard  to  the  two  magnets  will  then  be  the  same. 
All  these  remarks  apply  to  soft  iron  under  induction,  provided  the 
inducing  force  is  the  same — and  hence  include  Sir  William  Thomson's 
well-known  law  with  regard  to  similar  electromagnets;  and  they  are 
accurately  true  notwithstanding  the  approximate  nature  of  the  formula 
from  which  they  have  here  been  deduced. 

Our  theory  gives  us  the  means  of  determining  what  effect  the  boring 
of  a  hole  through  the  centre  of  a  magnet  would  have.     In  this  case  R' 


STUDIES  ON  MAGNETIC  DISTRIBUTION  127 

is  not  much  affected,  but  R  is  increased.  Where  the  magnet  is  used 
merely  to  affect  a  compass-needle,  we  should  then  see  that  the  hole 
through  the  centre  has  little  effect  where  the  magnet  is  short  and  thick ; 
but  where  it  is  long,  the  attraction  on  the  compass-needle  is  much  dimin- 
ished. Where  the  magnet  is  of  the  U-form,  and  is  to  be  used  for 
sustaining  weights,  the  practice  is  detrimental,  and  the  sustaining-power 
is  diminished  in  the  same  proportion  as  the  sectional  area  of  the  magnet. 
The  only  case  that  I  know  of  where  the  hole  through  the  centre  is  an 
advantage,  is  that  of  the  deflecting  magnets  for  determining  the  inten- 
sity of  the  earth's  magnetism,  which  may  be  thus  made  lighter  without 
much  diminishing  their  magnetic  moment. 

In  conclusion,  let  me  express  my  regret  at  the  imperfection  of  the 
theory  given  in  this  paper;  for  although  the  equations  are  more  general 
than  any  yet  given,  yet  still  they  rest  upon  two  quite  incorrect  hypoth- 
eses; and  so,  although  we  have  found  these  formula?  of  great  use  in 
pursuing  our  studies  on  magnetic  distribution,  yet  much  remains  to  be 
done.  A  nearer  approximation  to  the  true  distribution  could  readily 
be  obtained;  but  the  result  would,  without  doubt,  be  very  complicated, 
and  would  not  repay  us  for  the  trouble. 

In  this  paper,  as  well  as  in  all  others  which  I  have  published  on  the 
subject  of  magnetism,  my  object  has  not  only  been  to  bring  forth  new 
'results,  but  also  to  illustrate  Faraday's  method  of  lines  of  magnetic 
force,  and  to  show  how  readily  calculations  can  be  made  on  this  system. 
For  this  reason  many  points  have  been  developed  at  greater  length  than 
would  otherwise  be  desirable. 


12 

ON  THE  MAGNETIC  EFFECT  OF  ELECTEIC  CONVECTION  * 

[American  Journal  of  Science  13],  XV,  30-38,  1878] 

The  experiments  described  in  this  paper  were  made  with  a  view  of 
determining  whether  or  not  an  electrified  body  in  motion  produces 
magnetic  effects.  There  seems  to  be  no  theoretical  ground  upon  which 
we  can  settle  the  question,  seeing  that  the  magnetic  action  of  a  con- 
ducted electric  current  may  be  ascribed  to  some  mutual  action  between 
the  conductor  and  the  current.  Hence  an  experiment  is  of  value.  Pro- 
fessor Maxwell,  in  his  '  Treatise  on  Electricity/  Art.  770,  has  computed 
the  magnetic  action  of  a  moving  electrified  surface,  but  that  the  action 
exists  has  not  yet  been  proved  experimentally  or  theoretically. 

The  apparatus  employed  consisted  of  a  vulcanite  disc  21-1  centi- 
metres in  diameter  and  -5  centimetre  thick  which  could  be  made  to 
revolve  around  a  vertical  axis  with  a  velocity  of  61-  turns  per  second. 
On  either  side  of  the  disc  at  a  distance  of  -6  cm.  were  fixed  glass  plates 
having  a  diameter  of  38-9  cm.  and  a  hole  in  the  centre  of  7-8  cm.  The 
vulcanite  disc  was  gilded  on  both  sides  and  the  glass  plates  had  an 
annular  ring  of  gilt  on  one  side,  the  outside  and  inside  diameters  being 
24-0  cm.  and  8-9  cm.  respectively.  The  gilt  sides  could  be  turned 
toward  or  from  the  revolving  disc  but  were  usually  turned  toward  it  so 
that  the  problem  might  be  calculated  more  readily  and  there  should 
be  no  uncertainty  as  to  the  electrification.  The  outside  plates  were 
usually  connected  with  the  earth;  and  the  inside  disc  with  an  electric 
battery,  by  means  of  a  point  which  approached  within  one-third  of  a 
millimetre  of  the  edge  and  turned  toward  it.  As  the  edge  was  broad, 
the  point  would  not  discharge  unless  there  was  a  difference  of  potential 
between  it  and  the  edge.  Between  the  electric  battery  and  the  disc, 

1  The  experiments  described  were  made  in  the  laboratory  of  the  Berlin  University 
through  the  kindness  of  Professor  Helmholtz,  to  whose  advice  they  are  greatly  in- 
debted for  their  completeness.  The  idea  of  the  experiment  first  occurred  to  me  in 
1868  and  was  recorded  in  a  note  book  of  that  date. 


Ox  THE  MAGNETIC  EFFECT  OF  ELECTRIC  CONVECTION        129 

a  commutator  was  placed,  so  that  the  potential  of  the  latter  could  be 
made  plus  or  minus  at  will.  All  parts  of  the  apparatus  were  of  non- 
magnetic material. 

Over  the  surface  of  the  disc  was  suspended,  from  a  bracket  in  the 
wall,  an  extremely  delicate  astatic  needle,  protected  from  electric 
action  and  currents  of  air  by  a  brass  tube.  The  two  needles  were  1-5 
cm.  long  and  their  centres  17-98  cm.  distant  from  each  other.  The 
readings  were  by  a  telescope  and  scale.  The  opening  in  the  tube  for 
observing  the  mirror  was  protected  from  electrical  action  by  a  metallic 
cone,  the  mirror  being  at  its  vertex.  So  perfectly  was  this  accom- 
plished that  no  effect  of  electrical  action  was  apparent  either  on  charg- 
ing the  battery  or  reversing  the  electrification  of  the  disc.  The  needles 
were  so  far  apart  that  any  action  of  the  disc  would  be  many  fold  greater 
on  the  lower  needle  than  the  upper.  The  direction  of  the  needles  was 
that  of  the  motion  of  the  disc  directly  below  them,  that  is,  perpendicular 
to  the  radius  drawn  from  the  axis  to  the  needle.  As  the  support  of 
the  needle  was  the  wall  of  the  laboratory  and  the  revolving  disc  was  on  a 
table  beneath  it,  the  needle  was  reasonably  free  from  vibration. 

In  the  first  experiments  with  this  apparatus  no  effect  was  observed 
other  than  a  constant  deflection  which  was  reversed  with  the  direction 
of  the  motion.  This  was  finally  traced  to  the  magnetism  of  rotation 
of  the  axis  and  was  afterward  greatly  reduced  by  turning  down  the 
axis  to  -9  cm.  diameter.  On  now  rendering  the  needle  more  sensitive 
and  taking  several  other  precautions  a  distinct  effect  was  observed  of 
several  millimetres  on  reversing  the  electrification  and  it  was  separated 
from  the  effect  of  magnetism  of  rotation  by  keeping  the  motion  con- 
stant and  reversing  the  electrification.  As  the  effect  of  the  magnetism 
of  rotation  was  several  times  that  of  the  moving  electricity,  and  the 
needle  was  so  extremely  sensitive,  numerical  results  were  extremely 
hard  to  be  obtained,  and  it  is  only  after  weeks  of  trial  that  reasonably 
accurate  results  have  been  obtained.  But  the  qualitative  effect,  after 
once  being  obtained,  never  failed.  In  hundreds  of  observations  extend- 
ing over  many  weeks,  the  needle  always  answered  to  a  change  of  electri- 
fication of  the  disc.  Also  on  raising  the  potential  above  zero  the  action 
was  the  reverse  of  that  when  it  was  lowered  below.  The  swing  of  the 
needle  on  reversing  the  electrification  was  about  10-  or  15-  millimetres 
and  therefore  the  point  of  equilibrium  was  altered  5  or  7|  millimetres. 
This  quantity  varied  with  the  electrification,  the  velocity  of  motion, 
the  sensitiveness  of  the  needle,  etc. 
9 


130  HENRY  A.  EOWLAND 

The  direction  of  the  action  may  be  thus  defined.  Calling  the  motion 
of  the  disc  -\-  when  it  moved  like  the  hands  of  a  watch  laid  on  the 
table  with  its  face  up,  we  have  the  following,  the  needles  being  over 
one  side  of  the  disc  with  the  north  pole  pointing  in  the  direction  of 
positive  motion.  The  motion  being  -f>  on  electrifying  the  disc  -)-  the 
north  pole  moved  toward  the  axis,  and  on  changing  the  electrification, 
the  north  pole  moved  away  from  the  axis.  With  — motion  and  -(- 
electrification,  the  north  pole  moved  away  from  the  axis,  and  with  — 
electrification,  it  moved  toward  the  axis.  The  direction  is  therefore 
that  in  which  we  should  expect  it  to  be. 

To  prevent  any  suspicion  of  currents  in  the  gilded  surfaces,  the 
latter,  in  many  experiments,  were  divided  into  small  portions  by  radial 
scratches,  so  that  no  tangential  currents  could  take  place  without  suffi- 
cient difference  of  potential  to  produce  sparks.  But  to  be  perfectly 
certain,  the  gilded  disc  was  replaced  by  a  plane  thin  glass  plate  which 
could  be  electrified  by  points  on  one  side,  a  gilder  induction  plate  at 
zero  potential  being  on  the  other.  With  this  arrangement,  effects  in 
the  same  direction  as  before  were  obtained,  but  smaller  in  quantity, 
seeing  that  only  one  side  of  the  plate  could  be  electrified. 

The  inductor  plates  were  now  removed,  leaving  the  disc  perfectly 
free,  and  the  latter  was  once  more  gilded  with  a  continuous  gold  sur- 
face, having  only  an  opening  around  the  axis  of  3-5  cm.  The  gilding  of 
the  disc  was  connected  with  the  axis  and  so  was  at  a  potential  of  zero. 
On  one  side  of  the  plate,  two  small  inductors  formed  of  pieces  of  tin- 
foil on  glass  plates,  were  supported,  having  the  disc  between  them.  On 
electrifying  these,  the  disc  at  the  points  opposite  them  was  electrified 
by  induction  but  there  could  be  no  electrification  except  at  points  near 
the  inductors.  On  now  revolving  the  disc,  if  the  inductors  were  very 
small,  the  electricity  would  remain  nearly  at  rest  and  the  plate 
would  as  it  were  revolve  through  it.  Hence  in  this  case  we  should 
have  conduction  without  motion  of  electricity,  while  in  the  first  experi- 
ment we  had  motion  without  conduction.  I  have  used  the  term 
"  nearly  at  rest "  in  the  above,  for  the  following  reasons.  As  the  disc 
revolves  the  electricity  is  being  constantly  conducted  in  the  plate  so  as 
to  retain  its  position.  Now  the  function  which  expresses  the  potential 
producing  these  currents  and  its  differential  coefficients  must  be  con- 
tinuous throughout  the  disc,  and  so  these  currents  must  pervade  the 
whole  disc. 


Ox  THE  MAGNETIC  EFFECT  OF  ELECTRIC  CONVECTION        131 

To  calculate  these  currents  we  have  two  ways.  Either  we  can  con- 
sider the  electricity  at  rest  and  the  motion  of  the  disc  through  it  to 
produce  an  electromotive  force  in  the  direction  of  motion  and  propor- 
tional to  the  velocity  of  motion,  to  the  electrification,  and  to  the  surface 
resistance;  or,  as  Professor  Helmholtz  has  suggested,  we  can  consider 
the  electricity  to  move  with  the  disc  and  as  it  comes  to  the  edge  of  the 
inductor  to  he  set  free  to  return  by  conduction  currents  to  the  other 
edge  of  the  inductor  so  as  to  supply  the  loss  there.  The  problem  is 
capable  of  solution  in  the  case  of  a  disc  without  a  hole  in  the  centre  but 
the  results  are  too  complicated  to  be  of  much  use.  Hence  scratches 
were  made  on  the  disc  in  concentric  circles  about  -6  cm.  apart  by  which 
the  radial  component  of  the  currents  was  destroyed  and  the  problem 
became  easily  calculable. 

For,  let  the  inductor  cover  -th  part  of  the  circumference  of  any 

n 

one  of  the  conducting  circles;  then,  if  C  is  a  constant,  the  current  in 

the  circle  outside  the  inductor  will  be  +-,  and  inside  the  area  of  the 

1  n 

inductor  —  C^n~l\     On  the  latter  is  superposed  the  convection  cur- 

fi 

rent  equal  to  -\-C.     Hence  the  motion  of  electricity  throughout  the 

whole  circle  is  -  what  it  would  have  been  had  the  inductor  covered  the 
n 

whole  circle. 

In  one  experiment  n  was  about  8.  By  comparison  with  the  other 
experiments  we  know  that  had  electric  conduction  alone  produced  effect 
we  should  have  observed  at  the  telescope  —  5-  mm.  Had  electric  con- 
vection alone  produced  magnetic  effect  we  should  have  had  -j-  5- 7  mm. 
And  if  they  both  had  effect  it  would  have  been  -f-  -7  mm.,  which  is  prac- 
tically zero  in  the  presence  of  so  many  disturbing  causes.  No  effect 
was  discovered,  or  at  least  no  certain  effect,  though  every  care  was  used. 
Hence  we  may  conclude  with  reasonable  certainty  that  electricity  pro- 
duces nearly  if  not  quite  the  same  magnetic  effect  in  the  case  of  con- 
vection as  of  conduction,  provided  the  same  quantity  of  electricity 
passes  a  given  point  in  the  convection  stream  as  in  the  conduction 
stream. 

The  currents  in  the  disc  were  actually  detected  by  using  inductors 
covering  half  the  plate  and  placing  the  needle  over  the  uncovered  por- 
tion; but  the  effect  was  too  small  to  be  measured  accurately.  To  prove 


132  HENRY  A.  KOWLAXD 

this  more  thoroughly  numerical  results  were  attempted,  and,  after 
weeks  of  labor,  obtained.  I  give  below  the  last  results  which,  from 
the  precautions  taken  and  the  increase  of  experience,  have  the  greatest 
weight. 

The  magnetizing  force  of  the  disc  was  obtained  from  the  deflection 
of  the  astatic  needle  as  follows.  Turning  the  two  needles  with  poles 
in  the  same  direction  and  observing  the  number  n  of  vibrations,  and 
then  turning  them  opposite  and  finding  the  number  n'  of  vibrations  in 
that  position,  we  shall  find,  when  the  lower  needle  is  the  strongest, 

Y       -p,  w2  —  n"1  n'2        A    w  n. 

JL   —  JL      —5—; jz  =  —*—. 72     77  •**  I  ....       (1) 

w2  +  n '      i?  +  n     D 

where  X'  and  X  are  the  forces  on  the  upper  and  lower  needle  re- 
spectively, A  the  deflection,  D  the  distance  of  the  scale  and  H  the 
horizontal  component  of  the  earth's  magnetism.  As  X'  and  n'  are  very 
small  the  first  term  is  nearly  X  —  X'.  The  torsion  of  the  silk  fibre  was 
too  small  to  affect  the  result,  or  at  least  was  almost  eliminated  by  the 
method  of  experiment. 

The  electricity  was  in  the  first  experiment  distributed  nearly  uni- 
formly over  the  disc  with  the  exception  of  the  opening  in  the  centre 
and  the  excess  of  distribution  on  the  edge.  The  surface  density  on 
either  side  was 

V y 


a*  £  - 


V  -  -V  being  the  difference  of  potential  between  the  disc  and  the 
outside  plates,  /?  the  thickness  of  the  disc  and  B  the  whole  distance 
apart  of  the  outside  plates.  The  excess  on  the  edge  was  (Maxwell's 
Electricity,  Art.  196,  Eq.  18), 


*=*<?-  ^  **•*  "*>      •    '    •    <3> 


where  C  is  the  radius  of  the  disc. 

We  may  calculate  the  magnetic  effect  on  the  supposition  that,  as  in 
the  conducted  current,  the  magnetizing  force  due  to  any  element  of 
surface  is  proportional  to  the  quantity  of  electricity  passing  that 
element  in  a  unit  of  time.  The  magnetic  effect  due  to  the  uniform 
distribution  has  the  greatest  effect.  With  an  error  of  only  a  small 


Ox  THE  MAGNETIC  EFFECT  OF  ELECTEIC  CONVECTION         133 

fraction  of  a  per  cent,  we  may  consider  the  two  sides  of  the  disc  to 
coincide  in  the  centre.  Taking  the  origin  of  coordinates  at  the  point 
of  the  disc  under  the  needle  and  the  centre  of  the  disc  on  the  axis  of  X. 
we  find  for  both  sides  of  the  disc,  the  radial  component  of  the  force 
parallel  to  the  disc, 


rc~»     f 
J_(C+b)J. 


x)dxdy 


(a1  +  a?  + 


f>  -  (b 


where  a  is  the  distance  of  the  needle  from  the  disc  and  &  that  from 
the  axis;  N  is  the  number  of  revolutions  of  the  disc  per  second  and 
v  =  28,800,000,000  centimetres  per  second  according  to  Maxwell's  de- 
termination. The  above  integral  can  be  obtained  exactly  by  elliptic 
integrals,  but  as  it  introduces  a  great  variety  of  complete  and  incom- 
plete elliptic  integrals  of  all  three  orders,  we  shall  do  best  by  expanding 
as  follows: 

V  4-JW     7,  faNff   f     .  .  A  a         >.  -r.v 

X=  -     —  P  —  -  (A!  +  A*  +  A3  +  &c.),      ...     (4) 

A,  =  2jfarc  tan  £-=^  +  arc  tan  ^±-^  -  a  log,  4£  , 
\  a  a     ]  JV 


2sb  +  a2)  loge 


(5s3 


&c.,  &c., 
where 


-,  ,  . 

/it) 

From  this  must  be  subtracted  the  effect  of  the  opening  in  the  centre, 
for  which  the  same  formula  will  apply. 

The  magnetic  action  of  the  excess  at  the  edge  may  be  calculated  on 
the  supposition  that  that  excess  is  concentrated  in  a  circle  of  a  little 
smaller  diameter,  C",  than  the  disc;  therefore, 


134  HEXEY  A.  EOWLAXD 


where  fc  = —        ^-i^jL^,  and  F(Jc)  and  E(k)  are  complete  elliptic 
V  c?  +  ( C?  +  0) 

integrals  of  the  second  and  first  orders  respectively. 

The  determination  of  the  potential  was  by  means  of  the  spark  which 
Thomson  has  experimented  on  in  absolute  measure.  For  sparks  of 
length  I  between  two  surfaces  nearly  plane,  we  have  on  the  centimetre, 
gram,  second  system,  from  Thomson's  experiments, 

V-  V  =  117-5  (1  +  . 0135), 

and  for  two  balls  of  finite  radius,  we  find,  by  considering  the  distribu- 
tion on  the  two  sheets  of  an  hyperboloid  of  revolution, 


V-V'  =  117-5  (I  +  -0135) 


where  r  is  the  ratio  of  the  length  of  spark  to  diameter  of  balls  and  had 
in  these  experiments  a  value  of  about  8.     In  this  case  • 

V—  V  =  109-6  (I  +  -0135)  .  (6) 

A  battery  of  nine  large  jars,  each  48-  cm.  high,  contained  the  store 
of  electricity  supplied  to  the  disc,  and  the  difference  of  potential  was 
determined  before  and  after  the  experiment  by  charging  a  small  jar  and 
testing  its  length  of  spark.  Two  determinations  were  made  before  and 
two  after  each  experiment,  and  the  mean  taken  as  representing  the 
potential  during  the  experiment. 

The  velocity  of  the  disc  was  kept  constant  by  observing  a  governor. 
The  number  of  revolutions  was  the  same,  nearly,  as  determined  by  the 
sizes  of  the  pulleys  or  the  sound  of  a  Seebeck  siren  attached  to  the 
axis  of  the  disc;  the  secret  of  this  agreement  was  that  the  driving  cords 
were  well  supplied  with  rosin.  The  number  of  revolutions  was  61-  per 
second. 

In  such  a  delicate  experiment,  the  disturbing  causes,  such  as  the 
changes  of  the  earth's  magnetism,  the  changing  temperature  of  the 
room,  &c.,  were  so  numerous  that  only  on  few  days  could  numerical 
results  be  obtained,  and  even  then  the  accuracy  could  not  be  great. 
The  centimetre,  gram,  second  system,  was  used. 

First  Series,  a  =  2-05,  &  =  9-08,  w=-697,  Z>  =  110-,  H—  -182 
nearly,  5  =  1-68,  /?=-50,  (7  =  10-55,  N  —  61-,  v  =  28,800,000,000-, 
7Z'  =-0533,  C"  =  10. 


ON  THE  MAGNETIC  EFFECT  OF  ELECTRIC  CONVECTION        135 


Direction  of     Electrifica- 
motion.         tion  of  disc. 

Scale  reading 
in  mm. 

Deflection  on 
reversing 
electriflcat'n 
in  mm. 

Length  of 
spark. 

- 

— 

99- 
107-5 
101-5 

7-25 

•295 

— 

7 

68-5 
76-5 
68-0 

8-25 

•290 

- 

— 

97- 
91-5 
100- 

7-00 

•282 

— 

1 

59- 
65-5 
58-5 

6-75 

•265 

- 

i 

92-5 
85- 
91-0 

6-75 

•290 

'  — 

— 

52-5 
57-5 
51-5 

5-50 

•285 

+ 

— 

82-0 
76-0 
81-7 

5-85 

•285 

— 

1 

36-5 
43-0 
36-5 

6-50 

•275 

- 

— 

68-0 
61-0 
68-0 

7-00 

•290 

— 

— 

27-5 
33-5 
26-5 

6-50 

•288 

Mean  values. 

6-735 

•2845 

Hence 


From  equation  (1), 


X-  -99X'  =, 


305700' 
Bv  calculation  from  the  electrification  we  find 


=  •00000327. 


136 


HENEY  A.  ROWLAND 
1 


X--992T1  =; 


=  •00000337. 


296800- 

The  effect  on  the  upper  needle,  X',  was  about  Jg-  of  that  on  the 
lower  X. 

Second  Series.  Everything  the  same  as  before  except  the  following. 
&  =  7-65,  n'=-Q525. 


Direction  of 
motion. 

Electrifica- 
tion of  disc. 

Scale  reading 
in  mm. 

Deflection  on 
reversing 
electriflcat'n 
in  mm. 

Length  of 
spark. 

+ 

172-5 

+ 

— 

165-5 

7-0 

•300 

+ 

172-5 

+ 

120-0 

— 

+ 

127-5      « 
121-5 

7-5 

•295 

— 

129-0 



163-5 

+ 

+ 

170-5 
163-0 

7-25 

•297 

+ 

170-5 

+ 

118-0 

— 

+ 

127-0 
120-0 

8-25 

•270 

— 

127-5 

Mean  values. 

7-50 

•2955 

Hence  for  this  case  we  have  from  equation  (1), 

1 


315000- 


And  from  the  electrification, 

T       -QQ  JT'  — 

- 


=•00000317. 


=  -00000349 . 


Third  Series.     Everything  the  same  as  in  the  first  series,  except 
=  8-1,  n'  =  -0521,  D  =  114. 


ON  THE  MAGNETIC  EFFECT  OF  ELECTRIC  CONVECTION 


137 


Direction  of 
motion. 

Electrifica- 
tion of  disc. 

Scale  reading 
in  mm. 

Deflection  on 
reversing 
electrificat'n 
in  mm. 

Length  of 
spark. 

+ 

151-0 

— 



158-5 

7.50 

•287 

+ 

151-0 

+ 

192-0 

+ 

— 

185-5 

7-25 

•292. 

+ 

193-5 



157-5 

— 

+ 

148-5 
157-5 

8-25 

•295 

+ 

150-0 



185-0 

+ 

+ 

192-5 
185-5 

7-75 

•302 

+ 

193-5 



151-0 

— 

-1- 

143-5 

7-25 

•287 

— 

150-5 

Mean  values. 

7-60 

•2926 

J  =  -380, 
For  this  case  from  equation  (1) 

1 


295000 


and  from  the  electrification 


= -2926. 


=  -00000339 , 


=  -00000355 . 


281500- 

The  error  amounts  to  3,  10  and  4  per  cent  respectively  in  the  three 
series.  Had  we  taken  Weber's  value  of  v  the  agreement  would  have 
been  still  nearer.  Considering  the  difficulty  of  the  experiment  and 
the  many  sources  of  error,  we  may  consider  the  agreement  very  satis- 
factory. The  force  measured  is,  we  observe,  about  ^inr  of  the  hori- 
zontal force  of  the  earth's  magnetism. 

The  difference  of  readings  with  -f-  and  -  -  motion  is  due  to  the 
magnetism  of  rotation  of  the  brass  axis.  This  action  is  eliminated 
from  the  result. 

It  will  be  observed  that  this  method  gives  a  determination  of  v,  the 
ratio  of  the  electromagnetic  to  the  electrostatic  system  of  units,  and  if 
carried  out  on  a  large  scale  with  perfect  instruments  might  give  good 
results.  The  value  v  =  300,000,000-  metres  per  second  satisfies  the 
first  and  last  series  of  the  experiments  the  best. 

Berlin,  February  15,  1876. 


13 

NOTE  ON  THE  MAGNETIC  EFFECT  OF  ELECTRIC 
CONVECTION 

[Philosophical  Magazine  [5],   VII,  442,  443,  18791 

JOHNS  HOPKINS  UNIVERSITY,  BALTIMORE,  April  8,  1878. 
To  the  Editors  of  the  Philosophical  Magazine  and  Journal. 

GENTLEMEN: — Some  three  years  since,  while  in  Berlin,  I  made  some 
experiments  on  the  magnetic  effect  of  electric  convection,  which  have 
since  been  published  in  the  '  American  Journal  of  Science '  for  Jan- 
uary, 1878.  But  previous  to  that,  in  1876,  Professor  Helmholtz  had 
presented  to  the  Berlin  Academy  an  abstract  of  my  paper,  which  has 
been  widely  translated  into  many  languages.  But,  although  Helm- 
holtz distinctly  says,  "  Ich  bemerke  dabei,  das  derselbe  den  Plan  f  iir 
seine  (Rowland's)  Versuche  schon  gefasst  und  vollstandig  iiberlegt 
hatte,  als  er  in  Berlin  ankam,  ohne  vorausgehende  Einwirkung  von 
meiner  Seite,"  yet  nevertheless  I  now  find  that  the  experiment  is  being 
constantly  referred  to  as  Helmholtz's  experiment — and  that  if  I  get 
any  credit  for  it  whatever,  it  is  merely  in  the  way  of  carrying  out 
Helmholtz's  ideas,  instead  of  all  the  credit  for  ideas,  design  of  appar- 
atus, the  carrying  out  of  the  experiment,  the  calculation  of  results,  and 
everything  which  gives  the  experiment  its  value. 

Unfortunately  for  me,  Helmholtz  had  already  experimented  on  the 
subject  with  negative  results;  and  I  found,  in  travelling  through  Ger- 
many that  others  had  done  the  same.  The  idea  occurred  in  nearly 
the  same  form  to  me  eleven  years  ago;  but  as  I  recognized  that  the 
experiment  would  be  an  extremely  delicate  one,  I  did  not  attempt  it 
until  I  could  have  every  facility,  which  Helmholtz  kindly  gave  me. 

Helmholtz  kindly  suggested  a  more  simple  form  of  commutator  than 
I  was  about  to  use,  and  also  that  I  should  extend  my  experiments  so 
as  to  include  an  uncoated  glass  disk  as  well  as  my  gilded  vulcanite 
ones;  but  all  else  I  claim  as  my  own, — the  method  of  experiment  in  all 
its  details,  the  laboratory  work,  the  method  of  calculation — indeed  every- 
thing connected  with  the  experiment  in  any  way,  as  completely  as  if  it  had 
been  carried  out  in  my  own  laboratory  4000  miles  from  the  Berlin  labor- 
atory. Yours  truly,  H.  A.  ROWLAND. 


14 

XOTE  OX  THE  THEORY  OF  ELECTRIC  ABSORPTION 

[American  Journal  of  Mathematics,  J,  53-58,  1878] 

In  experimenting  with  Leyden  jars,  telegraph  cables  and  condensers 
of  other  forms  in  which  there  is  a  solid  dielectric,  we  observe  that  after 
complete  discharge  a  portion  of  the  charge  reappears  and  forms  what 
is  known  as  the  residual  charge.  This  has  generally  been  explained 
by  supposing  that  a  portion  of  the  charge  was  conducted  below  the 
surface  of  the  dielectric,  and  that  this  was  afterwards  conducted  back 
again  to  its  former  position.  But  from  the  ordinary  mathematical 
theory  of  the  subject,  no  such  consequence  can  be  deduced,  and  we 
must  conclude  that  this  explanation  is  false.  Maxwell,  in  his  '  Trea- 
tise on  Electricity  and  Magnetism,'  vol.  2,  chap  X,  has  shown  that  a 
substance  composed  of  layers  of  different  substances  can  have  this 
property.  But  the  theory  of  the  whole  subject  does  not  yet  seem  to 
have  been  given. 

Indeed,  the  general  theory  would  involve  us  in  very  complicated 
mathematics,  and  our  equations  would  have  to  apply  to  non-homo- 
geneous, crystalline  bodies  in  which  Ohm's  law  was  departed  from  and 
the  specific  inductive  capacity  was  not  constant;  we  should,  moreover, 
have  to  take  account  of  thermo-electric  currents,  electrolysis,  and 
electro-magnetic  induction.  Hence  in  this  paper  I  do  not  propose  to 
do  more  than  to  slightly  extend  the  subject  beyond  its  present  state 
and  to  give  the  general  method  of  still  further  extending  it. 

Let  us  at  first,  then,  take  the  case  of  an  isotropic  body  in  general,  in 
which  thermo-electric  currents  and  electrolysis  do  not  exist,  and  on 
and  in  which  the  changes  of  currents  are  so  slow  that  we  can  omit 
electro-magnetic  induction.  The  equations  then  become1 


, 

in  which  y  is  the  specific  inductive  capacity  of  the  substance,  If  the 

'Maxwell's  Treatise,  Art.  325. 


140  HENET  A.  BOWLAND 

electric  conductivity,  V  the  potential,  p  the  volume  density  of  the  elec- 
tricity, and  t  the  time. 

The  subtraction  of  one  equation  from  the  other  gives 


To  introduce  the  condition  that  there  shall  be  no  electric  absorption, 
we  must  observe  that  when  that  phenomenon  exists,  a  charge  of  elecr 
tricity  appears  at  a  point  where  there  was  no  charge  before;  in  other 
words,  the  relative  distribution  has  been  changed.  Hence,  if  the  rela- 
tive distribution  remains  the  same,  no  electric  absorption  can  take 
place.  Our  condition  is,  then, 


where  c  is  independent  of  t,  and  //  and  p'  are  the  densities  at  the  points 
x,  y,  z,  and  x',  y'  z'.     This  gives 


where  c  is  a  function  of  t  only  and  not  of  x,  y,  z,  and  p0  is  the  value  of  p 
at  the  time  t  =  0.     As  we  have 

1    dV  dm      dV    d   /,-.  k\  .  dV  d  /,       k\   .   dV  d  /,       k 


where  m  =  -  and  n  is  a  line  in  the  direction  of  the  current  at  the  given 

I 
point,  equation  (1)  becomes 

_1_  d  V  dm        1     dp       4rr p  _  ft 
m    dn    dn      ~lc    ^IT  ~    ~^~        ' 
From  equation  (2) 

P  =  f 


and  hence 


_!_   dV  dm 
m    dn    dn 


If  we  denote  the  strength  of  current  at  the  point  by  8,  we  have 


NOTE  ox  THE  THEORY  OF  ELECTRIC  ABSORPTION  141 

8-   -kdV 
kWi' 

and 

1          dm  _.      j^   /*. 
cm  -  4:rw8  dn  IS 

JL 

this  equation  (3)  gives  the  value  of    -  =m  at  all  points  of  the  body 

and  at  all  times  so  that  the  phenomenon  of  electric  absorption  shall  not 
take  place.  As  this  equation  makes  m  a  function  of  x,  y,  z,  S  and  t, 
the  relation  in  general  is  entirely  too  complicated  to  ever  apply  to 
physical  phenomena,  without  some  limitation.  Firstly  then,  as  c  is  only 
an  arbitrary  function  of  t,  we  shall  assume  that  it  is  constant  ; 


..  . 

cm  —  47:w2   dn  6' 

The  most  important  case  is  where  m  is  a  constant.     Then 

dm  _  ~ 
~dn  ~ 
and 

c  =  4:xm,    S=Sas-«,    p  =  p.e-«. 

In  this  case,  therefore,  we  see  that  both  the  electrification  and  the 
currents  die  away  at  the  rate  c.  The  case  where  Ohm's  law  is  true  and 
the  specific  inductive  capacity  is  constant  is  included  in  this  case,  seeing 
that  when  Jc  and  %  are  both  constants  their  ratio,  m,  is  constant.  But 
it  also  includes  the  cases  where  k  and  #  are  both  the  same  functions  of 
V,  S,  or  x,  y,  z,  seeing  that  their  ratio,  m,  would  be  constant  in  this 
case  also. 

When  m  is  not  constant,  the  chances  are  very  small  against  its  satis- 
fying equation  (4). 

Hence,  we  may  in  general  conclude,  that  electric  absorption  will  almost 
certainly  take  place  unless  the  ratio  of  conductivity  to  the  specific  inductive 
capacity  is  constant  throughout  the  body. 

This  ratio,  m,  may  become  a  variable  in  several  manners,  as  follows  : 

1st  manner.  —  The  body  may  not  be  homogeneous.  This  includes  the 
case,  which  Maxwell  has  given,  where  the  dielectric  was  composed  of 
layers  of  different  substances. 

2d  manner.  —  The  body  may  not  obey  Ohm's  law;  in  this  case  k  would 
be  variable. 

3d  manner.  The  specific  inductive  capacity,  £,  may  vary  with  the 
electric  force. 


142  HEXRY  A.  KOWLAND 

It  is  to  be  noted  that  the  cases  of  electric  absorption  which  we 
observe  are  mostly  those  of  condensers  formed  of  two  planes,  or  of  one 
cylinder  inside  another,  as  in  a  telegraph  cable.  Our  theory  shows 
that  different  explanations  can  be  given  of  these  two  cases. 

The  case  of  parallel  plates  does  not  admit  of  being  explained,  except 
on  the  supposition  that  m  varies  in  the  first  manner  above  given,  or  in 
this  manner  in  combination  with  the  others,  for  we  can  only  conceive 
of  the  conductivity  and  the  specific  inductive  capacity  as  being  func- 
tions of  the  ordinate  or  of  the  electric  force.  As  the  latter  is  constant 
for  all  points  between  the  plates,  m  would  still  be  constant  although  it 
were  a  function  of  the  electric  force,  and  thus  electric  absorption  would 
not  take  place. 

We  may  then  conclude  that  in  the  case  of  parallel  plates,  omitting 
explanations  based  on  electrolysis  or  thermo-electric  currents,  the  only 
explanation  that  we  can  give  at  present  is  that  which  depends  on  the 
non-homogeneity  of  the  body,  and  is  the  case  which  Maxwell  has  given 
in  the  form  of  two  different  materials.  Our  equations  show  that  the 
form  of  layers  is  not  necessary,  but  that  any  departure  from  homo- 
geneity is  sufficient.  It  is  to  be  noted  that  the  homogeneity,  which  we 
speak  of,  is  electrical  homogeneity,  and  that  a  mass  of  crystals  with 
their  axes  in  different  directions  would  evidently  not  be  electrically 
homogeneous  and  would  thus  possess  the  property  in  question.  In  the 
case  of  glass  it  is  very  possible  that  this  may  be  the  case  and  it  would 
certainly  be  so  for  ice  or  any  other  crystalline  substance  which  had 
been  melted  and  cooled. 

In  the  case  of  hard  india  rubber,  the  black  color  is  due  to  the  particles 
of  carbon,  and  as  other  materials  are  incorporated  into  it  during  the 
process  of  manufacture,  it  is  certainly  not  electrically  homogeneous. 

As  to  the  ordinary  explanation  that  the  electricity  penetrates  a  little 
below  the  surface  and  then  reappears  again  to  form  the  residual  charge, 
we  see  that  it  is  in  general  entirely  false.  We  could,  indeed,  form  a 
condenser  in  which  the  surface  of  the  dielectric  would  be  a  better  con- 
ductor than  the  interior  and  which  would  act  thus.  But  in  general, 
the  theory  shows  that  the  action  takes  place  throughout  the  mass  of 
the  dielectric,  where  that  is  of  a  fine  grained  structure  and  apparently 
homogeneous,  as  in  the  case  of  glass,  and  consists  of  a  polarization  of 
every  part  of  the  dielectric. 

To  consider  more  fully  the  case  of  a  condenser  made  of  parallel 
plates,  let  us  resume  our  original  equations.  Without  much  loss  of 
generality  we  can  assume  a  laminated  structure  of  the  substance  in 


NOTE  ON  THE  THEORY  OF  ELECTRIC  ABSORPTION  143 

the  direction  of  the  plane  YZ,  so  that  m  and  V  will  be  only  functions 
of  the  ordinate  x.     Our  equations  then  become 

d 


A      ~- 

dx       dx  j       dt 

Eliminating  p  we  find 

•if  A  _ 

4-    dt    dx  \dx         dx       dx 
Now  let  us  make  p  =  x  -=-    and  as  t  and  x  are  independent,  we  find 

CvtC 

on  integration, 

(P  —  Pj  +  4"  (Pm  —  jOoWo)  =  0, 


where  p0  is  the  value  of  p  for  some  initial  value  of  x,  say  at  the  surface 
of  the  condenser,  and  is  an  arbitrary  function  of  t,  seeing  that  we  may 
vary  the  charge  at  the  surface  of  the  body  in  any  arbitrary  manner. 
This  equation  establishes  p  as  a  function  of  m  and  t  only,  and  as  we  have 

1     dp 
~~      - 


p  will  also  be  a  function  of  these  only. 

Let  us  now  suppose  that  at  the  time  t  =  0,  the  condenser  is  charged, 
having  had  no  charge  before,  and  let  us  also  suppose  that  the  different 
strata  of  the  dielectric  are  infinitely  thin  and  are  placed  in  the  same 
order  and  are  of  the  same  thickness  at  every  'part  of  the  substance,  so 
that  a  finite  portion  of  the  substance  will  have  the  same  properties  at 
every  part. 

In  this  case  m  will  be  a  periodic  function  of  x,  returning  to  the  same 
value  again  and  again.  As  p  is  a  function  of  this  and  of  t  only,  at  a 
given  time  t,  it  must  return  again  and  again  to  the  same  value  as  we 
pass  through  the  substance,  indicating  a  uniform  polarized  structure 
throughout  the  body. 

This  conclusion  would  have  been  the  same  had  we  not  assumed  a 
laminated  structure  of  the  dielectric.  In  all  other  cases,  except  that 
of  two  planes,  electric  absorption  can  take  place,  as  we  have  before 
remarked,  even  in  perfectly  homogeneous  bodies,  provided  that  Ohm's 
law  is  departed  from  or  that  the  electric  induction  is  not  proportional 
to  the  electric  force,  as  well  as  in  non-homogeneous  bodies.  But  where 
the  body  is  thus  homogeneous,  electric  absorption  is  not  due  to  a  uni- 


144  HENRY  A.  KOWLAND 

form  polarization,  but   to   distinct  regions   of  positive   and  negative 
electrification. 

In  the  whole  of  the  investigation  thus  far  we  have  sought  for  the 
means  of  explaining  the  phenomenon  solely  by  means  of  the  known 
laws  of  electric  induction  and  conduction.  But  many  of  the  phenomena 
of  electric  absorption  indicate  electrolytic  action,  and  it  is  possible  that 
in  many  cases  this  is  the  cause  of  the  phenomenon.  The  only  object 
of  this  note  is  to  partially  generalize  Maxwell's  explanation,  leaving 
the  electrolytic  and  other  theories  for  the  future. 


15 


RESEARCH  ON  THE  ABSOLUTE  UNIT  OF  ELECTEICAL 

RESISTANCE  * 

[American  Journal  of  Science  [3],  XV,  281-291,  325-336,  430-439,  1878] 

PEELIMINAEY  REMABKS 

Since  the  classical  determination  of  the  absolute  unit  of  electrical 
resistance  by  the  Committee  on  Electrical  Standards  of  the  British 
Association,  two  re-determinations  have  been  made,  one  in  Germany  and 
the  other  in  Denmark,  which  each  differ  two  per  cent  from  the  British 
Association  determination,  the  one  on  one  side  and  the  other  on  the 
other  side,  making  a  total  difference  of  four  per  cent  between  the  two. 
Such  a  great  difference  in  experiments  which  are  capable  of  consider- 
able exactness,  seems  so  strange  that  I  decided  to  make  a  new  deter- 
mination by  a  method  different  from  any  yet  used,  and  which  seemed 
capable  of  the  greatest  exactness;  and  to  guard  against  all  error,  it  was 
decided  to  determine  all  the  important  factors  in  at  least  two  different 
ways,  and  to  eliminate  most  of  the  corrections  by  the  method  of  experi- 
ment, rather  than  by  calculation.  The  method  of  experiment  depended 
upon  the  induction  of  a  current  on  a  closed  circuit,  and  in  this  respect, 
resembled  that  of  Kirchhoff,  but  it  differed  from  his  inasmuch  as,  in 
my  experiment,  the  indiiction  current  was  produced  by  reversing  the 
main  current,  and  in  Kirchhoff's  by  removing  the  circuits  to  a  distance 
from  each  other.  And  it  seems  to  me  that  this  method  is  capable  of 
greater  exactness  than  any  other,  and  it  certainly  possessed  the  greatest 
simplicity  in  theory  and  facility  in  experiment. 

In  the  carrying  out  of  the  experiment  I  have  partly  availed  myself 
of  my  own  instruments  and  have  partly  drawn  on  the  collection  of  the 
University,  which  possesses  many  unique  and  accurate  instruments  for 
electric  and  magnetic  measurements.  To  insure  uniformity  and  accur- 
acy, the  coils  of  all  these  instruments  have  been  wound  with  my  own 
hands  and  the  measurements  reduced  to  a  standard  rule  which  was 

1 1  am  greatly  indebted  to  Mr.  Jacques,  Fellow  of  the  University,  who  is  an  excel- 
lent observer,  for  his  assistance  during  the  experiment,  particularly  in  reading  the 
tangent  galvanometer. 
10 


146  HENRY  A.  KOWLAND 

again  compared  with  the  standard  at  Washington.  Unlike  many  Ger- 
man instruments,  quite  fine  wire  has  always  been  used  and  the  number 
of  coils  multiplied,  for  in  this  way  the  constants  of  the  coils  can  be 
more  exactly  determined,  there  is  less  relative  action  from  the  wire 
connecting  the  coils,  and  above  all  we  know  exactly  where  the  current 
passes. 

The  experiment  was  performed  in  the  back  room  of  a  small  house 
near  the  University,  which  was  reasonably  free  from  magnetic  and  other 
physical  disturbances.  As  the  magnetic  disturbance  was  eliminated 
in  the  experiment,  it  was  not  necessary  to  select  a  region  entirely  free 
from  such  disturbance.  The  small  probable  error  proves  that  sufficient 
precaution  was  taken  in  this  respect. 

The  result  of  the  experiment  that  the  British  Association  unit  is  too 
great  by  about  -88  per  cent,  agrees  well  with  Joule's  experiment  on  the 
heat  generated  in  a  wire  by  a  current,  and  makes  the  mechanical  equiv- 
alent as  thus  obtained  very  nearly  that  which  he  found  from  friction: 
it  is  intermediate  between  the  result  of  Lorenz  and  the  British  Asso- 
ciation Committee;  and  it  agrees  almost  exactly  with  the  British  Asso- 
ciation Committee's  experiments,  if  we  accept  the  correction  which  I 
have  applied  below. 

The  difference  of  nearly  three  per  cent  which  remains  between  my 
result  and  that  of  Kohlrausch  is  difficult  to  explain,  but  it  is  thought 
that  something  has  been  done  in  this  direction  in  the  criticism  of  his 
method  and  results  which  are  entered  into  below.  My  value,  when 
introduced  into  Thomson's  and  Maxwell's  values  of  the  ratio  of  the 
electromagnetic  to  the  electrostatic  units  of  electricity,  caused  a  yet 
further  deviation  from  its  value  as  given  in  Maxwell's  electromagnetic 
theory  of  light:  but  experiments  on  this  ratio  have  not  yet  attained 
the  highest  accuracy. 

HISTORY 

The  first  determination  of  the  resistance  of  a  wire  in  absolute  meas- 
ure was  made  by  Kirchhoff 2  in  1849  in  answer  to  a  question  propounded 
by  Neumann,  in  whose  theory  of  electrodynamic  induction  a  constant 
appeared  whose  numerical  value  was  unknown  until  that  time.  His 
method,  like  that  of  this  paper,  depended  on  induction  from  currents: 
only  one  galvanometer  was  used  and  the  primary  current  was  measured 
by  allowing  only  a  small  proportion  of  it  to  pass  through  the  galvano- 

2Bestimmung  der  Constanten  von  welcher  die  Intensitat  inducirter  elektrischer 
Strome  abhangt.     Fogg.  Ann.,  Bd.  76,  S.  412. 


Ox  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  RESISTANCE         147 

meter  by  means  of  a  shunt,  while  all  the  induced  current  passed  through 
it.  But,  owing  to  the  heating  of  the  wires,  the  shunt  ratio  cannot  be 
relied  upon  as  constant,  and  hence  the  defect  of  the  method.  At  pres- 
ent this  experiment  has  only  historical  value,  seeing  that  no  exact 
record  was  kept  of  it  in  a  standard  resistance.  However,  we  know  that 
the  wire  was  of  copper  and  the  temperature  0°  R.  and  that  the  result 
obtained  gave  the  resistance  of  the  wire  $  smaller  than  Weber  found 
for  the  same  wire  at  20°  R.  in  1851. 

In  1851,  "Weber  published8  experiments  by  two  methods,  first  by 
means  of  an  earth  inductor,  and  second  by  observing  the  damping  of  a 
swinging  needle.  Three  experiments  gave  for  the  resistance  of  the 

circuit  1903  -108,  1898  -108,  and  1900 -10s,    — ,  but  it  is  to  be  noted 

sec. 

that  a  correction  of  five-eighths  per  cent  was  made  on  account  of  the 
time,  two  seconds,  which  it  took  to  turn  the  earth-inductor,  and  that 
no  account  was  taken  of  the  temperature,  although  the  material  was 

copper.     He  finds  for  the  value  of  the  Jacobi  unit,  598  -107^.    Three 

OCC'B 

years  after  that,  in  1853,  Weber  made  another  determination  of  the 
specific  resistance  of  copper.4  But  these  determinations  were  more  to 
develope  the  method  than  for  exact  measurement,  and  it  was  not  until 
1862  5  that  Weber  made  an  exact  determination  which  he  expected  to 
be  standard.  In  this  last  determination  he  used  a  method  compounded 
of  his  first  two  methods  by  which  the  constant  of  the  galvanometer  was 
eliminated,  and  the  same  method  has  since  been  used  by  Kohlrausch 
in  his  experiments  of  1870.  The  results  of  these  experiments  were 
embodied  in  a  determination  of  the  value  of  the  Siemens  unit  and  of 
a  standard  which  was  sent  by  Sir  Wm.  Thomson.  As  the  old  Siemens 
units  seem  to  vary  among  themselves  one  or  two  per  cent,  and  as  the 
result  from  Thomson's  coil  differs  more  than  one  per  cent  from  that 
which  would  be  obtained  with  any  known  value  of  the  Siemens  unit, 
we  cannot  be  said  to  know  the  exact  result  of  these  experiments  at  the 
present  time.  Beside  which,  it  was  not  until  the  experiments  of  Dr. 
Matthiessen  on  the  electric  permanence  of  metals  and  alloys,  that  a 
suitable  material  could  be  selected  for  the  standard  resistance. 

The  matter  was  in  this  state  when  a  committee  was  appointed  by  the 

3Elektrodynamische  Maasbestimmungen  ;  or  Pogg.  Ann.,  Bd.  82,  S.  337. 
4Abh.  d.  Kon.  Ges.  d.  Wissenchaften  zu  Gottingen,  Bd.  5. 

5Zur  Galvanometrie,  Gottingen,  1862.  Also  Abb.  d.  K.  Ges.  d.  Wis.  zu  Gottingen, 
Bd.  10. 


148  HENRY  A.  BOWLAXD 

British  Association  in  1861,  who,  by  their  experiments  which  have  ex- 
tended through  eight  years,  have  done  so  much  for  the  absolute  system 
of  electrical  measurements.  But  the  actual  determination  of  the  unit 
was  made  in  1863-4.  The  method  used  was  that  of  the  revolving  coil 
of  Sir  William  Thomson,  the  principal  advantage  of  which  was  its  sim- 
plicity and  the  fact  that  the  local  variation  of  the  earth's  magnetism 
was  entirely  eliminated  and  only  entered  into  the  calculation  as  a  small 
correction.  The  principle  of  the  method  is  of  extreme  beauty,  seeing 
that  the  same  earth's  magnetism  which  causes  the  needle  at  the  centre 
of  the  coil  to  point  in  the  magnetic  meridian  also  causes  the  current  in 
the  revolving  coil  which  deflects  the  needle  from  that  meridian.  When- 
ever a  conducting  body  moves  in  a  magnetic  field,  currents  are  gener- 
ated in  it  in  such  direction  that  the  total  resultant  action  is  such  that 
the  lines  of  force  are  apparently  dragged  after  the  body  as  though  they 
met  with  resistance  in  passing  through  it :  and  so  we  may  regard  Thom- 
son's method  as  a  means  of  measuring  the  amount  of  this  dragging 
action. 

But,  however  beautiful  and  apparently  simple  the  method  may  appear 
in  theory,  yet  when  we  come  to  the  details  we  find  many  reasons  for 
not  expecting  the  finest  results  from  it.  Nearly  all  these  reasons  have 
been  stated  by  Kohlrausch,  and  I  can  do  barely  more  in  this  direction 
than  review  his  objections,  point  out  the  direction  in  which  each  would 
affect  the  result,  and  perhaps  in  some  cases  estimate  the  amount. 

In  the  first  place,  as  the  needle  also  induced  currents  in  the  coil 
which  tended  in  turn  to  deflect  the  needle,  the  needle  must  have  a  very 
small  magnetic  moment  in  order  that  this  term  may  be  small  enough 
to  be  treated  as  a  correction.  For  this  reason  the  magnetic  needle 
was  a  small  steel  sphere  8  mm.  diameter,  and  not  magnetized  to  satur- 
ation. It  is  evident  that  in  a  quiescent  magnetic  field  such  a  magnet 
would  give  the  direction  of  the  lines  of  force  as  accurately  as  the  large 
magnets  of  Gauss  and  Weber,  weighing  many  pounds.  But  the  mag- 
netic force  due  to  the  revolving  coil  is  intermittent  and  the  needle  must 
show  as  it  were  the  average  force,  together  with  the  action  due  to 
induced  magnetization.  Whether  the  magnet  shows  the  average  force 
acting  on  it  or  not,  depends  upon  the  constancy  of  the  magnetic  axis, 
and  there  seems  to  be  no  reason  to  suppose  that  this  would  change  in 
the  slightest,  though  it  would  have  been  better  to  have  made  the  form 
of  the  magnet  such  that  it  would  have  been  impossible.  The  induced 
magnetism  of  the  sphere  would  not  affect  the  result,  were  it  not  for  the 
time  taken  in  magnetization:  on  this  account  the  needle  is  dragged 


Ox  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  EESISTAXCE         149 

with  the  coil,  and  hence  makes  the  deflection  greater  than  it  should  be, 
and  the  absolute  value  of  the  Ohm  too  small  by  a  very  small  quantity. 
The  currents  induced  in  the  suspended  parts  also  act  in  the  same 
direction.  Neither  of  these  can  be  estimated,  but  they  are  evidently 
very  minute. 

The  mere  fact  that  this  small  magnet  was  attached  to  a  comparatively 
large  mirror  which  was  exposed  to  air  currents  could  hardly  have 
affected  the  results,  seeing  that  the  disturbances  would  have  been  all 
eliminated  except  those  due  to  air  currents  from  the  revolving  coil,  and 
which  we  are  assured  did  not  exist  from  the  fact  that  no  deflection  took 
place  when  the  coil  was  revolved  with  the  circuit  broken.  In  revolving 
the  coil  in  opposite  directions  very  different  results  were  obtained,  and 
the  explanation  of  this  has  caused  considerable  discussion.  As  this  is 
of  fundamental  importance  I  shall  consider  it  in  detail. 

The  magnet  was  suspended  by  a  single  fibre  seven  feet  long,  and  the 
deflection  was  diminished  by  its  torsion  -00132.  No  mention  is  made 
of  the  method  used  for  untwisting  the  fibre,  and  we  see  that  it  would 
require  only  2-11  turns  to  deflect  the  needle  1°  from  the  meridian. 
To  estimate  the  approximate  effect  of  this,  we  may  omit  from  Maxwell's 
equation  *  all  the  other  minor  corrections  and  we  have 

GKw  cos  <f     _        GKw ]_ 

:*tan?>(l  +  /)/7~  $t       "\nearly, 

1 — ; 


sin 

where  we  have  substituted  <p  —  /3  for  <p  in  Maxwell's  equation  in  the 
term  involving  t.  In  this  equation  <p  is  measured  from  the  magnetic 
meridian;  but  let  us  take  (p  as  the  angle  from  the  point  of  equilibrium. 
Then  tp'  =  <p'  +  a  and  (p"  =  <p"  —  «,  where  <p'  and  (f '  are  for  negativa 

OJ 

rotation  and  (p"  and  <p"  for  positive  rotation  and  « =  arc  sin 

Let 

Then  CR  = 

CR"  = 


_ 

tan  4'"  (1  +  0  ' 
R,=  l(R'  +  R"}. 

Where  R'  and  R"  are  the  apparent  values  of  the  resistance  as  calculated 
from  the  negative  and  positive  rotations,  and  R,  is  the  mean  of  the 


Reports  on  Electrical  Standards,'  p.  103. 


150  HENRY  A.  KOWLAXD 

two  as  taken  from  the  table  published  by  the  British  Association  Com- 
mittee.    If  R  is  the  true  resistance, 

1  1 


We  shall  then  find  approximately 

n  _  1  +  tan  v';'  tan  a  _  I  —  tan  <l'"  tan  a 

~  „„  /.,       sin  a  V-       tan  a 
-ft      1  — 


tan  f/  \         sin  ^"/\         tan 

When  a  is  small  compared  with  </'"  or  0',  and  when  these  are  also  small, 
we  have 

R  =  R,  (1  +  a2  (a2  -  |  0»)  +  &c.). 

So  that  by  taking  the  mean  of  positive  and  negative  rotations,  the 
effect  of  torsion  is  almost  entirely  eliminated.  Now  a  is  the  angle  by 
which  the  needle  is  deflected  from  the  magnetic  meridian  by  the  torsion 

1    /          /?'  \ 
and  its  value  is  —  ( 1  —  -^ )  nearly,  when  a  is  small,  and  this,  in  one 

«Kr  \  **  I 

or  two  of  their  experiments,  exceeds  unity  or  a  exceeds  28°. 6,  which 

Tf 

is  absurd.     Taking  even  one  of  the  ordinary  cases  where  -™>  =  102 

and  (p  is  about  ^V»  we  have  a=  12  °-  nearly,  which  is  a  value  so  large 
that  it  would  surely  have  been  noticed.  Hence  we  may  conclude 
that  no  reasonable  amount  of  torsion  in  the  silk  fibre  could  have 
produced  the  difference  in  the  results  from  positive  and  negative 
rotation,  as  has  been  stated  by  Mr.  Fleming  Jenkin  in  his  '  Keport  on 
the  New  Unit  of  Electrical  Eesistance/ r 

The  greatest  value  which  we  can  possibly  assign  to  a  which  might 
have  remained  unnoticed  is  y1^,  which  would  not  have  affected  the 
the  experiment  to  any  appreciable  extent. 

Another  source  of  error  which  may  produce  the  difference  we  are 
discussing  is  connected  with  the  heavy  metal  frame  of  the  apparatus, 
in  which  currents  can  be  induced  by  the  revolving  coil.  The  coil 
passes  so  near  the  frame-work  that  the  currents  in  it  must  be  quite 
strong  and  produce  considerable  magnetic  effect.  Kohlrausch  has 
pointed  out  the  existence  of  these  currents,  but  has  failed  to  consider 
the  theory  of  them.  Now,  from  the  fact  that  after  any  number  of 
revolutions  the  number  of  lines  of  force  passing  through  any  part 
of  the  apparatus  is  the  same  as  before,  we  immediately  deduce  the 

1 '  Reports  on  Electrical  Standards,'  London,  1873,  p.  191. 


ON  THE  ABSOLUTE  UNIT  OF  ELECTEICAL  EESISTAXCE         151 

fact  that,  if  Ohm's  law  be  correct,  the  algebraical  sum  of  the  currents 
at  every  point  in  the  frame  is  zero,  and  hence  the  average  magnetic 
action  on  the  needle  zero.  But  although  these  currents  can  have 
no  direct  action,  they  can  still  act  by  modifying  the  current  in  the 
coil;  for  while  the  coil  is  nearing  one  of  the  supports  the  current 
in  the  coil  is  less  than  the  normal  amount,  and  while  it  is  leaving 
it  is  greater;  and  although  the  total  current  in  the  coil  is  the  normal 
amount,  yet  it  acts  on  the  needle  at  a  different  angle.  By  changing 
the  direction  of  rotation,  the  effect  is  nearly  but  not  quite  eliminated. 
The  amount  of  the  effect  is  evidently  dependent  upon  the  velocity 
of  rotation  and  increases  with  it  in  some  unknown  proportion,  and 
the  residual  effect  is  evidently  in  the  direction  of  making  the  action 
on  the  needle  too  small  and  thus  of  increasing  R.  If  these  currents 
are  the  cause  of  the  different  values  of  R  obtained  with  positive  and 
negative  rotation,  we  should  find  that  if  we  picked  out  those  experi- 
ments in  which  this  difference  was  the  greatest,  they  should  give 
a  larger  value  of  R  than  the  others.  Taking  the  mean  of  all  the 
results "  in  which  this  difference  is  greater  than  one  per  cent,  we  find 

for  the  Ohm  1.0033  earth  ^uadt,  and  when  it  is  less  than  one  per 

sec. 

cent,  -9966   — r- — SC*r   which  is  in  accordance  with  the  theory,  the 
sec. 

average   velocities   being    ^    and    *^°    nearly.     But   the   individual 
observations  have  too  great  a  probable  error  for  an  exact  comparison. 

But  whatever  the  cause  of  the  effect  we  are  considering,  the  follow- 
ing method  of  correction  must  apply.  The  experiments  show  that  R 
is  a  function  of  the  velocity  of  rotation,  and  hence,  by  Taylor's  theorem, 
the  true  resistance  R0  must  be 

R0  =  R  (1  -f-  Aw  +  Bw2  +  &c.), 

and  when  R  is  the  mean  of  results  with  positive  and  negative  rotations, 
R0  =  R  (1  -f  Bw2  +  DW*  +  &c.). 

Supposing  that  all  the  terms  can  be  omitted  except  the  first  two,  and 
using  the  above  results  for  large  and  small  velocities,  we  find  .R0 

_  .9926earth  quad.      But  if  we       -ect  the  two  resuits  in  wnich  the 
sec. 

8  In  the  table  published  by  the  Committee  the  different  columns  do  not  agree,  and 
I  have  thought  it  probable  that  the  last  two  numbers  in  the  next  to  the  last  column 
should  read  1-0032  and  1-0065  instead  of  1-0040  and  -9981,  and  in  my  discussion  I 
have  considered  them  to  read  thus. 


152  HENEY  A.  EOWLAND 

difference  of  positive  and  negative  rotations  is  over  seven  per  cent, 
we  find 


sec. 

The  rejection  of  all  the  higher  powers  of  w  renders  the  correction 
uncertain,  but  it  at  least  shows  that  the  Ohm  is  somewhat  smaller 
than  it  was  meant  to  be,  which  agrees  with  my  experiments. 

It  is  to  be  regretted  that  the  details  of  these  experiments  have 
never  been  published,  and  so  an  exact  estimate  of  their  value  can 
never  be  made.  Indeed  we  have  no  data  for  determining  the  value 
of  the  Ohm  from  the  experiments  of  1863.  All  we  know  is  that,  in 
the  final  result,  the  1864  experiments  had  five  times  the  weight  of 
those  of  1863,  and  that  the  two  results  differed  -16  per  cent,  but 
which  was  the  larger  is  not  stated.  Now  the  table  of  results  pub- 
lished in  the  report  of  the  1864  experiments  contains  many  errors, 
some  of  which  we  can  find  out  by  comparison  of  the  columns.  The 
following  corrections  seem  probable  in  the  eleven  experiments  :  No.  4, 
second  column,  read  4-6375  for  4-6275.  No.  10,  fourth  and  fifth 
columns,  read  1-0032  and  +  0-32  in  place  of  1-0040  and  +0-40.  No. 
11,  fourth  and  fifth  columns,  read  1-0065  and  +  0-65  in  place  of  0-9981 
and  —  0-19.  Whether  we  make  these  corrections  or  not  the  mean 
value  is  entirely  incompatible  with  the  statement  with  respect  to  the 
1863  experiments.  With  the  corrections  the  mean  value  of  the  1864 

experiments  is  1  Ohm  =  1-00071  earth  ^uad\  and  without  them,  using 

sec. 

the  fourth  column,  it  is  1-00014.  With  the  corrections  the  difference 
between  fast  and  slow  rotation  is  •  6  per  cent. 

In  the  year  1870  Professor  F.  Kohlrausch  made  a  new  determination 
of  Siemen's  unit  in  absolute  measure,  the  method  being  one  formed 
out  of  a  combination  of  Weber's  two  methods  of  the  earth  inductor  and 
of  damping,  by  which  the  constant  of  the  galvanometer  was  eliminated, 
and  is  the  same  as  Weber  used  in  his  experiments  of  1862.  His  formula 
for  the  resistance  of  the  circuit,  omitting  small  corrections,  is 

approximately, 


where  8  is  the  surface  of  the  earth  inductor,  T  is  the  horizontal  inten- 
sity of  the  earth's  magnetism,  K  the  moment  of  inertia  of  the  magnet, 
t0  the  time  of  vibration  of  the  magnet,  ^  the  logarithmic  decrement, 
and  A  and  B  are  the  arcs  in  the  method  of  recoil. 


ON  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  EESISTANCE         153 

One  of  the  principal  criticisms  I  have  to  offer  with  respect  to  this 
method  is  the  great  numher  of  quantities  difficult  to  observe,  which 
enter  the  equation  as  squares,  cubes,  or  even  fourth  powers.  Thus  S2 
depends  upon  the  fourth  power  of  the  radius  of  the  earth  inductor. 
Now  this  earth  inductor  was  wound  years  before  by  W.  Weber,  and  the 
mean  radius  determined  from  the  length  of  wire  and  controlled  by 
measuring  the  circumference  of  the  layers.  Now  the  wire  was  nearly 
3-2  mm.  diameter  with  its  coating,  and  the  outer  and  inner  radii  were 
115-  mm.  and  142  mm.  Hence  the  diameter  of  the  wire  occupied  two 
per  cent  of  the  radius  of  the  coil,  making  it  uncertain  to  what  point 
the  radius  should  be  measured.  As  the  coil  is  wound,  each  winding 
sinks  into  the  space  between  the  two  wires  beneath,  except  at  one  spot 
where  it  must  pass  over  the  tops  of  the  lower  wires.  The  wire  must 
also  be  wound  in  a  helix.  All  these  facts  tend  to  diminish  8  and  make 
its  value  as  deduced  from  the  length  of  the  wire  too  large;  and  any 
kinks  or  irregularities  in  the  wire  tend  in  the  same  direction.  And 
these  errors  must  be  large  in  an  earth-inductor  of  such  dimensions, 
where  the  wire  is  so  large  and  many  layers  are  piled  on  each  other. 
If  we  admit  an  error  of  one-half  a  millimetre  in  the  radius  as  deter- 
mined in  this  way,  it  would  diminish  the  value  of  S2  1-4  per  cent,  and 
make  Kohlrausch's  result  only  -6  per  cent  greater  than  the  result  of 
the  British  Association  Committee. 

Three  other  quantities,  T,  X  and  K,  are  very  hard  to  determine  with 
accuracy,  and  yet  T  enters  as  a  square.  It  is  to  be  noted  that  this 
earth-inductor  is  the  same  as  that  used  by  Weber  in  his  experiment  of 
1862,  and  which  also  gave  a  larger  value  to  the  Ohm  than  those  of  the 
British  Association  Committee.  Indeed,  the  results  with  this  inductor 
and  by  this  method  form  the  only  cases  where  the  absolute  resistance  of  the 
Ohm  has  been  found  greater  than  that  from  the  experiments  of  the  British 
Association  Committee, 

There  seems  to  be  a  small  one-sided  error  in  A  and  B  which  Kohl- 
rausch  does  not  mention,  but  which  Weber,  in  his  old  experiments  of 
1851,  considered  worthy  of  a  -6  per  cent  correction,  and  which  would 


diminish  by  1-2  per  cent.     This  is  the  error  due  to  loss  of 

time  in  turning  the  earth-inductor.  As  Kohlrausch's  needle  had  a 
longer  time  of  vibration  than  Weber's,  the  correction  will  be  much 
smaller.  In  Weber's  estimate  the  damping  was  not  taken  into  account, 
and  indeed  it  is  impossible  to  do  so  with  exactness.  To  get  some  idea 
of  the  value  of  the  correction,  however,  we  can  assume  that  the  current 


154  HENRY  A.  KOWLAND 

from  the  earth-inductor  is  uniform  through  a  time  t'",  and  the  com- 
plete solution  then  depends  on  the  elimination  of  nine  quantities  from 
ten  complicated  equations,  and  which  can  only  be  accomplished  approx- 
imately. If  f  is  the  true  value  of  the  angular  velocity,  as  given  to  the 
needle  by  the  earth-inductor,  and  f  is  the  velocity  as  deduced  from  the 
ordinary  equation  for  the  method  of  recoil,  I  find 


where  A  is  the  logarithmic  decrement,  £  the  base  of  the  natural  system 
of  logarithms,  T  the  time  of  vibration  of  the  needle,  and  t  the  time 
during  which  the  uniform  current  from  the  earth-inductor  flows.  In 
the  actual  case,  the  current  from  the  earth-inductor  is  nearly  propor- 
tional to  sin  t,  and  hence  it  will  be  more  exact  to  substitute 

/     /     \2     /»iir  /     / 

4 (--)   I  taiiitdt  =  l(  — 
V  *  /  «/•  v  * 

in  the  place  of  t2.     The  formula  then  becomes 


This  modification  is  more  exact  when  ),  is  small  than  when  it  is  large, 
but  it  is  sufficiently  exact  in  all  cases  to  give  some  idea  of  the  magni- 
tude of  the  error  to  be  feared  from  this  source.  Kohlrausch  does  not 
state  how  long  it  took  him  to  turn  his  earth-inductor,  but  as  T  =  34 

seconds,  we  shall  assume  -^  —  J^  and  as  /  =  \  nearly,  we  have 

-?-  =  1-0008, 

r« 

which  would  diminish  the  value  of  the  resistance  by  -16  per  cent. 

As  the  time  we  have  allowed  for  turning  the  earth-inductor  is  prob- 
ably greater  than  it  actually  was,  the  actual  correction  will  be  less  than 
this. 

The  correction  for  the  extra  current  induced  in  the  inductor  and 
galvanometer,  as  given  by  Maxwell's  equation,9  has  been  shown  by 
Stoletow  to  be  too  small  to  affect  the  result  appreciably. 

We  may  sum  up  our  criticism  of  this  experiment  in  a  few  words. 
The  method  is  defective  because,  although  absolute  resistance  has  the 

dimensions  of   -     — ,  yet  in  this  method  the  fourth  power  of  space  and 
9  '  Electricity  and  Magnetism,'  art.  762. 


ON  THE  ABSOLUTE  UNIT  OF  ELECTEICAL  RESISTANCE         155 

the  square  of  time  enter,  besides  other  quantities  which  are  difficult  to 
determine.  The  instruments  are  defective,  because  the  earth-inductor 
was  of  such  poor  proportion  and  made  of  such  large  wire  that  its 
average  radius  was  difficult  to  determine,  and  was  undoubtedly  over- 
estimated. 

It  seems  probable  that  a  paper  scale,  which  expands  and  contracts 
with  the  weather  was  used.  And  lastly,  the  results  with  this  inductor 
and  by  this  method  have  twice  given  greater  results  than  anybody  else 
has  ever  found,  and  greater  than  the  known  values  of  the  mechanical 
equivalent  of  heat  would  indicate. 

The  latest  experiments  on  resistance  have  been  made  by  Lorenz  of 
Copenhagen,10  by  a  new  method  of  his  own,  or  rather  by  an  application 
of  an  experiment  of  Faraday's.  It  consists  in  measuring  the  difference 
of  potential  between  the  centre  and  edge  of  a  disc  in  rapid  rotation 
in  a  field  of  known  magnetic  intensity. 

A  lengthy  criticism  of  this  experiment  is  not  needed,  seeing  that  it 
was  made  more  to  illustrate  the  method  than  to  give  a  new  value  to 
the  Ohm.  The  quantity  primarily  determined  by  the  experiment  was 
the  absolute  resistance  of  mercury,  and  the  Ohm  will  have  various 
values  according  to  the  different  values  which  we  assume  for  the  resist- 
ance of  mercury  in  Ohms. 

One  of  the  principal  defects  of  the  experiment  is  the  large  ratio 
between  the  radius  of  the  revolving  disc  and  the  coil  in  which  it 
revolved. 

In  conclusion  I  give  the  following  table  of  results,  reduced  as  nearly 

as  possible  to  the  absolute  value  of  the  Ohm  in  earth  quad\" 

sec. 

i°Pogg.  Ann.,  Bd.  cxlix,  (1873),  p.  251. 

11  Since  this  was  written,  a  new  determination  has  been  made  by  H.  F.  Weber,  of 
Zurich,  in  which  the  different  results  agree  with  great  accuracy.  The  result  has 
been  expressed  in  Siemen's  units,  and  the  comparison  seems  to  have  been  made 
simply  with  a  set  of  resistance  coils  and  not  with  standards.  The  modern  Siemen's 
units  seem  to  be  reasonably  exact,  but  from  the  table  published  by  the  British 
Association  Committee  in  1864,  it  seems  that  at  that  time  there  was  uncertainty  as 

to  its  value.     He  obtains  1  8.  U.  =  -9550  —  ---',  which  is  greater  or  less  than 

sec. 

the  British  Association  determination,  according  as  we  take  the  different  ratios  of 
the  Siemen's  to  the  British  Association  unit,  ranging  from  -14  per  cent  above  to  1-92 
per  cent  below.  In  any  case  the  result  agrees  reasonably  well  with  my  own.  The 
apparatus  used  does  not  seem  to  have  been  of  the  best,  and  the  exact  details  are  not 
given.  But  wooden  coils  to  wind  the  wire  on  seem  to  have  been  used,  which  should 
immediately  condemn  the  experiment  where  a  pair  of  coils  is  used,  seeing  that  in 
that  case  the  constant,  both  of  magnetic  effect  and  of  induction,  depend  on  the  dis- 
tance of  the  coils.  It  is  unfortunate  that  sufficient  details  are  not  given  for  me  to 
enter  into  a  criticism  of  the  experiment. 


156 


HENRY  A.  EOWLAND 


Date. 

Observer. 

Value  of  Ohm. 

Remarks. 

1849 

Kirchhoff  

•88  to  -90 

Approximately. 

1851 

Weber  

•95  to  -97 

1862 

Weber  

(  1-088 

From  Thomson's  unit. 

1863-4 
1870 

B.  A.  Committee. 
Kohlrausch  

{  1-075 
1-0000 
*     -993 
1-0196 

From  Weber's  value  of  Siemen's  unit. 
Mean  of  all  results. 
Corrected  to  a  zero  velocity  of  coil. 

1873 

Lorenz  

£     -970 

Taking  ratio  of  quicksilver  unit  to  Ohm  = 
•962. 

1876 

Rowland  

\    -980 
•9912 

Taking  ratio  of  quicksilver  unit  to  Ohm= 
•953. 
From  a  preliminary  comparison  with  the  B. 

A.  unit. 

THEORY  OF  THE  METHOD 

When  a  current  is  induced  in  a  circuit  by  magnetic  action  of  any  kind, 
Faraday  has  shown  that  the  induced  current  is  proportional  to  the 
number  of  lines  of  force  cut  by  the  circuit  and  inversely  as  the  resist- 
ance of  the  circuit.  If  we  have  two  circuits  near  each  other,  the  first 
of  which  carries  a  current,  and  the  second  is  then  removed  to  an  infinite 
distance,  there  will  be  a  current  in  it  proportional  to  the  number  of 
lines  of  force  cut.  Let  now  a  unit  current  be  sent  through  the  second 
circuit  and  one  of  strength  E  through  the  first;  then,  on  removing 
the  second  circuit,  work  will  be  performed  which  we  easily  see  is  also 
proportional  to  the  number  of  lines  of  force  cut.  Hence,  if  EM  is 
the  work  done,  Q  is  the  induced  current,  and  R  is  the  resistance  of  the 
second  circuit, 


-, 

where  C  is  a  constant  whose  value  is  unity  on  the  absolute  system. 

When  the  current  in  the  first  circuit  is  broken,  the  lines  of  force 
contract  on  themselves,  and  the  induced  current  is  the  same  as  if  the 
second  circuit  had  been  removed  to  an  infinite  distance.  If  the  current 
is  reversed  the  induced  current  is  twice  as  great;  hence  in  this  case 


=  ^  or        = 

K  V 

Hence,  to  measure  the  absolute  resistance  of  a  circuit  on  this  method, 
we  must  calculate  M  and  measure  the  ratio  of  Q  to  E.  M  is  known 
as  the  mutual  potential  of  the  two  circuits  with  unit  currents,  and 
mathematical  methods  are  known  for  its  calculation. 

The  simplest  and  best  form  in  which  the  wire  can  be  wound  for  the 


Ox  THE  ABSOLUTE  UXIT  OF  ELECTKICAL  KESISTAXCE         157 

calculation  of  M  is  in  parallel  circular  coils  of  equal  size  and  of  as 
small  sectional  area  as  possible.  For  measuring  E  a  tangent  galvano- 
meter is  needed,  and  we  shall  then  have 

E=  ^  tanfl. 

6r 

where  H  is  the  horizontal  intensity  of  the  earth's  magnetism  at  the 
place  of  the  tangent  galvanometer,  and  G  the  constant  of  the  galvano- 
meter. 

For  measuring  Q  we  must  use  the  ballistic  method,  and  we  have 


. 

which  for  very  small  values  of  ),  becomes 


^        G'     -     s  ' ' 


H'    ~W   Tain*?  I  +  *A  -  *  A2 ' 

where  H'  is  the  horizontal  component  of  the  earth's  magnetism  at  the 
place  of  the  small  galvanometer,  G'  its  constant,  T  the  time  of  vibra- 
tion of  the  needle,  and  X  the  logarithmic  decrement. 

The  ratio  of  H'  to  H  can  be  determined  by  allowing  a  needle  to 
vibrate  in  the  two  positions.  But  this  introduces  error,  and  by  the 
following  method  we  can  eliminate  both  this  and  the  distance  of  the 
mirror  from  the  scale  by  which  we  find  0'  and  the  error  of  tangent 
galvanometer  due  to  length  of  needle.  The  method  merely  consists 
in  placing  a  circle  around  the  small  galvanometer  and  then  taking 
simultaneous  readings  with  the  current  passing  through  it  and  the 
tangent  galvanometer,  before  and  after  each  experiment.  Let  «  and  a' 
be  the  deflections  of  the  tangent  galvanometer  and  the  other  galvano- 
meter respectively,  and  let  G"  be  the  constant  of  the  circle  at  the  point 
where  the  needle  hangs,  then 

TT  JJ  I 

-^  tan  a  =  -^j-  tan  a', 

and  we  have  finally 

TT     G    tan  a'    tan  6  \ 


R=M- 


T   G71' ta.na   sin*0'  l+JA  —  U' 

which  does  not  contain  H  or  H',  and  the  distance  of  the  mirror  from 
the  scale  does  not  enter  except  as  a  correction  in  the  ratio  pf  sin  £# 
and  tan  a';  and,  as  a  and  0  can  be  made  nearly  equal,  the  correction 


158  HENEY  A.  EOWLAND 

of  the  tangent  galvanometer  for  the  length  of  needle  is  almost  elimi- 
nated.    When  the  method  of  recoil  is  used,  we  must  substitute  -      ~TA 


for  the  term  involving  /,  and  sin  $Af  -f-  sin  %B'  in  the  place  of  sin  ^  6' 
A'  and  B'  being  the  greater  and  smaller  arcs  in  that  method.  This  is 
on  the  supposition  that  X  is  small. 

The  ratio  of  G"  to  G  must  be  so  large,  say  12,000,  that  it  is  difficult 
to  determine  it  by  direct  experiment,  but  it  is  found  readily  by  measure- 
ment or  indirect  comparison. 

It  is  seen  that  in  this  equation  the  quantities  only  enter  as  the  first 
powers,  and  that  the  only  constants  to  be  determined  which  enter  the 
equation  are  M,  G  and  G",  which  all  vary  in  simple  proportion  to  the 
linear  measurement.  It  is  to  be  noted  also  that  the  only  quantities 
which  require  to  be  reduced  to  standard  measure  are  M  and  T,  and 
that  the  others  may  all  be  made  on  any  arbitrary  scale.  No  correction 
is  needed  for  temperature  except  to  M.  Indeed,  I  believe  that  this 
method  exceeds  all  others  in  simplicity  and  probable  accuracy  and  its 
freedom  from  constant  errors,  seeing  that  every  quantity  was  varied 
except  G"  and  G,  whose  ratio  was  determined  within  probably  one  in 
three  thousand  by  two  methods. 

Having  obtained  the  resistance  of  the  circuit  by  this  method,  we 
have  next  to  measure  it  in  ohms.  For  this  purpose  the  resistance  of 
the  circuit  was  always  adjusted  until  it  was  equal  to  a  certain  German 
silver  standard,  which  was  afterward  carefully  compared  with  the  ohm. 
This  standard  was  about  thirty-five  ohms. 

By  this  method,  the  following  data  are  needed. 

1.  Eatio  of  constants  of  galvanometer  and  circle. 

2.  Eatio  of  the  tangents  of  the  two  deflections  of  tangent  galvano- 
meter. 

3.  Eatio  of  the  deflection  to  the  swing  of  the  other  galvanometer. 

4.  Mutual  potential  of  induction  coils  on  each  other. 

5.  Time  of  vibration  of  the  needle. 

6.  Eesistance  of  standard  in  ohms. 
For  correction  we  need  the  following  : 

1.  The  logarithmic  decrement. 

2.  Distance  of  mirror  from  scale. 

3.  Coefficient  of  torsion  of  suspending  fibre. 

4.  Eate  of  chronometer. 

5.  Correction  to  reduce  to  standard  metre. 


Ox  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  KESISTANCE         159 

6.  Variation  of  the  resistance  of  German  silver  with  the  temperature. 

7.  Temperature  of  standard  resistance. 

8.  Arc  of  swing  when  the  time  of  vibration  is  determined. 

9.  Length  of  needle  in  tangent  and  other  galvanometer  (nearly  com- 
pensated by  the  method). 

10.  The  variation  of  resistance  of  circuit  during  the  experiment. 
The  following  errors  are  compensated  by  the  method  of  experiment. 

1.  The  local  and  daily  variation  of  the  earth's  magnetism. 

2.  The  variation  of  the  magnetism  of  the  needle. 

3.  The  magnetic  and  inductive  action  of  the  parts  of  the  apparatus 
on  each  other. 

4.  The  correction  for  length  of  needle  in  the  tangent  galvanometer 
(nearly). 

5.  The  axial  displacement  of  the  wires  in  the  coils  for  induction. 

6.  The  error  due  to  not  having  the  coils  of  the  galvanometer  and  the 
circle  parallel  to  the  needle. 

7.  Scale  error  (partly). 

8.  The  zero  error  of  galvanometers. 

CALCULATION  OF  CONSTANTS 

Circle.  —  For  obtaining  the  ratio  of  G  to  G",  it  is  best  to  calculate 
them  separately  and  then  take  their  ratio,  though  it  might  be  found 
by  Maxwell's  method  ('Electricity,'  article  753).  But  as  the  ratio  is 
great,  the  heating  of  the  resistances  would  produce  error  in  this  latter 
method. 

For  the  simple  circle, 


where  A  is  its  radius  and  B  the  distance  of  the  plane  of  the  circle  to 
the  needle  on  its  axis. 

Galvanometer  for  Induction  Current.  —  For  the  more  sensitive  galvano- 
meter, we  must  first  assume  some  form  which  will  produce  a  nearly 
uniform  field  in  its  interior,  without  impairing  its  sensitiveness.  If  we 
make  the  galvanometer  of  two  circular  coils  of  rectangular  section 
whose  depth  is  to  its  width  as  108  to  100,  and  whose  centres  of  sections 
are  at  a  radius  apart  from  each  other,  we  shall  have  Maxwell's  modifi- 
cation of  Helmholtz's  arrangement.  The  constant  can  then  be  found 
by  calculation  or  comparison  with  another  coil. 


160  HEXKY  A.  EOWLAXD 

Maxwell's  formulae  are  only  adapted  to  coils  of  small  section.    Hence 
we  must  investigate  a  new  formula.13 

Let  N  be  the  total  number  of  windings  in  the  galvanometer. 
Let  R  and  r  be  the  outer  and  inner  radii  of  the  coils. 
Let  X  and  x  be  the  distances  of  the  planes  of  the  edges  of  the  coils 

from  the  centre. 

Let  a  be  the  angle  subtended  by  the  radius  of  any  winding  at  the  centre. 
Let  &  be  the  length  of  the  radius  vector  drawn  from  the  centre  to  the 

point  where  we  measure  the  force. 
Let  6  be  the  angle  between  this  line  and  the  axis. 
Let  c  be  the  distance  from  the  centre  to  any  winding. 
Let  w  be  the  potential  of  the  coil  at  the  given  point. 

Then  (Maxwell's  'Electricity,'  Art.  695),  for  one  winding. 

W  =  —  2n  •]  1  —  COS  a  +  sin2  a  ( —  Q[  (a)  $1  (#) 
(  \c 


and  for  two  coils  symmetrically  placed  on  each  side  of  the  origin, 

W  =  4:r  \  COS  a  —  sin2  a  (  *  f — )   O2'  (a)  Q2  (0) 

I  \  *  \  c  1 


where  Q2(0),  Q^(0),  &c.,  denote  zonal  spherical  harmonics,  and  Q2'(«)> 
Q'i(a)  &c.,  denote  the  differential  coefficients  of  spherical  harmonics 
with  respect  to  cos  a. 

As  the  needle  never  makes  a  large  angle  with  the  plane  of  the  coils, 
it  will  be  sufficient  to  compute  only  the  axial  component  of  the  force, 
which  we  shall  call  F.  Let  us  make  the  first  computation  without 
substitution  of  the  limits  of  integration,  and  then  afterward  substitute 
these: 


F  = 


*  f  C^-dxdr, 

—  r)(X—  x)J  J   dx 


and  we  can  write 

%*N 


&c. 


12  A  formula  involving  the  first  two  terms  of  my  series,  but  applying  only  to  the 
special  case  of  a  needle  in  the  centre  of  a  single  circle  of  rectangular  section,  is 
given  by  Weber  in  his  'Elektrodynamische  Maasbestimmungen  inbesondere  Wider- 
standsmessungen,'  S.  872. 


ON  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  RESISTANCE         161 
where  H^  —  x  log.  (r  +  »/  y?  +  r2)  , 

o   _  1.3.5.  .     2t- 


'2»  —  1  (2*  -1)2 


'  2t  -  3  (it  -  l)(2i  -  3)  2.4 

D  =  C  2*'—  8_  i(t'-l)..(*  —  6) 

'2i  —  5       (2i-i)(2t  —  3)(2i  -  5)  2.4.6' 

Et  =  &c.,  &c. 

Substituting  the  limits  for  x,  r  and  a,  we  find 
+  V  ^2 


o  =        i  /  1  f         ^  ___  ^_  1  /      If  r3       \\ 

\  X  \(ff  +  Xz)l       (r2  +  JT')i      "^  ^  +  a?)l      (r2  +  z*)*J  J  ' 


The  needle  consisted  of  two  parallel  lamina?  of  steel  of  length,  Z,  and 
a  distance,  W,  from  each  other.  As  the  correction  for  length  is  small, 
we  may  assume  that  the  magnetism  of  each  lamina  is  concentrated  in 
two  points  at  a  distance  n  /  from  each  other,  where  n  is  a  quantity  to 
he  determined. 
Hence 


W 

where  cos  &  —    /71  —  ..,      _,,  seeing  that  the  needle  hangs  parallel  to 

* 


the  coils.  In  short  thick  magnets,  the  polar  distance  is  about  §  Z  and 
the  value  of  n  will  be  about  f  .  For  all  other  magnets  it  will  be  between 
this  and  unity.  In  the  present  case  n  =  f  nearly. 

As  all  the  terms  after  the  first  are  very  minute,  this  approximation 
is  sufficient,  and  will  at  least  give  us  an  idea  of  the  amount  of  this 

source  of  error. 
11 


162  HENRY  A.  KOWLAND 

INDUCTION  COILS 

The  induction  coils  were  in  the  shape  of  two  parallel  coils  of  nearly 
equal  size  and  of  nearly  square  section. 

Let  A  and  a  he  the  mean  radii  of  the  coils.  Let  &  he  the  mean 
distance  apart  of  the  coils. 

Let 


C  — 


Supposing  the  coils  concentrated  at  their  centre  of  section  we  know  that 


where  F(c)  and  E(c)  are  elliptic  integrals. 

If  £  and  y  are  the  depth  and  width  of  each  coil,  the  total  value  of 
M  will  he,  when  A  =  a  nearly, 


and  we  find 


nc 


(1 
O  -2    _    12^    A 

^2 


COEBECTIONS 

Calling  /?  and  <5  the  scale  deflections  corresponding  to  tan  a'  and  sin 
,  we  may  write  our  equation  for  the  value  of  the  resistance 


8    1--35 


where  R'  is  the  resistance  of  the  circuit  at  a  given  temperature  17-0°  C., 
and  E  =  2^M-^Ff(l  +  a  -f  &  +  etc.),  in  which  ^,  5,  etc.  and  a,  6,  etc. 

are  the  variable  and  constant  corrections  respectively. 
a.  Correction  for  damping. 


ON  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  KESISTANCE         163 

I.  Torsion  of  fibre. 

The  needle  of  the  tangent  galvanometer  was  sustained  on  a  point 
and  so  required  no  correction.  The  correction  for  the  torsion  in  the 
other  galvanometer  is  the  same  for  /?  and  d  and  hence  only  affects  T. 
Therefore,  if  t  is  the  coefficient  of  torsion, 

b=  -  It. 

c.  Rate  of  chronometer. 

Let  p  be  the  number  of  seconds  gained  in  a  day  above  the  normal 
time 

P 
~  86400* 

d.  Reduction  to  normal  metre.     The  portion  of  this  reduction  which 
depends  on  temperature  must  be  treated  under  the  variable  corrections. 
Let  m  be  the  excess  of  the  metre  used  above  the  normal  metre,  ex- 
pressed in  metres;  then 

d  =  +  m. 

e.  Correction  of  T  for  the  arc  of  vibration.     This  arc  was  always  the 
same,  starting  at  c^  and  being  reduced  by  damping  to  about  cn , 


where  c^  and  c  a  are  the  total  arcs  of  oscillation. 

/.  Correction  for  length  of  needles.     For  the  tangent  galvanometer, 
the  correction  is  variable.     For  the  circle  it  is 

/=  + 

where  I  is  half  the  distance  between  the  poles  of  the  needle  and  A  the 
radius  of  circle.  For  the  other  galvanometer  it  is  included  in  the 
formula  for  G. 

A.  Reduction  to  normal  metre.     As  the  dimension  of  R  is  a  velocity 
and  the  induction  coils  were  wound  on  brass,  the  correction  is 

where  f  is  the  coefficient  of  expansion  of  brass  or  copper,  t'  the  actual 
and  t"  the  normal  temperature. 

B.  Correction  of  standard  resistance  for  temperature.     Let  a  be  the 
variation  of  the  resistance  for  1°  C.,  ?"  be  the  actual  and  T  the  normal 
temperature  17- °0  C. ;  then 


164  HENRY  A.  BOWL  AND 

C.  Correction  for  length  of  needle  in  tangent  galvanometer, 

C  =  +  J^  sin  (a  +  «')f -|r-Y(a'  ~  a) ' 
\-A-l 

where  V  is  half  the  distance  between  the  poles  of  the  needle  and  A'  is 
the  radius  of  the  coil. 

D.  The  resistance   of   the   circuit  was   constantly  adjusted   to   the 
standard,  but  during  the  time  of  the  experiment  the  change  of  temper- 
ature of  the  room  altered  the  resistance  slightly;  this  change  was 
measured  and  the  correction  will  be  plus  or  minus  one-half  this.     The 
resistance  was  adjusted  several  times  during  each  experiment.     The 
correction  is  ±Z). 

Some  of  the  errors  which  are  compensated  by  the  experiment  need 
no  remark  and  I  need  speak  only  of  the  following. 

No.  3.  By  the  introduction  of  commutators  at  various  points  all 
mutual  disturbance  of  instruments  could  be  compensated. 

No.  5.  In  winding  wire  in  a  groove,  it  may  be  one  side  or  the  other 
of  the  centre.  By  winding  the  coils  on  the  centre  of  cylinders  which 
set  end  to  end,  on  reversing  them  and  taking  the  mean  result,  this 
error  is  avoided. 

No.  6.  The  circle  was  always  adjusted  parallel  to  the  coils  of  the 
galvanometer.  Should  they  not  be  parallel  to  the  needle,  G  and  0" 
will  be  altered  in  exactly  the  same  ratios  and  will  thus  not  affect  the 
result.  The  same  may  be  said  of  the  deflection  of  the  magnet  from 
the  magnetic  meridian  due  to  torsion. 

No.  7.  /?  and  3  both  ranged  over  the  same  portion  of  the  scale  and 
so  scale  error  is  partly  compensated. 

No.  8.  The  zero-point  of  all  galvanometers  was  eliminated  by  equal 
deflections  on  opposite  sides  of  the  zero-point. 

INSTRUMENTS 

Wire  and  coils. — The  wire  used  in  all  instruments  was  quite  small 
silk-covered  copper  wire,  and  was  always  wound  in  accurately  turned  ls 
brass  grooves  in  which  a  single  layer  of  wire  just  fitted.  The  separate 
layers  always  had  the  same  number  of  windings,  and  the  wire  was 
wound  so  carefully  that  the  coils  preserved  their  proper  shape  through- 

13  To  obtain  an  accurate  coil  an  accurate  groove  is  necessary,  seeing  that  otherwise 
the  wire  will  be  heaped  up  in  certain  places.  The  circle  of  the  tangent  galvanometer, 
which  was  made  to  order  in  Germany,  had  to  be  returned  in  this  country  before  use, 
and  much  time  was  lost  before  finding  out  the  source  of  the  difficulty. 


ON  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  EESISTANCE         165 

out.  No  paper  was  used  between  the  layers.  As  the  wire  was  small, 
very  little  distortion  was  produced  at  the  point  where  one  layer  had 
to  rise  over  the  tops  of  the  wires  below.  Corrections  were  made  for 
the  thickness  of  the  steel  tape  used  to  measure  the  circumference  of 
each  layer;  also  for  the  sinking  of  each  layer  into  the  spaces  between 
the  wires  below,  seeing  that  the  tape  measures  the  circumference  of 
the  tops  of  the  wires.  The  steel  tape  was  then  compared  with  the 
standard. 

The  advantages  of  small  wire  over  large  are  many;  we  know  exactly 
where  the  current  passes;  it  adapts  itself  readily  to  the  groove  without 
kinks;  it  fills  up  the  grooves  more  uniformly;  the  connecting  wires 
have  less  proportional  magnetic  effect;  and  lastly,  we  can  get  the 
dimensions  more  exactly.  The  size  of  wire  adopted  was  about  No.  22 
for  most  of  the  instruments. 

The  mean  radius  having  been  computed,  the  exterior  and  interior 
radii  are  found  by  addition  and  substraction  of  half  the  depth  of  the 
coil.  The  sides  of  the  coil  were  taken  as  those  of  the  brass  groove. 

All  coils  were  wound  by  myself  personally  to  insure  uniformity  and 
exactness. 

Tangent  galvanometer. — This  was  entirely  of  brass  or  bronze,  and 
had  a  circle  about  50  cm.  diameter.  The  needle  was  2-7  cm.  long  and 
its  position  was  read  on  a  circle  20-  cm.  diameter,  graduated  to  15'. 
The  graduated  circle  was  raised  so  that  the  aluminium  pointer  was  on 
a  level  with  it,  thus  avoiding  parallax.  The  needle  and  pointer  only 
weighed  a  gram  or  two,  and  rested  on  a  point  at  the  centre  which  was 
so  nicely  made  that  it  would  make  several  oscillations  within  1°  and 
would  come  to  rest  within  1'  or  2'  of  the  same  point  every  time.  I 
much  prefer  a  point  with  a  light  needle  carefully  made  to  any  suspended 
needle  for  the  tangent  galvanometer,  especially  as  a  raised  circle  can 
then  alone  be  used.  The  needle  was  suspended  at  a  distance  from  any 
brass  which  might  have  been  magnetic.  There  were  a  series  of  coils 
ascending  nearly  as  the  numbers  1,  3,  9,  27,  81,  243,  whose  constants 
were  all  known,  but  only  one  was  used  in  this  experiment.  The  proba- 
ble error  of  a  single  reading  was  about  ±  1'. 

Galvanometer  for  induction  current. — This  was  a  galvanometer  on  a 
new  plan,  especially  adapted  for  the  absolute  measurement  of  weak 
currents.  It  was  entirely  of  brass,  except  the  wooden  base,  and  was 
large  and  heavy,  weighing  twenty  or  twenty-five  pounds.  It  could  be 
used  with  a  mirror  and  scale  or  as  a  sine  galvanometer.  It  will  be 


166  HENKY  A.  EOWLAND 

necessary  to  describe  here  only  those  portions  which  affect  the  accuracy 
of  the  present  experiment. 

The  coils  were  of  the  form  described  above  in  the  theoretical  portion, 
and  were  wound  on  a  brass  cylinder  about  8-2  cm.  long  and  11-6  cm. 
diameter  in  two  deep  grooves  about  3-  cm.  deep  and  2-5  cm.  wide.  The 
opening  in  the  centre  for  the  needle  was  about  5-5  cm.  diameter  and 
the  cylinder  was  split  by  a  saw-cut  so  as  to  diminish  the  damping 
effect.  This  coil  was  mounted  on  a  brass  column  rising  from  a  gradu- 
ated circle  by  which  the  azimuth  of  the  coil  could  be  determined  by 
two  verniers  reading  to  30".  Through  the  opening  in  the  coil  beneath 
the  needle  passed  a  brass  bar  95  cm.  long  and  2  cm.  broad,  carrying  a 
small  telescope  at  one  end.  In  the  present  experiment,  this  bar  was 
merely  used  in  the  comparison  of  the  constant  of  the  instrument  with 
that  of  another  instrument.  For  this  purpose  the  instrument  is  used 
as  a  sine  galvanometer  by  which  a  great  range  can  be  secured,  and  it 
could  be  compared  with  a  coil  having  a  constant  twenty-three  times 
less  and  which  was  used  with  telescope  and  scale. 

The  coils  contained  about  five  pounds  of  No.  22  silk-covered  copper 
wire  in  1790-  turns. 

Two  needles  were  used  in  this  galvanometer,  each  constructed  so  that 
its  magnetic  axis  should  be  invariable;  this  was  accomplished  by  affixing 
two  thin  laminae  of  glass-hard  steel,  to  the  two  sides  of  a  square  piece 
of  wood,  with  their  planes  vertical.  This  made  a  sort  of  compound 
magnet  very  strong  for  its  length,  and  with  a  constant  magnetic  axis. 
The  first  needle  had  a  nearly  rectangular  mirror  2-4  by  1-8  cm.  on 
the  sides  and  -22  cm.  thick.  The  other  needle  had  a  circular  mirror 
2-05  cm.  diameter  and  about  1  mm.  thick.  The  needle  of  the  first  was 
1-27  cm.  and  of  the  second  1-20  cm.  long,  and  the  pieces  of  wood  were 
about  -45  cm.  and  -6  cm.  square  respectively.  The  moment  of  inertia 
of  both  was  much  increased  by  two  small  brass  weights  attached  to 
wires  in  extension  of  the  magnetic  axis,  thus  extending  the  needles  to 
a  length  of  4-9  cm.  and  4-2  cm.  respectively.  The  total  weights  were 
5-1  and  5-6  grams  and  the  times  of  vibration  about  7-8  and  11-5 
seconds.  They  were  suspended  by  three  single  fibres  of  silk  about  43 
cm.  long. 

In  front  of  the  needle  was  a  piece  of  plane-parallel  glass.  This  and 
the  mirrors  were  made  by  Steinheil  of  Munich,  and  were  most  perfect 
in  every  way. 

In  the  winding  of  the  coils  every  care  was  taken,  seeing  that  a  small 
error  in  so  small  a  coil  would  produce  great  relative  error.  And  for 


Ox  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  RESISTANCE         167 

this  reason  the  constant  was  also  found  by  comparison  with  another 
coil.  The  following  were  the  dimensions: 

Mean  radius  4-3212  cm. 
R  -  5-6212  r  =  3-0212 

X=  3-475565  x=    -935565 

R  —  r  =  2-6000  X  —  x  =  2-54000 

^=1790- 
whence 

F=  1832-25  —  1-70&'&  (0)  -  4-50i4&  (0)  +  -90£6()6  (0)  -  &c. 
Taking  the  mean  dimensions  of  the  two  needles,  we  have 

1  =  1-23,     w  =  -52,    w  =  |,    cos  6'  =  -748. 
Qt  (0')  =  +  339 ,     Qt  (6'}  =  -  -354 ,     Q6  (a')  =  -  -275 . 
.-.      G  =  1832-25  —  -083  +  -071  -  -002  +  &c.  =  1832-24. 

The  coil  with  which  this  galvanometer  was  compared  was  the  large 
coil  of  an  electro-dynamometer  similar  to  that  described  in  Maxwell's 
'Electricity/  Art.  725,  but  smaller.  The  coil  was  on  Helmholtz's 
principle  with  a  diameter  of  27-5  cm.,  and  was  very  accurately  wound 
on  the  brass  cylinder.  There  was  a  total  of  240  windings  in  the  coil. 
The  constant  of  this  coil  was  78-371  by  calculation. 

To  eliminate  the  difference  of  intensity  of  the  earth's  magnetism,  an 
observation  was  first  made  and  then  the  positions  of  the  instruments 
were  changed  so  that  each  occupied  exactly  the  position  of  the  other: 
the  square  root  of  the  product  of  the  two  results  was  the  true  result 
free  from  error. 

The  coils  of  the  galvanometer  could  be  separated  so  that  an  outer 
and  inner  pair  could  be  used  together.  By  comparing  these  parts 
separately  and  adding  the  constants  together  we  find  G.  Hence  two 
comparisons  are  possible,  one  with  the  coils  together  and  the  other  with 
them  separate.  The  results  were  for  the  ratio  of  the  constants 

23-3931     and     23-4008, 
which  give 

G  =  1833-37     and     1833-98. 
The  mean  result  is 

1833-67     ±  -09, 

and  this  includes  seven  determinations  with  two  reversals  of  instru- 
ments. This  result  is  one  part  in  thirteen  hundred  greater  than  found 
by  direct  calculation,  which  is  to  be  accounted  for  by  the  small  size  of 
the  galvanometer  coils  and  the  consequent  difficulty  of  their  accurate 
measurement.  As  comparison  with  the  electro-dynamometer  has  such 


168  HENET  A.  KOWLAND 

a  small  probable  error,  and  as  it  is  a  much  larger  coil,  it  seems  best  to 
give  this  number  twice  the  weight  of  that  found  by  calculation :  we  thus 
obtain 

(7  =  1833-19 
as  the  final  result. 

It  does  not  seem  probable  that  this  can  be  in  error  more  than  one 
part  in  two  or  three  thousand. 

Telescope,  scale,  &c. — The  telescope,  mirrors  and  plane-parallel  glass 
were  all  from  Steinheil  in  Munich,  and  left  nothing  to  be  desired  in 
this  direction,  the  image  of  the  scale  being  so  perfect  that  fine  scratches 
on  it  could  be  distinguished.  The  telescope  had  an  aperture  of  4  cm. 
and  a  magnifying  power  of  20  was  used.  The  scale  was  of  silvered 
brass,  one  metre  long  and  graduated  to  millimetres. 

Induction  coils. — A  coil  was  wound  in  a  groove  in  the  centre  of  each 
of  three  accurately  turned  brass  cylinders  of  different  lengths.  Two 
of  them  only  were  used  at  a  time,  by  placing  them  end  to  end,  the  ends 
being  ground  so  that  they  laid  on  each  other  nicely.  The  two  coils 
could  be  placed  in  four  positions  with  respect  to  each  other,  in  each  of 
which  they  were  very  exactly  the  same  distance  apart.  This  distance 
for  each  of  the  four  positions,  was  determined  at  three  parts  of  the 
circumference  by  means  of  a  cathetometer,  with  microscopic  objective, 
reading  to  ^  mm.  The  mean  of  all  twelve  determinations  was  the 
mean  distance.  In  using  the  coils  they  were  always  used  in  all  four 
positions.  The  probable  error  of  each  set  of  twelve  readings  was 
±  -001  mm.  The  data  are  as  follows,  naming  the  coils,  A,  B  and  C : 

Mean  radius  of  A  =  13-710,  of  B  =  13-690,  of  C  =  13-720. 

Mean  distance  apart  of  A  and  5  =  6-534,  of  A  and  (7  =  9-574,  of 
B  and  (7=11-471. 

N=  154  for  each  coil,  £==  -90,  y  =  -84. 
For  A  and  B  we  have 

M=  3774860-  +  TV  (74250-  —  66510-)  =  3775500- 
The  remaining  terms  of  the  series  are  practically  zero,  as  was  found 
by  dividing  one  of  the  coils  into  parts  and  calculating  the  parts  sepa- 
rately and  adding  them. 

For  A  and  C 

M  =  2561410-  -f  TV  (34000-  —  27230-)  =  2561974- 
For  B  and  (7 

M  =  2050600-  +  TV  (27500-  —  19800-)  =  2051320- 
The  calculation  of  the  elliptic  integrals  was  made  by  aid  of  the  tables 
of  the  Jacobi  function,  q,  given  in  Bertrand's  '  Traite  de  Calcul  Inte- 


ON  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  RESISTANCE         169 

grale '  as  well  as  by  the  expansions  in  terms  of  the  modulus  after  trans- 
forming them  hy  the  Landen  substitution. 

The  Circle. — The  circle  whose  constant  we  have  called  G"  and  which 
was  around  the  galvanometer  whose  constant  was  G,  was  a  large  wooden 
one  containing  a  single  coil  of  No.  22  wire.14  To  prevent  warping,  it 
was  laid  up  out  of  small  pieces  of  wood  with  the  grain  in  the  direction 
of  the  circumference,  and  was  carefully  turned  with  a  minute  groove 
near  one  edge  in  which  the  wire  could  just  lie.  It  was  about  5-  cm. 
broad,  1-8  thick  and  82-7  cm.  diameter.  As  the  room  had  no  fire  in 
it,  the  circle  remained  perfect  throughout  the  experiment.  The  wire 
was  straightened  by  stretching  and  measured  before  placing  on  the 
circle,  which  last  was  done  with  great  care  to  prevent  stretching;  after 
the  experiment  it  was  measured  and  found  exact  to  T'T  mm. 

The  circle  was  adjusted  parallel  and  concentric  with  the  coils  of  the 
galvanometer,  but  at  a  distance  of  1-1  cm.  to  one  side,  in  order  to  allow 
the  glass  tube  with  the  suspending  fibre  to  pass.  The  length  of  wire 
was  259-58  cm.  which  gives  a  mean  radius  of  41-31344  cm.  These  data 
give  G"  =  -151925.  Preliminary  results  were  also  obtained  by  use  of 
another  circle. 

Chronometer. — To  obtain  the  time  of  vibration,  a  marine  chronometer 
giving  mean  solar  time  was  used.  The  rate  was  only  half  a  second 
per  day. 

Wheatstone  bridge. — To  compare  the  resistance  of  the  circuit  with  the 
arbitrary  German  silver  standard,  a  bridge  on  Jenkin's  plan,  made  by 
Elliott  of  London,  was  used.  A  Thomson  galvanometer  with  a  single 
battery  cell  gave  the  means  of  accurately  adjusting  the  resistance,  one 
division  of  the  scale  representing  one  part  in  fifty  thousand. 

4  Thermometers. — Accurate  thermometers  graduated  to  half  degrees 
were  used  for  finding  the  temperature  of  the  standard. 

The  arbitrary  standard. — This  was  made  of  about  seventy  feet  of 
German  silver  wire,  mounted  in  the  same  way  as  the  British  Association 
Standard.  Immediately  after  use,  two  copies,  one  in  German  silver  and 
the  other  in  platinum-silver  alloy,  were  made.  It  had  a  resistance  of 
about  35  ohms.  The  temperature  was  taken  as  17°  C. 

To  obtain  the  accurate  resistance  of  this  standard  in  ohms,  I  had  two 
standards  of  10  ohms  and  one  of  1,  100,  and  1,000  ohms.  The  1-ohm, 
and  one  of  the  10-ohm  standards,  were  made  by  Elliott  of  London,  and 

uln  another  part  of  my  paper  I  have  criticised  the  use  of  wooden  circles  for  coil, 
but  it  is  unobjectionable  in  the  case  of  a  single  wire,  especially  when  the  needle  i& 
suspended  near  its  centre. 


170  HENRY  A.  EOWLAND 

the  others  by  Messrs.  Warden,  Muirhead  and  Clark  of  the  same  place. 
But  on  careful  comparison  I  found  that  Warden,  Muirhead  and  Clark's 
10-ohm  standard  was  1-00171  times  that  of  Messrs.  Elliott  Bros.  On 
stating  these  facts  to  the  two  firms  I  met  no  response  from  the  first 
firm,  but  the  second  kindly  undertook  to  make  me  a  standard  which 
should  be  true  by  the  standards  in  charge  of  Professor  Maxwell  at 
Cambridge."  At  present  I  give  the  result  of  the  comparison  with 
these  standards,  as  well  as  some  others,  and  also  with  a  set  of  resistance 
coils  by  Messrs.  Elliott  Bros. 

Commutators. — No  commutators  except  those  having  mercury  con- 
nections were  used,  and  those  in  the  circuit  whose  resistance  was  deter- 
mined were  so  constructed  as  to  offer  no  appreciable  resistance.  The 
commutator  by  which  the  main  current  was  reversed,  could  be  operated 
in  a  fraction  of  a  second,  so  as  to  cause  no  delay  in  the  reversal. 

Connecting  wires. — These  were  of  No.  22  or  No.  16  wire  and  were  all 
carefully  twisted  together.  The  insulation  was  tested  and  found  to  be 
excellent. 

Inductor  for  damping. — This  has  already  been  described  in  my  first 
paper  on  '  Magnetic  Permeability,'  and  merely  consisted  of  a  small 
horse-shoe  magnet  with  a  sliding  coil,  which  was  introduced  into  the 
secondary  circuit.  By  moving  it  back  and  forth,  the  induced  current 
could  be  used  to  stop  the  vibrations  of  the  needle  and  make  it  stationary 
at  the  zero  point.  This  is  necessary  in  the  method  where  the  first  throw 
of  the  galvanometer  needle  constitutes  the  observation,  but  in  the 
method  of  recoil  it  is  not  necessary  to  use  it  very  often.  I  prefer  the 
method  of  the  first  throw  as  a  general  rule,  but  I  have  used  both 
methods. 

This  method  of  damping  will  be  found  much  more  efficient  than  that 
of  the  damping  magnet  as  taught  by  Weber,  and  after  practice  a  single 
movement  will  often  bring  the  needle  exactly  to  rest  at  the  zero  point. 

Arrangement  of  apparatus. — Two  rooms  on  the  ground  floor  of  a 
small  building  near  the  University  were  set  aside  for  the  experiment, 
making  a  space  8  m.  long  by  3-7  m.  wide.  The  plan  of  the  arrange- 
ment is  seen  at  Fig.  1.  The  current  from  the  battery,  in  the  Univer- 
sity, entered  at  A,  the  battery  being  eighteen  one-gallon  cells  of  a 
•chromate  battery,  arranged  two  abreast  and  eight  for  tension.  The 

18  As  this  is  nearly  a  year  since,  and  as  I  cannot  tell  when  the  standard  will  arrive, 
I  now  publish  the  results  as  so  far  obtained,  hoping  to  make  a  more  exact  comparison 
in  future. 


ON  THE  ABSOLUTE  UXIT  OF  ELECTRICAL  EESISTANCE 


171 


resistance  of  the  circuit  was  about  20  ohms,  and  of  the  whole  battery 
about  ^  ohm,  thus  insuring  a  reasonably  constant  current. 

At  B  some  resistance  could  be  inserted  by  withdrawing  plugs  so  as 
to  vary  the  current. 

At  C  is  the  tangent  galvanometer  with  commutator  on  a  brick  pier. 
The  nearness  of  the  commutator  produces  no  error,  seeing  that  we  only 
wish  to  determine  the  ratio  of  two  currents.  The  effect  of  currents  in 
the  commutator  was,  however,  vanishingly  small  in  any  case. 

At  D  is  the  principal  commutator  which  reversed  the  current  in  the 
induction  coils,  L,  or  in  the  circle,  F,  when  it  was  in  the  circuit. 


FIG.  1. 

The  secondary  circuit  included  the  induction  coil,  L,  the  damping 
inductor,  M,  and  the  galvanometer  0. 

At  H  was  the  Jenkin's  bridge,  with  standard  at  P,  in  a  beaker  of 
water,  and  a  Thomson  galvanometer  at  J  K.  The  secondary  circuit 
could  be  joined  to  the  bridge  by  raising  a  U-shaped  piece  of  wire  out  of 
the  mercury  cups. 

The  telescope  and  scale,  E,  were  on  a  heavy  wooden  table,  and  the 
two  galvanometers  on  brick  piers  with  marble  tops. 

A  row  of  gas-burners  at  Q  illuminated  the  silvered  scale  in  the  most 
perfect  manner. 

Adjustments  and  tests. — The  circle,  F,  must  be  parallel  to  coils  of 
galvanometer,  G.  The  circle  and  coils  of  galvanometer  were  first 
adjusted  with  their  planes  vertical  and  then  adjusted  in  azimuth  by 


172  HENKY  A.  EOWLAND 

measurement  from  the  end  of  the  bar,  R,  to  the  sides  of  the  circle,  F. 
The  adjustment  was  always  within  30',  which  would  only  cause  an  error 
of  one  part  in  25000. 

The  needle  must  hang  in  the  magnetic  meridian  by  a  fibre  without 
torsion,  and  the  coils  must  be  parallel  to  it.  These  adjustments  were 
carefully  made,  but,  as  has  been  shown,  the  error  from  this  source  is 
compensated. 

The  needle  must  hang  in  the  centre  of  the  galvanometer  coils  and 
on  the  axis  of  the  circle.  The  error  from  this  source  is  vanishingly 
small. 

The  scale  must  be  perpendicular  to  the  line  joining  the  zero  point 
and  the  galvanometer  needle,  it  must  be  level  and  not  too  much  below 
the  galvanometer  needle.  All  errors  from  this  source  are  partially  or 
entirely  compensated  by  the  method  of  experiment. 

The  induction  coils,  L,  must  be  horizontal,  and  at  the  same  level  as 
the  two  galvanometers,  so  as  not  to  produce  any  magnetic  action  on 
them.  The  error  from  this  source  is  exactly  compensated  by  this 
method  of  experiment,  but  could  never  amount  to  more  than  1  part  in 
2000. 

The  tangent  galvanometer  should  have  the  plane  of  its  coils  in  the 
magnetic  meridian,  but  all  errors  are  compensated. 

The  connecting  wires  must  be  so  twisted  together  and  arranged  as 
to  produce  no  magnetic  action,  but  tests  were  made  in  all  cases  where 
the  error  was  not  compensated,  and  found  to  be  practically  zero.  The 
insulation  of  all  coils,  wires  and  commutators  was  carefully  tested. 

Method  of  experiment. — As  has  been  stated  before,  the  method  gener- 
ally used  was  that  of  the  first  throw  of  the  needle,  though  the  method 
of  recoil  was  also  used.  For  the  successful  use  of  the  first  method  a 
quickly  vibrating  needle  and  the  damping  inductor  are  indispensable, 
seeing  that  with  a  slow  moving  needle  we  can  never  be  certain  of  its 
being  at  rest.  By  this  method  it  is  not  necessary  to  have  the  needle 
at  rest  at  the  zero  point,  but,  if  it  vibrates  in  an  arc  of  only  a  millimetre 
or  two,  we  have  only  to  wait  till  it  comes  to  rest  at  its  point  of  greatest 
elongation  on  either  side  of  the  zero  point  and  then  reverse  the  commu- 
tator. The  error  by  this  method  is  in  the  direction  of  making  the 
throw  greater  in  proportion  of  the  cosine  of  the  phase  to  unity.  The 
smallest  throw  used  was  100  mm.  Hence,  if  the  needle  vibrated 
through  a  total  arc  of  2  mm.,  the  error  would  be  1  in  17,000.  In  reality 
the  needle  was  always  brought  to  rest  much  more  nearly  than  this. 

The  method  of  recoil  was  used  once  with  the  needle  vibrating  in  7-8 


ON  THE  ABSOLUTE  UNIT  OF  ELECTRICAL  EESISTANCE         173 

seconds,  but  the  time  of  vibration  was  too  short  and  another  needle  was 
constructed  vibrating  in  11-5  seconds,  which  was  a  sufficiently  long 
period  to  be  used  successfully  after  practice. 

There  seems  to  be  no  error  introduced  by  the  time  taken  to  reverse 
the  commutator  in  the  method  of  recoil,  seeing  that  the  breaking  of 
the  current  stops  the  needle  and  the  making  starts  it  in  the  opposite 
direction.  As  the  time  was  only  a  fraction  of  a  second  the  error  is 
minute  in  any  case. 

While  the  current  is  broken  in  the  reversal,  the  battery  may  re- 
cuperate a  little  and  there  is  also  some  action  from  the  extra  current, 
but  there  seems  to  be  no  doubt  that  long  before  the  four  or  six  seconds 
which  the  needle  takes  to  reach  its  greatest  elongation  everything  has 
again  settled  to  its  normal  condition  and  the  current  resumes  its 
original  strength.  Hence  the  error  from  these  sources  may  be  con- 
sidered as  vanishingly  small. 

Some  experiments  were  made  by  simply  breaking  the  current  and 
they  gave  the  same  result  as  by  reversal. 

The  following  is  the  order  of  observations  corresponding  to  each 
experiment. 

1st.  The  time  of  vibration  of  needle  was  observed. 

2d.  The  current  was  passed  around  the  circle,  F,  so  as  to  observe 
y3  and  a.  Simultaneous  readings  were  taken  at  the  two  galvanometers. 
The  commutator  at  the  tangent  galvanometer  was  then  reversed  and 
readings  again  taken.  After  that  the  commutator  to  the  circle  was 
reversed  and  the  operation  repeated.  This  gave  four  readings  for  the 
circle  and  eight  for  the  tangent  galvanometer,  as  both  ends  of  the 
needle  were  read.  In  some  cases  these  were  increased  to  six  and  twelve 
respectively.  This  operation  was  repeated  three  times  with  currents 
of  different  strengths,  constituting  three  observations  each  of  a  and  /?. 
To  eliminate  any  action  due  to  the  induction  coils,  they  were  sometimes 
connected  in  one  way  and  sometimes  in  the  opposite  way. 

3d.  The  resistance  of  the  circuit  was  adjusted  equal  to  the  arbitrary 
standard. 

4th.  The  circle,  F,  was  thrown  out  of  the  circuit  and  the  observations 
of  6  and  d  begun.  Two  throws,  d,  one  on  either  side  of  zero  were 
observed  and  one  reading  of  d  taken.  The  commutators  at  s  and  C 
were  then  reversed,  and  the  operation  repeated.  This  whole  operation 
was  then  repeated  with  currents  of  three  different  strengths.  The 
position  of  the  two  induction  coils  was  now  reversed  and  observations 
again  made  with  the  three  currents.  The  resistance  was  now  com- 


174  HENRY  A.  ROWLAND 

pared  with  the  standard,  the  difference  noted,  and  the  resistance  again 
adjusted.  The  observations  were  completed  by  turning  the  induction 
coils  into  the  two  other  positions  which  they  could  occupy  with  respect 
to  each  other,  followed  by  another  comparison  of  resistance  with 
standard. 

5th.  Observations  of  a  and  ft  were  again  made  as  before. 

6th.  The  time  of  vibration  was  again  determined. 

The  observations  as  here  explained  furnished  data  for  three  compu- 
tations of  the  resistance  of  the  circuit,  one  with  each  of  the  three  cur- 
rents. In  each  of  these  three  computations,  a  was  the  mean  of  16 
readings,  ft  of  8  or  sometimes  12,  6  of  16  and  3  of  16.  In  using  the 
method  of  recoil  nearly  the  same  order  was  observed. 

The  time  of  vibration  was  determined  by  allowing  the  needle  to 
vibrate  for  about  ten  seconds  and  making  ten  observations  of  transits 
before  and  after  that  period.  During  the  experiment,  I  usually  ob- 
served at  the  telescope  and  Mr.  Jacques  at  the  tangent  galvanometer. 

The  methods  of  obtaining  the  corrections  require  no  explanation. 

RESULTS 
The  constant  corrections  are  as  follows  for  the  first  needle. 

a=-J^+T^A»=  -  -00711. 

J  =  -  H  =  —  -00020  , 

c  =  —  -000006  , 

d  =  +  -000074  at  20'°  C  . 


/  =  +  -00003  , 

a  +  b  +  c  +  d  +  e  +/—  —  '00718. 
For  method  of  recoil  it  becomes  —  -00016. 
Hence  for  A  and  B,  log  JT=  11-4536030 
Hence  for  A  and  0,  log  #  =  11-2852033 
Hence  for  B  and  C,  log  #=11-1886619 
For  method  of  recoil  using  A  and  B,  log  K  =  11-4566.630. 
For  second  needle  and  method  of  recoil, 


a  =  —  }  f — V  =  -  -000050 , 

V  *  / 
&=—}$=  - -00025, 

c  =  —  -000006  , 
d  =  +  -000074 , 


ON  THE  ABSOLUTE  UNIT  or  ELECTRICAL  EESIRTANCB         175 


e*Tt<t-ooe>»<Mi«T-io     w 


t-OOOOOOOO«O«COO      CO       CO7»O5OOOOOCOO5S»NOO 


COCOCO       CO      COCOCOCOCOCOCOCOCOCOCOCO 


-^  (Mooascoioaot-co 


Ti'COCO-^COCO^COCOCOCOWCOeOCOCOCOCO'l'COCOCOCOCO 


l-t-ICOOO'*<?O5«Ol»'-lO«a—ICOCO*-i 


176  HENRY  A.  ROWLAND 

e  =  +  -00003  , 
/  =  +  '00003  , 
a  +  'b  +  c  +  d  +  e  +f=  —  '00017. 

For  A  and  B,  log  £"=11-4566587 
For  A  and  C,  log  £"=11-2882590 
For  B  and  C,  log  £"  =  11-1917176 

The  distance  of  the  mirror  from  the  scale  varied  between  192-3  and 
193-5  cm. 

Should  we  reject  the  quantity  34-831  in  the  third  experiment  so  as 
to  make  the  mean  result  of  that  experiment  34-744  instead  of  34-773, 
we  should  obtain  as  a  mean  result  of  the  whole 

34-7156  ±  -0053, 

which  has  a  less  probable  error  than  when  the  above  observation  is  re- 
tained.    The  number  of  plus  and  minus  errors  are  also  more  nearly 
equal  and  the  greatest   difference  from  the  mean   1   part  in   1100. 
However  the  two  results  do  not  differ  more  than  1  part  in  10,000. 
We  shall  take 


R  =  34-719  ±  -007  earth          -  at  17'°  C  . 
second. 

as  the  final  result. 

DISCUSSION 

On  glancing  over  the  table  we  see  that  the  number  of  negative  errors 
greatly  exceed  the  number  of  positive,  but,  if  we  take  only  the  four 
errors  which  are  greater  than  1  part  in  5,000,  we  shall  find  two  of  them 
negative  and  two  positive. 

Combining  the  results  with  the  different  coils  we  have 

A  and  B  ....................  34-696  ±  -005 

A  and  C  ....................  34-744  ±  -Oil 

B  and  C  ....................  34-716  ±  -007 

Had  we  no  other  results  to  go  by,  we  might  suppose  that  the  value  of 
M  might  not  have  been  found  as  exactly  for  these  coils  as  we  have 
supposed  them  to  be.     But  if  we  include  the  preliminary  results  re- 
jected on  account  of  the  imperfect  circle  used,  we  shall  find 
A  and  B  ....................  34-704  ±  -006 

A  and  C  ....................  34-718  ±  -017 

B  and  C  ....................  34-758  ±  -016 

which  has  the  greatest  error  in  an  entirely  different  place. 

From  the  first  series  the  probable  error  of  each  determination  of  M 
is  1  in  about  2,000.     But  as  this  includes  the  experimental  errors  which 


177 

are  about  equal  to  ±TfrW,  the  real  probable  error  of  M  must  be  about 
1  part  in  2,500.     The  number  of  observations  is  however  too  small  for 
an  exact  estimate  of  the  probable  errors. 

Taking  the  results  with  currents  of  different  strengths,  we  find 
For  strongest  current   ....................  34-716 

For  medium  current  ......................  34-715 

For  weakest  current  ......................  34-727 

which  are  almost  perfectly  accordant.     Taking  the  results  from  the 
method  of  recoil  and  the  ordinary  method,  we  find 

For  ordinary  method  ..............  34-726  ±  -010 

For  method  of  recoil  ..............  34-705  ±  -006 

If  the  probable  error  is  subtracted  from  the  first  and  added  to  the 
second  they  will  very  nearly  equal  each  other.  Hence  the  difference  is 
probably  accidental.  Indeed,  by  the  combination  of  the  results  it  does 
not  seem  possible  to  find  any  constant  source  of  error,  and  therefore 
the  errors  should  be  eliminated  by  the  combination  of  the  results. 
In  the  final  result 

£  =  34-7192  ±  -0070 

the  probable  error,  ±  -0070,  includes  all  errors  except  the  ratio  of  G 
to  G".     We  may  estimate  the  probable  error  of  G  at  ±  ^jVff  and  of  G" 


Hence  the  final  probable  error  of  R,  including  all  variables,  is  ± 
or  ±  -04  per  cent, 

or  #  =  34-7  19  ±'015. 

The  probable  error  of  the  British  Association  determination  was  ±  -08 
per  cent,  not  including  the  probable  error  of  the  constants;  and  of  Kohl- 
rausch's  determination  db  -33  per  cent,  including  constant  errors. 

COMPARISON  WITH  THE  OHM 

The  difficulty  in  obtaining  proper  standards  for  comparison  has  been 
explained  above  and  I  shall  have  to  wait  until  the  arrival  of  the  new 
standard  before  making  the  exact  comparison.  At  present  I  give  the 
following  results,  which  seem  to  warrant  the  rejection  of  Messrs.  Elliott 
Bros'.  10-ohm  standard  and  to  make  that  of  Messrs.  Warden,  Muirhead 
and  Clark  correct.  I  shall  designate  the  coils  by  the  letter  of  the  firm 
and  by  the  number  of  ohms.  Experiment  gave  the  following  results: 

W  (10)  =  1-00171  X  E  (10),  experiment  of  June  8,  1877. 

W  (10)  =  1-00166  X  E  (10),  experiment  of  Feb.  23,  1878. 

W  (1,000):  W  (100)::  W  (10):  -999876  E  (I),  experiment  of  Febru- 
ary 23,  1878. 
12 


178  HENRY  A.  EOWLAND 

Now  the  greatest  source  of  error  in  making  coils  is  in  passing  from 
the  unit  to  the  higher  numbers.  As  the  reproduction  of  single  units 
is  a  very  simple  process  the  single  ohm  is  without  much  doubt  correct, 
and  as  the  above  proportion  is  correct  within  one  part  in  8,000  of  what 
it  should  be,  it  seems  to  point  to  the  great  exactness  of  the  standards 
then  used,  seeing  that  the  exactness  of  the  proportion  could  hardly  have 
been  accidental.  It  is  also  to  be  noted  that  Messrs.  Warden,  Muirhead 
&  Clark's  10-ohm  standard  agreed  more  exactly  with  a  set  of  coils  by 
Messrs.  Elliott  Bros,  than  their  own  unit  E  (10). 

The  resistance  of  my  coil  as  derived  from  the  different  standards  is 
as  follows : 

From  Elliott  Bros,  resistance  coils 34-979  ohms. 

From  Elliott  Bros.  10-ohm  standard 35-083  ohms. 

From  W.,  M.  &  C.'s  10-ohm  standard 35-024  ohms. 

From  W.,  M.  &  C.'s  100-ohm  standard 35-035  ohms. 

These  give  for  my  determination  the  values  of  the  ohm  as  follows : 

From  Elliott  Bros,  resistance  coils  .  .  .-99257  earth  q^*' 

sec. 

From  Elliott  Bros.  10-ohm  standard -98963  " 

From  W.,  M.  &  C.'s  10-ohm  standard -99129 

From  W.,  M.  &  C/s  100-ohm  standard -99098 

For  the  reasons  given  above  I  accept  the  mean  of  the  last  two  results 
as  the  value  of  the  ohm. 

To  preserve  my  standard  I  have  made  two  extra  copies  of  it,  the  one 
in  German  silver  and  the  other  in  platinum  silver  alloy.  The  com- 
parisons are  given  below.  No.  1  is  in  German  silver  and  the  other  in 
platinum  silver  alloy.  The  temperature  is  17-°  C. 

No.  1 1-00034           June,  1877. 

No.  1 1-00029  Feb.,  1878. 

No.  II   -99630           June,  1877. 

No.  II   -99932  Feb.,  1878. 

These  are  the  values  of  the  copies  in  terms  of  the  original  standard 

whose  resistance  is  34-719  earth  quad\ 

sec. 

From  these  results  it  would  seem  that  the  German  silver  of  which 
the  standard  and  No.  I  were  composed  was  perfectly  constant  in  resist- 
ance. The  wire  has  been  in  my  possession  for  several  years  and  seems 
to  have  reached  its  constant  state. 

The  final  result  of  the  experiment  is 

1  ohm  =  -9911  earth 

sec. 


17 

ON  PEOFESSOES  AYETON  AND  PEEEY'S  NEW  THEOEY  OF 
THE  EAETH'S  MAGNETISM,  WITH  A  NOTE  ON  A  NEW 
THEOEY  OF  THE  AUEOEA  l 

[Philosophical  Magazine,  [5],  VIII,  102-106,  1879.     Proceedings  of  the  Physical  Society, 

III,  93-98,  1879] 

Some  years  ago,  while  in  Berlin,  I  proved  by  direct  experiment  that 
electric  convection  produced  magnetic  action;  and  I  then  suggested  to 
Professor  Helmholtz  that  a  theory  of  the  earth's  magnetism  might  be 
based  upon  the  experiment.  But  upon  calculating  the  potential  of 
the  earth  required  to  produce  the  effect,  I  found  that  it  was  entirely 
too  great  to  exist  without  producing  violent  perturbations  in  the  planet- 
ary movements,  and  other  violent  actions. 

I  have  lately  read  Professors  Ayrton  and  Perry's  publication  of  the 
same  theory;  and  as  they  seem  to  have  arrived  at  a  result  for  the 
potential  much  less  than  I  did,  I  have  thought  it  worth  while  to  publish 
my  reasons  for  the  rejection  of  the  theory. 

The  first  objection  to  the  theory  that  struck  me  was,  that  not  only 
the  relative  motion  but  also  the  absolute  motion  through  space  of  the 
earth  around  the  sun  might  also  produce  action.  And  to  this  end  I 
instituted  an  experiment  as  soon  as  I  came  home  from  Berlin. 

I  made  a  condenser  of  two  parallel  plates  with  a  magnetic  needle 
enclosed  in  a  minute  metal  box  between  them;  for  I  reasoned  that,  when 
the  plates  were  charged  and  were  moved  forward  by  the  motion  of  the 
earth  around  the  sun,  they  would  then  act  in  opposite  directions  on 
the  enclosed  needle,  and  so  cause  a  deflection  when  the  electrification 
of  the  condenser  was  reversed.  On  trying  the  experiment  in  the  most 
careful  manner,  there  was  not  the  slightest  trace  of  action  after  all 
sources  of  error  had  been  eliminated. 

But  the  experiment  did  not  satisfy  me,  as  I  saw  there  was  some 
electricity  on  the  metal  case  surrounding  the  needle.  And  so  I  attacked 
the  problem  analytically,  and  arrived  at  the  curious  result  that  if  an 
electrified  system  moves  forward  without  rotation  through  space,  the 

1  Read  before  the  Physical  Society,  June  29th. 


180  HENRY  A.  KOWLAND 

magnetic  force  at  any  point  is  dependent  on  the  electrical  force  at  that 
same  point — or,  in  other  words,  that  all  the  equipotential  surfaces  have 
the  same  magnetic  action.  Hence,  when  we  shield  a  needle  from  elec- 
trostatic action,  we  also  shield  it  from  magnetic  action. 

This  theorem  only  applies  to  irrotational  motion,  and  assumes  that 
the  elementary  law  for  the  magnetic  action  of  electric  convection  is  the 
same  as  the  most  simple  elementary  law  for  closed  circuits.  Hence  we 
see  that,  provided  the  earth  were  uniformly  electrified  on  the  exterior 
of  the  atmosphere,  there  would  be  no  magnetic  action  on  the  earth's 
surface  due  to  mere  motion  of  translation  through  space. 

In  calculating  the  magnetic  action  due  to  the  rotation,  I  have  taken 
the  most  favorable  case,  and  so  have  assumed  the  earth  to  be  a  sphere 
of  magnetic  material  of  great  permeability,  ft.  It  does  not  seem  prob- 
able that  it  would  make  much  difference  whether  the  inside  sphere 
rotated  or  was  stationary;  or  at  least  the  magnetic  action  would  be 
greatest  in  the  latter  case;  and  hence  by  considering  it  stationary  we 
should  get  the  superior  limit  to  the  amount  of  magnetism. 

Let  a  be  the  radius  of  the  sphere  moving  with  angular  velocity  w, 
and  let  a  be  its  surface-density  in  electrostatic  measure,  and  n  the  ratio 
of  the  electromagnetic  to  the  electrostatic  unit  of  electricity.  Then  the 
current-function  will  be 

<p  —  —  we?  I  sin  Odd  = —  wa?  cos  0 . 

n        J  n 

Hence  (Maxwell's  '  Treatise/  §  672)  the  magnetic  potential  inside  the 
sphere  is 

8::     ff 
u  =  — 

and  outside  the  sphere 


=  —  -TT  — -  war  cos  0 , 
o     n 


^     n  r2 

The  magnetic  force  in  the  interior  of  the  sphere  is  thus 

F=i*  —  wa. 

n 

or  the  field  is  uniform.     If  the  electric  potential  of  the  sphere  on  the 
electrostatic  system  is  V,  we  may  write 

^T 
which  is  independent  of  the  dimensions  of  the  sphere. 


AYRTOX  AND  PEEEY'S  THEOEY  OF  THE  EAETH'S  MAGNETISM    181 

In  this  uniform  field  in  the  interior  of  the  sphere,  let  a  smaller 
sphere  of  radius  a!  be  situated;  the  potential  of  its  induced  magnetiza- 
tion will  he 

^  —  1  ./»'  C08<? 


Hence  the  expression  for  the  potential  for  the  space  between  the  two 
spheres  will  be 


and  outside  the  electrified  sphere  it  will  be 


••—  i       *ww  r\    I  Q         • 

w       \  fi  +  2/    r2 

Let  us  now  take  the  most  favorable  case  for  the  production  of  mag- 
netism that  we  can  conceive,  making  a!  =  a  and  fj.  =  °° ;  we  then  have 


-, 

n  r2 

which  is  the  potential  of  an  elementary  magnet  of  magnetic  moment 

^Va\ 
n 

But  Gauss  *  has  estimated  the  magnetic  moment  of  the  earth  to  be 

3-3092a3. 
on  the  millimetre  rag.  second  system.     Hence  we  have 

V=  3-3092  — 
w 

for  the  potential  in  electrostatic  units  on  the  mm.  mg.  second  system. 
In  electromagnetic  units  it  is  thus 

V,  =  3-3092  —  ; 
w 

and  hence  in  volts  it  is  this  quantity  divided  by  1011. 

As  the  earth  makes  one  revolution  in  23»  56'  4",  or  in  86164  seconds, 
we  have 

2* 

"86164' 
and 

n  =  299,000,000,000  *  millims.  per  second. 

8 Taylor's  Sclent.  Mem.,  vol.  ii,  p.  225. 

3  From  a  preliminary  calculation  of  a  new  determination  made  with  the  greatest 
care,  and  having  a  probable  error  of  1  in  1300. 


182  HENRY  A.  KOWLAND 

Hence  the  earth  must  be  electrified  to  a  potential  of  about 

41  X  1015  volts  * 

in  order,  under  the  most  favorable  circumstances,  to  account  for  the 
earth's  magnetism.  This  would  be  sufficient  to  produce  a  spark  in 
atmospheric  air  of  ordinary  density  of  about 

6,000,000  miles! 

Professors  Ayrton  and  Perry  have  only  found  the  potential  108  volts, 
or  400,000,000  times  less  than  I  find  it. 

It  was  this  large  quantity  which  caused  me  to  reject  the  theory;  for 
I  saw  what  an  immense  effect  it  would  have  in  planetary  perturbations ; 
and  I  even  imagined  to  myself  the  atmosphere  flying  away,  and  the 
lighter  bodies  on  the  earth  carried  away  into  space  by  the  repulsion. 
And,  doubtless,  had  not  Professors  Ayrton  and  Perry  made  some  mis- 
take in  their  calculation  by  which  the  force  was  diminished  16  x  1016 
times,  they  would  have  feared  like  results. 

For  according  to  Thomson's  formula,  the  force  would  be  equal  to  a 
pressure  outwards  of 

r-    V* 
~  8*a*  ' 

which  amounts  to  no  less  than 

1,800,000  grms. 

per  square  centimetre!  or  10,000  kil.  per  square  inch!  Such  an  electro- 
static force  as  this  would  undoubtedly  tear  the  earth  to  pieces,  and  dis- 
tribute its  fragments  to  the  uttermost  parts  of  the  universe.  If  the 
moon  were  electrified  to  a  like  potential,  the  force  of  repulsion  would 
be  greater  than  the  gravitation  attraction  to  the  earth,  and  it  would 
fly  off  through  space. 

For  these  reasons  I  rejected  the  theory,  and  now  believe  that  the 
magnetism  of  the  earth  still  remains,  as  before,  one  of  the  great  mys- 
teries of  the  universe,  toward  the  solution  of  which  we  have  not  yet 
made  the  most  distant  approach. 

4  That  this  is  not  too  great  may  be  estimated  from  my  Berlin  experiment,  where  a 
disk  moving  5,000,000  times  as  fast  as  the  earth  with  a  potential  of  10,000  volts, 
produced  a  magnetic  force  of  T]^ffTr  of  the  earth's  magnetism, 

5,000,000  x  10,000  x  50,000=2,500,000,000,000,000, 

which  is  of  the  same  order  of  magnitude  as  the  quantity  calculated,  namely  61  x 
1015.  It  can  be  seen  that  this  reasoning  is  correct,  because  the  formulae  show  that 
two  spheres  of  unequal  size,  rotating  with  equal  angular  velocity  and  charged  to  the 
same  potential,  produce  the  same  magnetic  force  at  similar  points  in  the  two  systems. 


AYRTOX  AND  PERRY'S  THEORY  OF  THE  EARTH'S  MAGNETISM    183 

In  connection  with  the  theory  of  the  earth's  magnetism,  I  had  also 
framed  a  theory  of  the  Aurora  which  may  still  hold.  It  is  that  the 
earth  is  electrified,  and  naturally  that  the  electricity  resides  for  the 
most  part  on  the  exterior  of  the  atmosphere — and  that  the  air-currents 
thus  carry  the  electricity  toward  the  poles,  where  the  air  descending 
leaves  it — and  that  the  condensation  so  produced  is  finally  relieved 
by  discharge. 

The  total  effect  would  thus  be  to  cause  a  difference  of  potential  be- 
tween the  earth  and  the  upper  regions  of  the  air  both  at  the  poles  and 
the  equator.  At  the  poles  the  discharge  of  the  aurora  takes  place  in 
the  dry  atmosphere.  At  the  equator  the  electrostatic  attraction  of  the 
earth  for  the  upper  atmospheric  layers  causes  the  atmosphere  to  be  in 
unstable  equilibrium.  At  some  spot  of  least  resistance  the  upper  atmos- 
phere rushes  toward  the  earth,  moisture  is  condensed,  and  a  conductor 
thus  formed  on  which  electricity  can  collect;  and  so  the  whole  forms  a 
conducting  system  by  which  the  electric  potential  of  the  upper  air  and 
the  earth  become  more  nearly  equal.  This  is  the  phenomenon  known 
as  the  thunderstorm. 

Hence,  were  the  earth  electrified,  the  electricity  would  be  carried  to 
the  higher  latitudes  by  convection,  would  there  discharge  to  the  earth 
as  an  aurora,  and  passing  back  to  the  equator  would  get  to  the  upper 
regions  as  a  lightning  discharge,  once  more  to  go  on  its  unending  cycle. 
I  leave  the  details  of  this  theory  to  the  future. 

Baltimore,  May  30,  1879. 

Appendix. — Since  writing  the  above,  Professors  Ayrton  and  Perry's 
paper  has  appeared  in  full ;  and  I  am  thus  able  to  point  out  their  error 
more  exactly.  Their  formula  at  the  foot  of  page  40G  is  almost  the 
same  as  mine;  but  on  page  407,  in  the  fourth  equation,  the  exponent  of 
n  should  be  -f-  £  instead  of  —  \,  which  increases  their  result  by  about 
600,000,000,  and  makes  it  practically  the  same  as  my  own. 

Rotterdam,  July  13. 


18 

ON  THE  DIAMAGNETIC  CONSTANTS  OF  BISMUTH  AND 
CALC-SPAK  IN  ABSOLUTE  MEASUKE 

[American  Journal  of  Science  [3],  XVIII,  360-371,  1879] 


PART  I. — BY  H.  A.  ROWLAND 

Since  my  experiments  on  the  magnetic  constants  of  iron,  nickel  and 
cobalt,  I  have  sought  the  means  of  determining  those  of  some  diamag- 
netic  substances,  and  to  that  end  have  described  a  method  in  this 
Journal  for  May,  1875  (vol.  ix,  page  357).  As  Mr.  Jacques,  Fellow  of 
the  University,  was  willing  to  take  up  the  experimental  portion,  I  have 
here  worked  up  the  subject  more  in  detail  and  brought  the  formulae 
into  practical  shape.  No  experiments  have  been  made  on  this  subject 
so  far,  but  some  rough  comparisons  with  iron  have  been  made  by 
Becquerel,  Plucker  and  Weber.  But  as  iron  varies  so  greatly,  and  as 
the  methods  of  experiment  are  inexact,  we  cannot  be  said  to  know 
much  about  the  subject.  As,  however,  the  relative  results  of  these 
experiments  and  those  of  Faraday  can  be  accepted  as  reasonably  exact 
for  diamagnetic  substances  and  weak  paramagnetic  ones,  it  is  only 
necessary  to  make  a  determination  of  one  substance  such  as  bismuth, 
and  then  the  rest  can  be  readily  found.  But  as  bismuth  is  very  crys- 
talline it  is  necessary  to  make  our  formulae  general,  unless  we  use  bis- 
muth in  a  powder,  which  would  introduce  error. 

The  general  method  of  experiment  has  been  indicated  in  the  paper 
before  referred  to,  but  I  may  here  state  that  it  consists  in  counting 
the  number  of  vibrations  made  by  a  bar  hung  in  the  usual  manner 
between  the  poles  of  an  electromagnet.  The  distribution  of  the  mag- 
netic force  in  the  field  being  known,  we  can  then  calculate  the  force 
acting  on  the  body,  and  the  comparison  of  thi?  with  the  time  of  vibra- 
tion gives  us  the  means  of  determining  the  constant  sought.  But  I 
will  leave  the  more  exact  description  to  be  given  by  Mr.  Jacques  in  the 
experimental  part. 


DlAMAGNETIC  CONSTANTS  OF  BlSMUTH  AND  CALC-SPAR       185 

EXPLORATION  OF  FIELD 

The  first  operation  to  be  performed  is  to  find  a  formula  to  express 
the  force  of  the  field  at  any  point,  and  an  experimental  means  of  deter- 
mining it  in  absolute  measure.  The  magnet  used  was  one  on  the 
method  of  Euhmkorff,  and  hence  the  field  was  nearly  symmetrical 
around  the  axis  of  the  two  branches,  and  also  with  respect  to  a  plane 
perpendicular  to  the  axis  at  a  point  midway  between  its  poles.  Should 
any  want  of  symmetry  exist  by  accident,  it  will  be  nearly  neutralized 
in  its  effect  on  the  final  result,  seeing  that  the  diamagnetic  bar  hangs 
symmetrically. 

The  proper  expansion  of  the  magnetic  potential  for  this  case  is 
therefore  a  series  of  zonal  spherical  harmonics,  including  only  the  un- 
even powers.  Hence,  if  V  is  the  potential, 

V=AlQtr  +  AHIQtili»+AwQS  +  etc.,     .     .    .    .     (1) 

where  r  is  the  distance  from  the  centre  of  symmetry,  Qt,  Qtit,  etc., 
are  the  spherical  harmonics  with  respect  to  the  angle  between  r  and 
the  axis,  and  At,  Altl,  Av,  etc.,  are  constants  to  be  found  by  experi- 
ment. The  only  method  known  of  measuring  a  strong  magnetic  field 
with  accuracy  is  by  means  of  induced  currents,  and  in  this  case  I  have 
used  a  modification  of  the  method  of  the  proof  plane  as  I  have  described 
it  in  this  Journal,  III,  vol.  x,  p.  14.  In  the  method  there  described  the 
coil  was  to  be  drawn  rapidly  away  from  the  given  point:  in  the  present 
case  the  coil  was  moved  along  the  axis,  thus  measuring  the  difference 
of  the  field  at  several  points;  on  then  placing  it  at  the  centre  and 
drawing  it  away,  the  field  was  measured  at  that  point.  The  field  at 
the  other  points  "along  this  axis  could  then  be  found  by  adding  the 
measured  difference  to  this  quantity.  This  method  is  far  more  accu- 
rate than  the  direct  measurement  at  the  different  points. 

When  a  wire  is  moved  in  a  magnetic  field  the  current  induced  in  it 
is  equal  to  the  change  of  its  potential  energy,  supposing  it  to  transmit 
a  unit  current,  divided  by  the  resistance  of  the  circuit.  The  potential 
energy  of  a  wire  in  a  magnetic  field  is  (Maxwell's  Elec.,  Art.  410), 


P=I(n-  +  m:V-  +  nV 

J  \   dx  dy          dz 

which  is  simply  the  surface  integral  of  V  over  any  surface  whose  edge 
is  in  the  wire. 

In  the  present  case,  take  the  axis  of  x  in  the  direction  of  the  axis  of 
the  poles  and  the  surface,  S,  parallel  to  the  plane  YZ,  and  let  p  be  the 


186  HENRY  A.  EOWLAND 

distance  in  this  plane  from  the  centre  of  the  coil  we  are  calculating. 
Then 


dV  '  •,  (  n 
-1 


for  a  single  circle. 
From(l) 


and  /^a--l;     r'  =  -      , 

where  //  =  cos  (9  , 


p  _ 

- 


For  a  circle  of  rectangular  section  we  must  obtain  the  mean  value  of 
this  quantity  throughout  the  section  of  the  coil. 


1        fxo  +  lr,    /»po+H 

M=-±r  I  I  Pdxdp, 

rlZ  t/x0  —  lr,    t/Po-H 


where  XQ  and  [)0  are  the  values  of  x  and  f>  at  the  centre  of  section  and 
27  and  c  are  the  width  and  depth  of  the  groove  in  which  the  coil  is 
wound.  We  can  calculate  this  quantity  best  by  the  formula  of  Maxwell 
(Electricity,  Art.  700), 


Thus  we  finally  find 

M=  ^At{l  +  TV          +  }  Atllrl    Q'tll  +  i  (5,««  -  3) 


etc. 


It  is  by  aid  of  this  equation  that  we  find  the  coefficients  At,  Alu, 
etc.  in  the  expansion  of  the  magnetic  potential,  V.  For,  let  the  coil 
be  moved  in  the  field  from  a  position  where  M  has  the  value  M'  to 
where  it  has  the  value  M  "  :  then  if  the  coil  be  joined  to  a  galvanometer 
the  current  induced  will  be  equal  to 

M'  -  M" 
R 

where  R  is  the  resistance  of  the  circuit.     If  an  earth  inductor  is  in- 
cluded in  the  circuit  whose  integral  area  is  E,  when  it  is  reversed  the 

2  J-fW 
current  is  —  ^-  where  H  is  the  component  of  the  earth's  magnetism 


DlAMAGNETIC    CONSTANTS    OF    BlSMUTH    AND    CALC-SPAR          187 

perpendicular  to  the  plane  of  the  inductor.     The  current  as  measured 
by  the  galvanometer  in  the  first  case  will  be  C  sin  \  S  (1  -j-  £/)  and  in 
the  second  C  sin  £  D  (1  +  £/),  where  C  is  the  constant  of  the  galvano- 
meter and  ^  is  the  logarithmic  decrement. 
Hence 

T[f'  _    Tif" 

* 


sm 

In  this  way  we  can  obtain  a  series  of  equations  containing  At,  Allt, 
etc.,  and  can  thus  find  these  by  elimination. 

This  completes  the  exploration,  and  we  have  as  a  result  a  formula 
giving  the  magnetic  potential  of  the  field  in  absolute  measure  through- 
out a  certain  small  region  in  which  we  can  experiment. 

The  next  process  is  to  consider  the  action  of  this  field  upon  any  body 
which  we  may  hang  in  it. 

CRYSTALLINE  BODY  IN  MAGNETIC  FIELD 

Let  the  body  have  such  feeble  magnetic  action  that  the  magnetic 
field  is  not  very  much  influenced  by  its  presence.  In  all  crystalline 
substances  we  know  there  exist  in  general  three  axes  at  right  angles 
to  each  other,  along  which  the  magnetic  induction  is  in  the  direction  of 
the  magnetic  force.  Let  k1}  Jc2  and  ka  be  the  coefficients  of  magnetiza- 
tion in  the  directions  of  these  axes  and  let  a  set  of  coordinate  axes  be 
drawn  parallel  to  these  crystalline  axes,  the  coordinates  referred  to 
which  are  designated  by  x',  y'  and  z',  and  the  magnetic  components  of 
the  force  parallel  to  which  are  X',  Y'  and  Z'. 

The  energy  of  the  crystalline  body  will  then  be 

E  =  -  \fff  (k,Z'2  +  Jc,  Yn  +  fcsZ")  dx'dy'dz' 

In  most  cases  it  is  more  convenient  to  refer  the  equation  to  axes  in 
some  other  direction  through  the  crystal.     Let  these  axes  be  X,  Y,  Z. 
Then 


Y,      dV    dV        dV       dV  „ 
X   =d^  =  ^a  +  ^a  +  dza 
Y'  =  etc. 


188  HENEY  A.  EOWLAND 

Hence 

Z'  -  Xa+Ya' 


where  a,  /?,  f  ;  a!,  /3',  -f  ;  and  a",  /5",  /'  are  the  direction  cosines  of  the 
new  axes  with  reference  to  the  old. 
We  then  find 


E=  -  \fff{  X*  (jfcy  +  JkJP  +  V)  +  Y*  (  V2  +  V  +  V2)  +  Z\k 

+  2YZ 


The  most  simple  and  in  many  respects  the  most  interesting  cases 
are  when  the  crystal  has  only  one  optic  or  magnetic  axis.     In  this 

CclSG   $2  '  '    ~  wy 

Hence 


where  «,  a!  and  a!'  are  the  direction  cosines  of  the  magnetic  axis  with 
respect  to  the  coordinate  axes. 

The  first  case  to  consider  is  that  of  a  mass  of  crystal  in  a  uniform 
magnetic  field.  The  magnetic  forces  which  enter  the  equation  are 
those  due  to  the  magnetic  action  of  the  body  as  well  as  to  the  field  in 
which  the  body  is  placed.  In  the  case  of  very  weak  magnetic  or 
diamagnetic  bodies  the  forces  are  almost  entirely  those  of  the  field  alone. 
Hence  in  the  case  under  consideration  we  may  put  F  =  0  and  Z  =  0. 

Hence 


and  if  v  is  the  volume  of  the  body 


As  this  expression  is  the  same  at  all  points  of  the  field  there  is  no 
force  acting  to  translate  the  body  from  one  part  of  the  field  to  another. 
The  moment  of  the  force  tending  to  increase  <p,  where  <p  —  cos-1«,  is 

j  pi 

—  -.-  =  v  X"1  (k^—Tc^  sin  <p  cos  <p  . 

By  observing  the  moment  of  the  force  which  acts  on  a  crystal  placed 
in  a  uniform  magnetic  field  we  can  thus  find  the  value  of  ki  —  k2  or 
the  difference  of  the  magnetic  constant  along  the  axis  and  at  right 
angles  to  it.  The  differences  of  the  constants  can  also  be  found  in  the 
case  of  crystals  with  three  axes  by  a  similar  process. 

The  next  case  which  I  shall  consider  is  that  of  a  bar  hanging  in  a 


DlAMAGNETIC    CONSTANTS    OF    BlSMUTH    AND    CALC-SPAR          189 

magnetic  field.  Let  the  field  be  symmetrical  around  an  horizontal  axis, 
and  also  with  reference  to  a  plane  perpendicular  to  that  axis  at  the 
centre.  If  the  bar  is  very  long  with  reference  to  its  section  and  a 
plane  can  be  passed  through  it  and  the  axis  we  must  have  Z  =  0,  and 
the  equation  becomes 


Let  the  axis  of  X  coincide  with  the  long  axis  of  the  bar,  as  this  will 
in  the  end  lead  to  the  most  simple  result,  seeing  that  we  have  to  inte- 
grate along  the  length  of  the  bar. 

Let  r  be  the  length  along  the  bar  from  the  centre  to  any  point,  and 
let  6  be  the  angle  made  by  the  bar  with  the  axis  of  symmetry  :  then 

1  dV 


j>-  v_ 

~~dr  ~ 

also  let  the  section  of  the  bar  be 

a  =  dy  dz 

and  let  the  axis  of  the  bar  pass  through  the  origin  from  which  we  have 
developed  the  potential  in  terms  of  spherical  harmonics.  We  can  then 
write  as  before 


where  Qt,  Qltl,  etc.,  are  zonal  spherical  harmonics  with  reference  to 
the  angle  6, 


from  which  we  have  the  following: 


X*  =  A'Q*  +  SA*,^  +  25^-#f  +  QA^Q.Q^ 

^Q&i*  +  MAlttA,QMQS  +  etc., 

*  +  ZA.A^Q'ff^ 
'&i*  +  ZA^A^&r*  +  etc.}  sin-*, 


The  moment  of  the  force  tending  to  increase  6  is 

dE 
~W 

whence  we  may  write, 

*i  «*  +  *,)  +  B  ((^  -  kj  «'*  +  h)  —  C  (Tc,  -  £2)  ««'  \, 


190  HENEY  A.  EOWLAND 


where  d      •+  l  V2  7         .     a  d 

X*ar  =  sin  0  - 


Y*dr  =  sin  0  -      I      Y2dr, 
diJL  J_, 

tJ    /*+'  fi    /»+' 

C  =  -  ~  I     ZXYdr  =  sin  6  "    I     ZXYdr, 
dv  J  -i  a/jLj_, 

where  I  is  half  the  length  of  the  bar  and     —  cosd. 


=  U*m0\  A]QtQ't  +  |  A*  ,#„&„]*  +  ^  A'Q.QP  +  AtAtll  ( 

+  Q,Q'J  P  +  AtAv  (Q'&  +  Q&  )  ^  +  V-  AUI  JT  (<?„#„ 
=  USin0\  A]  (QW  sin2  0  -  Q?  cos  0)  +  A]tl  ($„&'„  sin2  9 

-  Q'L  cos  o)  -jj-  +  ^v  (g;  $;'  sin2  0  -  c:  cos  o)  .£.  +  ^^ 


+  sn  tf  -  ,,,  cos  ^      -  +  A,A,  ((QW  +  Q'W  sin'  o 

-2QW  cos^)        +  AtllA,((Q'tll<?,'  +  Q'^Q'^  sitf  o 


C=+U\A*  ((Qff  +  QV  sin2  e  -  Q&  cos  9)  +  3A'tl  ((Q 


'^  sin2  e  -  QHIQfHI  cos  *)-.+  5  J2  ((^v^,'  -  #;2)  sin2 


-      cos 


2 


cos 


sn  e  -   5,V  +     tJ  cos  o)  -. 
+  *Q'<&  +  3  sin2  0  - 


Where 

Q,    =cos0, 

QM  =  J  (5  cos3  e  —  3  cos  0)  , 

Q,   =  i  (63  cos5  0  —  70  cos3  0  +  15  cos  0)  , 


^;   =Y  (21  cos4  0-14  cos2  0  +  1), 

<?'/  -o, 


cos30  —  7cos0), 

fj.    =  COS  0. 


DlAMAGNETIC    CONSTANTS    OF    BlSMUTH   AND    CALC-SPAR          191 

• 

A  =  ±1  sin  0\  (  A]  +  1  1  A*,?  +  -LV/  A*1*  —  ZA.A»F  +  Y-  AA# 
-  ^6)/'  +  (- 


=  4  sn  0     -  J  - 


-  m*  AniAJ?)  tjf  +  (—if  s  AIJI  _ 
+  -i  |s.  J/y^j6)  //  +  (i-W-5-  ^'  ^8  -  - 
(7  =  «     -^- 


Or  we  can  write 

A  =  41  sin  0  {  L>J.  +  L',u3+  L"  £  +  etc.  }, 
B  =  U  sin  e  \  MIL  +  M'ff  +  etc.  \, 
C  =  M{N+iytn  +  JV'V  +  etc.  }, 

where  the  values  of  L,  M,  etc.,  are  apparent. 
To  sum  up  we  may  then  write  as  before 

0  =  -  J  a\A  [(^  -  *,)  «2  +  &,]  +  5[(^  -  *,)  «'2  +  *s]  -  C'  (&,  -  *,)  ««'}• 

where  A,  B  and  (7  are  the  quantities  we  have  found,  a  is  the  cosine  of 
the  angle  made  by  the  axis  of  the  crystal  with  the  axis  of  the  bar,  and  a' 
is  the  cosine  of  the  angle  made  by  the  same  axis  with  a  horizontal  line 
at  right  angles  to  the  bar. 
The  equation 

#  =  0 

gives  equilibrium  at  some  angle  depending  on  a  and  a',  and  if  either  of 
these  is  zero  the  angle  can  be  either  0  =•  0  or  -J-,  one  of  which  will  be 
stable  and  the  other  unstable  according  as  the  body  is  para-  or  dia- 
magnetic. 

For  a  diamagnetic  crystal  like  bismuth  with  the  axis  at  right  angles 
to  the  bar  we  can  put 

n  =  cos  0  =  sin  (/>  and  a  =  0  , 
and  we  can  write 


192  HENEY  A.  EOWLAND 

0  =  —  J  a\4lk«  (Lfji  +  L>jf*  +  etc.) 


&,)  a'2  +  k,][M;j.  +  M'/S  +  etc.]} 
or  for  very  small  values  of  //  we  can  write  in  terms  of  </> 
0  -  —  2al<>>  \lc,L  +  ((&!  -  &,)  «'2  +  &2)  M\. 

If  I  is  the  moment  of  inertia  of  the  bar  and  t  is  the  time  of  a  single 
vibration,  we  may  write 

»=/-£#. 

If  we  hang  up  the  bar  so  that  a'  —  0  we  have 


and  if  we  hang  it  up  so  that  a'  =  %TT  we  have  again 


2a«" 
whence 

7T2/  1 


where 

x  -  ^  -  utAnF  +  (II  ^:/y  +  v-  ^  A)  ^-  -v/  *,„**  +  -VV/ 


For  a  cleavage  bar  of  calc  spar  we  must  use  the  general  equation. 
For  equilibrium  we  have 

h  {Aa*  +  Ba'3  -  Caa'\  +  k,  { A  (1  —  a2)  +  B  (1  -  a'2)  +  Caa'  \  =  0, 

which  gives  us  the  ratio  of  Jc1  to  Tc2.  For  this  experiment  it  is  best  to 
hang  up  the  bar  so  that  the  axis  is  in  the  horizontal  plane  and  we 
should  then  have 

a2  =  I  —  a'2. 

For  obtaining  another  relation  it  is  best  to  suspend  the  bar  with  «'  =  0 
and  we  then  have  the  position  of  stable  equilibrium  at  the  point  6  —  \K 
which  gives 

T?I 

t* 

whence 


DlAMAGNETIC    CONSTANTS    OF    BlSMUTH   AND    CALC-SPAR          193 


these  various  equations  give  the  complete  solution  of  the  problem  of 
finding  the  various  coefficients  of  magnetization. 


PART  II.— BY  W.  W.  JACQUES 

In  the  foregoing  part  of  this  paper  there  have  been  deduced  mathe- 
matical expressions  for  the  constants  He  and  ~k'  both  for  bismuth  and 
for  calc-spar  crystals.  In  these  expressions  it  is  necessary  to  substitute 
certain  quantities  obtained  by  a  series  of  experiments,  and  it  is  the 
purpose  of  the  remaining  portion  of  the  paper  to  describe  briefly  the 
way  in  which  these  quantities  were  obtained. 

These  experiments  are  naturally  divided  into  two  parts.  First,  the 
exploration  of  the  small  magnetic  field  between  the  two  poles  of  the 
electromagnet,  and  second,  the  determination  of  the  time  of  swing  and 
certain  other  constants  relating  to  little  bars  of  the  substances  experi- 
mented upon  when  suspended  in  this  field. 

In  order  to  insure  the  constancy  of  the  magnetic  field,  a  galvano- 
meter and  variable  resistance  were  inserted  in  the  circuit  through 
which  the  magnetizing  current  circulated.  This  space  between  the 
poles  of  the  electromagnet  in  which  the  experiments  were  performed 
was  a  little  larger  than  a  hen's  egg. 

The  method  of  exploring  this  field  was  as  follows :  In  the  line  join- 
ing the  centre  of  the  two  poles  was  placed  a  little  brass  rod,  along 
which  a  very  small  coil  of  fine  wire  was  made  to  slide.  To  this  rod 
were  fixed  two  little  set-screws  to  regulate  the  distance  through  which 
the  coil  could  be  moved.  Starting  now  always  from  the  centre,  the 
coil  was  moved  successively  through  distances  a,  &  and  c,  and  the  cor- 
responding deflections  of  a  delicate  mirror  galvanometer  contained  in 
the  circuit  were  noted.  To  each  of  these  deflections  was  added  the 
deflection  due  to  quickly  pulling  the  coil  away  from  the  centre  to  a 
distance  such  that  the  magnetic  potential  was  negligibly  small.  Of 
course,  experiments  were  made  on  both  sides  of  the  centre  of  the  field 
in  order  to  eliminate  any  want  of  symmetry,  and  the  distances  through 
which  the  coil  moved  were  all  carefully  measured  with  a  dividing  engine. 

In  order  to  reduce  the  deflections  of  the  galvanometer  to  absolute 
13 


194  HENRY  A.  EOWLAND 

measure,  an  earth  inductor  was  included  in  the  circuit  with  the  little 
coil  and  galvanometer  and  the  deflections  produced  by  this  were  com- 
pared with  those  produced  by  moving  the  little  coil.  These  deflections 
were  taken  between  every  two  observations  with  the  little  coil. 

The  deflections  due  to  moving  the  little  coil,  those  due  to  the  earth 
inductor  and  that  due  to  pulling  the  coil  away  from  the  centre  are 
given  in  the  following  table: 

Distance  a.  Distance  6.  Distance  c. 

Coil    4-407  cm.  9-655  cm.  6-363  cm. 

Earth  inductor 33-138  cm.         33-137  cm.         33-162  cm. 

Drawing  coil  away  from  centre 57-416  cm. 

In  order  to  determine  the  proper  quantities  for  substitution  in  the 
expression  for  the  magnetic  potential  of  the  field,  it  was  necessary  to 
measure,  besides,  the  deflections  due  to  the  little  coil  when  moved 
through  various  distances  and  those  due  to  the  earth  inductor. 

The  mean  radius  of  the  small  coil =  -3912  cm. 

Number  of  turns     =  83  • 

Width  if  coil    =  -182.4  cm. 

Depth  of  coil  =  -1212  cm. 

Integral  area  of  earth  inductor =  20716-2  cm. 

Horizontal  intensity  of  earth's  magnetism.  .  .  .  =  -1984cgs. 

The  quotient  of  the  mean  radius  of  the  coil  by  the  distance  moved 
gave  tan  d. 

The  linear  measurements  were  made  with  a  dividing  engine. 

The  horizontal  intensity  of  the  earth's  magnetism  was  determined 
by  measuring  the  time  of  swing  of  a  bar  magnet  and  its  effect  upon  a 
smaller  galvanometer  needle.  The  proper  substitution  of  these  quan- 
tities in  the  formula  given  gave  the  expression  in  absolute  measure 
for  the  magnetic  potential  at  any  part  of  the  field. 

The  remaining  part  of  the  experiment  and  the  part  that  was  attended 
with  greatest  difficulty,  was  to  prepare  little  bars  of  the  substances  and 
to  determine  the  times  of  vibration  of  these  when  suspended,  first  with 
the  axis  vertical  and  then  with  it  horizontal  in  the  magnetic  field. 
Besides  this,  the  dimensions  and  the  moment  of  inertia  of  each  bar  had 
to  be  determined,  and,  in  the  case  of  the  calc-spar,  the  angle  the  bar 
made  with  the  equatorial  line  of  the  poles  when  in  its  position  of  equi- 
librium, had  to  be  measured. 

Bismuth  and  calc-spar  were  the  two  crystals  experimented  upon; 
quite  a  number  of  other  substances  were  tried  but  failed  to  give  good 


DlAMAGNETIC    CONSTANTS    OF    BlSMUTH   AND    CALC-&PAR          195 

results  because  of  the  iron  contained  in  them  as  an  impurity.  The 
bars  were  each  about  15  mm.  long  and  about  2  mm.  in  cross  section. 
The  force  to  be  measured  being  only  about  -00000001  of  that  exerted  in 
the  case  of  iron  it  was  necessary  to  carry  out  the  experiments  with  the 
very  greatest  care. 

In  order  to  obtain  bars  free  from  iron,  very  fine  crystals  of  chemically 
pure  substances  were  selected  and  the  bars  cleaved  from  them.  They 
were  then  polished  with  their  various  sides  parallel  to  the  cleavage 
planes  by  rubbing  on  clean  plates  of  steatite  with  oil.  In  order  to 
remove  any  particles  of  iron  that  might  have  collected  upon  them 
during  these  processes,  they  were  carefully  washed  with  boiling  hydro- 
chloric acid  and  with  distilled  water  and  then  wrapped  in  clean  papers, 
and  never  touched  except  after  washing  the  hands  with  hydrochloric 
acid  and  distilled  water. 

In  order  to  reduce  to  a  minimum  the  causes  that  might  interfere 
with  the  accurate  determination  of  the  times  of  vibration  of  these  bars 
the  poles  of  the  magnet  were  encased  by  a  box  of  glass.  From  the  top 
of  this  a  tube  four  feet  long  extended  up  toward  the  ceiling,  and  inside 
this  was  hung  a  single  fibre  of  silk  so  small  as  to  be  barely  visible  to 
the  naked  eye.  The  bars  were  placed  in  little  slings  of  coarser  silk 
fibre  and  suspended  by  this.  Outside  the  glass  case  was  a  microscope 
placed  horizontally  and  having  a  focus  of  about  six  inches.  This  was 
directed  toward  the  suspended  bar,  and  when  the  latter  was  at  rest  the 
cross  hairs  of  the  microscope  fell  upon  a  little  scratch  in  one  end  of  the 
bar.  Near  by  was  a  telegraph  sounder  arranged  to  tick  seconds.  The 
bar  was  set  swinging  through  a  small  arc  by  making  and  breaking  the 
current,  and  the  interval  between  two  successive  transits  of  the  little 
scratch  on  the  bar  by  the  cross  hairs  of  the  microscope  was  measured 
in  seconds  and  tenths  of  a  second  by  the  ear.  By  keeping  count  through 
a  large  number  of  successive  transits  the  time  of  a  single  swing  could 
be  determined  with  very  great  accuracy.  The  bar  was  caused  to  swing 
only  through  a  few  degrees  of  arc  and  such  small  correction  for  ampli- 
tude as  was  found  necessary  was  applied.  The  time  of  swing  was  deter- 
mined first  with  the  axis  vertical  and  then  with  it  horizontal.  But 
besides  the  time  of  swing  of  each  bar  it  was  necessary  to  measure :  the 
length ;  area  of  section;  moment  of  inertia  in  each  position ;  and  for  the 
calc-spar  bar  the  angle  it  made  with  the  equatorial  plane  of  the  magnet 
when  in  its  position  of  equilibrium.  This  was  not  necessary  in  the 
case  of  bismuth,  because  its  position  of  equilibrium  lay  in  the  equatorial 
plane. 


196 


HENRY  A.  ROWLAND 


BISMUTH. 


Time  of 
swing. 

Axis,  vertical  7'18  sec. 

Axis,  horizontal 5'76  sec. 


Moment  of 

Half 

Area  of 

inertia. 

length. 

section. 

•10976  cgs. 
•10943  cgs. 

•7709  cm. 

•03778  cm, 

CALC-SPAR. 


Half 
length. 


Area  of 
section. 


•8015cm.    -0300cm.    50°  30' 


Time  of     Moment  of 
swing.  inertia. 

Axis,  vertical 46'35sec.   '0303cgs. 

Axis,  horizontal 43-39  sec.   '0300  cgs. 

The  linear  measurements  were  made  with  a  dividing  engine,  the 
moments  of  inertia  were  calculated  from  the  dimensions  of  the  bars. 
The  angle  at  which  the  calc-spar  stood  was  measured  by  projecting  the 
linear  axis  on  a  scale  placed  at  a  distance. 

The  above  quantities  being  all  determined  and  properly  substitutedj 
the  solution  of  the  equations  gave  for 

Bismuth    ,  .  .Tc,  =  — 


Calc-spar 


•000  000  012  554 
•000000014324 
•000  000  037  930 
•000000040330 


19 
PRELIMINARY  NOTES  ON  ME.  HALL'S  RECENT  DISCOVERY * 

[Philosophical  Magazine  [5],  IX,  432-434,  1880 ;  Proceedings  of  the  Physical  Society,  IV, 
10-13,  1880;  American  Journal  of  Mathematics,  II,  354-356,  1879] 

The  recent  discovery  by  Mr.  Hall 3  of  a  new  action  of  magnetism  on 
electric  currents  opens  a  wide  field  for  the  mathematician,  seeing  that 
we  must  now  regard  most  of  the  equations  which  we  have  hitherto  used 
in  electromagnetism  as  only  approximate,  and  as  applying  only  to  some 
ideal  substance  which  may  or  may  not  exist  in  nature,  but  which  cer- 
tainly does  not  include  the  ordinary  metals.  But  as  the  effect  is  very 
small,  probably  it  will  always  be  treated  as  a  correction  to  the  ordinary 
equations. 

The  facts  of  the  case  seem  to  be  as  follows,  as  nearly  as  they  have 
yet  been  determined: — Whenever  a  substance  transmitting  an  electric 
current  is  placed  in  a  magnetic  field,  besides  the  ordinary  electromotive 
force  in  the  medium,  we  now  have  another  acting  at  right  angles  to  the 
current  and  to  the  magnetic  lines  of  force.  Whether  there  may  not  be 
also  an  electromotive  force  in  the  direction  of  the  current  has  not  yet 
been  determined  with  accuracy;  but  it  has  been  proved,  within  the  limits 
of  accuracy  of  the  experiment,  that  no  electromotive  force  exists  in  the 
direction  of  the  lines  of  magnetic  force.  This  electromotive  force  in  a 
given  medium  is  proportional  to  the  strength  of  the  current  and  to 
the  magnetic  intensity,  and  is  reversed  when  either  the  primary  current 
or  the  magnetism  is  reversed.  It  has  also  been  lately  found  that  the 
direction  is  different  in  iron  from  what  it  is  in  gold  or  silver. 

To  analyze  the  phenomenon  in  gold,  let  us  suppose  that  the  line  A  B 
represents  the  original  current  at  the  point  A,  and  that  B  C  is  the  new 
effect.  The  magnetic  pole  is  supposed  to  be  either  above  or  below  the 
paper,  as  the  case  may  be.  The  line  A  C  will  represent  the  final 
resultant  electromotive  force  at  the  point  A.  The  circle  with  arrow 
represents  the  direction  in  which  the  current  is  rotated  by  the  mag- 
netism. 

1  From  the  American  Journal  of    Mathematics.     Communicated  by  the  Physical 
Society. 

*  Phil.  Mag.  [5],  vol.  ix,  p.  225. 


198 


HENKY  A.  ROWLAND 


It  is  seen  that  all  these  effects  are  such  as  would  happen  were  the 
electric  current  to  be  rotated  in  a  fixed  direction  with  respect  to  the 
lines  of  magnetic  force,  and  to  an  amount  depending  only  on  the  mag- 
netic force  and  not  on  the  current.  This  fact  seems  to  point  imme- 
diately to  that  other  very  important  case  of  rotation,  namely  the  rota- 
tion of  the  plane  of  polarization  of  light.  For,  by  Maxwell's  theory, 
light  is  an  electrical  phenomenon,  and  consists  of  waves  of  electrical 
displacement,  the  currents  of  displacement  being  at  right  angles  to  the 
direction  of  propagation  of  the  light.  If  the  action  we  are  now  con- 
sidering takes  place  in  dielectrics,  which  point  Mr.  Hall  is  now  investi- 
gating, the  rotation  of  the  plane  of  polarization  of  light  is  explained. 

I  give  the  following  very  imperfect  theory  at  this  stage  of  the  paper, 
hoping  to  finally  give  a  more  perfect  one  either  in  this  paper  or  a 
later  one. 

North  Pole  above. 


North  Pole  below. 


Let  $  be  the  intensity  of  the  magnetic  field,  and  let  E  be  the  original 
electromotive  force  at  any  point,  and  let  c  be  a  constant  for  the  given 
medium.  Then  the  new  electromotive  force  E'  will  be 


and  the  final  electromotive  force  will  be  rotated  through  an  angle  which 
will  be  very  nearly  equal  to  c£>.  As  the  wave  progresses  through  the 
medium,  each  time  it  (the  electromotive  force)  is  reversed  it  will  be 
rotated  through  this  angle;  so  that  the  total  rotation  will  be  this  quan- 
tity multiplied  by  the  number  of  waves.  If  ^  is  the  wave-length  in  air, 
and  i  is  the  index  of  refraction,  and  c  is  the  length  of  medium,  then 

the  number  of  waves  will  be       and  the  total  rotation 


The  direction  of  rotation  is  the  same  in  diamagnetic  and  ferromag- 
netic bodies  as  we  find  by  experiment,  being  different  in  the  two;  for  it 


PRELIMINARY  NOTES  ON  MR.  HALL'S  RECENT  DISCOVERY      199 

« 

is  well  known  that  the  rotation  of  the  plane  of  polarization  is  opposite 
in  the  two  media,  and  Mr.  Hall  now  finds  his  effect  to  be  opposite  in 
the  two  media.  This  result  I  anticipated  from  this  theory  of  the 
magnetic  rotation  of  light. 

But  the  formula  makes  the  rotation  inversely  proportional  to  the 
wave-length,  whereas  we  find  it  more  nearly  as  the  square  or  cube. 
This  I  consider  to  be  a  defect  due  to  the  imperfect  theory ;  and  it  would 
possibly  disappear  from  the  complete  dynamical  theory.  But  the  for- 
mula at  least  makes  the  rotation  increase  as  the  wave-length  decreases, 
which  is  according  to  experiment.  Should  an  exact  formula  be  finally 
obtained,  it  seems  to  me  that  it  would  constitute  a  very  important  link 
in  the  proof  of  Maxwell's  theory  of  light,  and,  together  with  a  very 
exact  measure  of  the  ratio  of  the  electromagnetic  to  the  electrostatic 
units  of  electricity  which  we  made  here  last  year,  will  raise  the  theory 
almost  to  a  demonstrated  fact.  The  determination  of  the  ratio  will 
be  published  shortly;  but  I  may  say  here  that  the  final  result  will  not 
vary  much,  when  all  the  corrections  have  been  applied,  from  299,700,000 
metres  per  second;  and  this  is  almost  exactly  the  velocity  of  light.  We 
cannot  but  lament  that  the  great  author  of  this  modern  theory  of  light 
is  not  now  here  to  work  up  this  new  confirmation  of  his  theory,  and 
that  it  is  left  for  so  much  weaker  hands. 

But  before  we  can  say  definitely  that  this  action  explains  the  rota- 
tion of  the  plane  of  polarization  of  light,  the  action  must  be  extended 
to  dielectrics,  and  it  must  be  proved  that  the  lines  of  electrostatic 
action  are  rotated  around  the  lines  of  force  as  well  as  the  electric  cur- 
rents. Mr.  Hall  is  about  to  try  an  experiment  of  this  nature. 

I  am  now  writing  the  full  mathematical  theory  of  the  new  action,  and 
hope  to  there  consider  the  full  consequences  of  the  new  discovery. 


Addition. — I  have  now  worked  out  the  complete  theory  of  the  rota- 
tion of  the  plane  of  polarization  of  light,  on  the  assumption  that  the 
displacement  currents  are  rotated  as  well  as  the  conducted  currents. 
The  result  is  very  satisfactory,  and  makes  the  rotation  proportional  to 

~  ,  which  agrees  very  perfectly  with  observation.  The  amount  of  rota- 
tion calculated  for  gold  is  also  very  nearly  what  is  found  in  some  of 
the  substances  which  rotate  the  light  the  least.  Hence  it  seems  to  me 
that  we  have  very  strong  ground  for  supposing  the  two  phenomena  to 
be  the  same. 


22 
ON  THE  EFFICIENCY  OF  EDISON'S  ELECTRIC  LIGHT 

BY  H.  A.  ROWLAND  AND  GEORGE  F.  BARKER 
\American  Journal  of  Science,  [31,  XIX,  337-339,  1880] 

The  great  interest  which  is  now  being  felt  throughout  the  civilized 
world  in  the  success  of  the  various  attempts  to  light  houses  by  elec- 
tricity, together  with  the  contradictory  statements  made  with  respect 
to  Mr.  Edison's  method,  have  induced  us  to  attempt  a  brief  examina- 
tion of  the  efficiency  of  his  light.  We  deemed  this  the  more  important 
because  most  of  the  information  on  the  subject  has  not  been  given  to 
the  public  in  a  trustworthy  form.  We  have  endeavored  to  make  a 
brief  but  conclusive  test  of  the  efficiency  of  the  light,  that  is,  the 
amount  of  light  which  could  be  obtained  from  one  horse  power  of  work 
given  out  by  the  steam  engine.  For  if  the  light  be  economical,  the 
minor  points,  such  as  making  the  carbon  strips  last,  can  undoubtedly 
be  put  into  practical  shape. 

Three  methods  of  testing  the  efficiency  presented  themselves  to  us. 
The  first  was  by  means  of  measuring  the  horse  power  required  to  drive 
the  machine,  together  with  the  number  of  lights  which  it  would  give. 
But  the  dynamometer  was  not  in  very  wood  working  order,  and  it  was 
difficult  to  determine  the  number  of  lights  and  their  photometric 
power,  as  they  were  scattered  throughout  a  long  distance,  and  so  this 
method  was  abandoned.  Another  method  was  by  measuring  the  resist- 
ance of,  and  amount  of,  current  passing  through  a  single  lamp.  But 
the  instruments  available  for  this  purpose  were  very  rough,  and  so 
this  method  was  abandoned  for  the  third  one.  This  method  consisted 
in  putting  the  lamp  under  water  and  observing  the  total  amount  of  heat 
generated  in  the  water  per  minute.  For  this  purpose,  a  calorimeter, 
holding  about  1^  kil.  of  water,  was  made  out  of  very  thin  copper:  the 
lamp  was  held  firmly  in  the  centre,  so  that  a  stirrer  could  work  around 
it.  The  temperature  was  noted  on  a  delicate  Baudin  thermometer 
graduated  to  0-1°  C. 

As  the  experiment  was  only  meant  to  give  a  rough  idea  of  the 
efficiency  within  two  or  three  per  cent,  no  correction  was  made  for 


ON  THE  EFFICIENCY  OF  EDISON'S  ELECTRIC  LIGHT 


201 


radiation,  but  the  error  was  avoided  as  much  as  possible  by  having  the 
mean  temperature  of  the  calorimeter  as  near  that  of  the  air  as  possible, 
and  the  rise  of  temperature  small.  The  error  would  then  be  much  less 
than  one  per  cent.  A  small  portion  of  the  light  escaped  through  the 
apertures  in  the  cover,  but  the  amount  of  energy  must  have  been  very 
minute. 

In  order  to  obtain  the  amount  of  light  and  eliminate  all  changes  of 
the  engine  and  machine,  two  lamps  of  nearly  equal  power  were  gener- 
ally used,  one  being  in  the  calorimeter  while  the  other  was  being 
measured.  They  were  then  reversed  and  the  mean  of  the  results  taken. 
The  apparatus  for  measuring  the  light  was  one  of  the  ordinary  Bunsen 
instruments  used  for  determining  gas-lights,  with  a  single  candle  at 
ten  inches  distance.  The  candles  used  were  the  ordinary  standards, 
burning  120  grains  per  hour.  They  were  weighed  before  and  after 
each  experiment,  but  as  the  amount  burned  did  not  vary  more  than 
one  per  cent  from  120  grains  per  hour,  no  correction  was  made. 

As  the  strips  of  carbonized  paper  were  flat,  very  much  more  light 
was  given  out  in  a  direction  perpendicular  to  the  surface  than  in  the 
plane  of  the  edge.  Two  observations  were  taken  of  the  photometric 
power,  one  in  a  direction  perpendicular  to  the  paper,  and  the  other 
in  the  direction  of  the  edge,  and  we  are  required  to  obtain  the  average 
light  from  these.  If  L  is  the  photometric  power  perpendicular  to  the 
paper,  and  I  that  of  the  edge,  then  the  average,  I,  will  evidently  be 
very  nearly 


Xo 


COS  a  sin  a  d  a  +  I  I       Sin2  a  d  a, 


/» 

I 

•Ft 


A  =  J  L  +  p. 

In  the  paper  lamps  we  found  l  = 
The  lamps  used  were  as  follows: 


nearly;  hence  x  =|L  nearly 


No. 

Kind  of  Carbon. 

Size  of  Carbon. 

Approximate 
resistance  when  cold. 

580 

Paper. 

Large. 

147  ohms. 

201 

n 

it 

147 

850 

it 

Small. 

170       " 

809 

it 

*i 

154       " 

817 

Fibre. 

Large. 

87       « 

The  capacity  of  the  calorimeter  was  obtained  by  adding  to  the  capac- 
ity of  the  water,  the  copper  of  the  calorimeter  and  the  glass  of  the 


202 


HENRY  A.  ROWLAND 


lamp  and  thermometer.  The  calorimeter  and  cover  weighed  0-103 
kil.  and  the  lamps  about  0-035  kil. 

First  experiment,  No.  201  in  calorimeter  and  No.  580  in  photometer; 
capacity  of  calorimeter  =  1-153  +  -009  +  -007  =  1-169  kil.  The 
temperature  rose  from  18° -28  C.  to  23° -11  C.  in  five  minutes,  or  l°-75 
F.  in  one  minute.  Taking  the  mechanical  equivalent  as  775-,  which  is 
about  right  for  the  degrees  of  this  thermometer,  this  corresponds  to 
an  expenditure  of  3486  foot  pounds  per  minute.  The  photometric 
power  of  No.  580  was  17-5  candles  maximum,  or  13-1  mean,  /. 

When  the  lamps  were  reversed,  the  result  was  3540  foot  pounds  for 
No.  580,  and  a  power  of  13-5  or  10-1  candles  mean.  The  mean  of 
these  two  gives,  therefore,  a  power  of  3513  foot  pounds  per  minute  for 
11-6  candles,  or  109-0  candles  to  the  horse  power. 

To  test  the  change  of  efficiency  when  the  temperature  varied,  we 
tried  another  experiment  with  the  same  pair  of  lamps,  and  also  used 
some  others  where  the  radiating  area  was  smaller,  and,  consequently, 
the  temperature  had  to  be  higher  to  give  out  an  equal  light. 

We  combine  the  results  in  the  following  table,  having  calculated  the 
number  of  candles  per  indicated  horse  power  by  taking  70  per  cent  of 
the  calculated  value,  thus  allowing  about  30  per  cent  for  the  friction 
of  the  engine,  and  the  loss  of  energy  in  the  magneto-electric  machine, 
heating  of  wires,  etc.  As  Mr.  Edison's  machine  is  undoubtedly  one  of 
the  most  efficient  now  made,  it  is  believed  that  this  estimate  will  be 
found  practically  correct.  The  experiment  on  No.  817  was  made  by 
observing  the  photometric  power  before  and  after  the  calorimeter 
experiment,  as  two  equal  lamps  could  not  be  found.  As  the  fibre  was 
round,  it  gave  a  nearly  equal  light  in  all  directions  as  was  found  by 
experiment. 


Lamps  used 
in 

Photometric  Power. 

-!•  06 
.     c 

i  on 

cS  <u 

~:i 

Con 

ST 

"3  53*0 

-  —  - 

|:||^ 

CM    I     i 

°* 

a  ® 
5« 

«  ° 

"a  °°  It? 

S  m        ®'S 

S  ^*^ 

Measured 

*$ 

~a 

P<w 

3^-*   »i-i 

3-2  oo  £-3 
2  ®  ®  o  o 

3-2-0^. 

Calori- 
meter. 

Photo- 
meter. 

perpen- 
dicular to 
paper,  L. 

Average, 

A. 

11 

03  c 

°g 

CO   £3,  " 

|® 
03 

§fl  ^S 

goo'S'S® 

gflj  5S  ®=" 

£  too  ao 

iaIS 

£  be-a  ft 

O 

P3 

3 

fl 

S 

201 

580 

580 
201 

17-5 
13-5 

13-1 
10-1 

2-57 

2.82 

l°-75 
l°-62 

3486  • 
3540- 

i    109-0 

6-8 

4-8 

580 
201 

201 
580 

38-5 
44-6 

28-9 
33-5 

2.74 
2   76 

2°  -44 
2°  -29 

5181- 

4898- 

1    204  3 

12-8 

8-9 

850 
809 

809 
850 

19-0 
12-2 

14-3 
9-2 

2.81 
2.79 

l°-54 

2483- 
3330- 

i    133-4 

8-3 

5-8 

817 

17-2 

2.73 

l°-28 

2708- 

209-6 

13-1 

9-2 

Ox  THE  EFFICIENCY  OF  EDISON'S  ELECTRIC  LIGHT  203 

The  increased  efficiency,  with  rise  of  temperature,  is  clearly  shown 
by  the  table,  and  there  is  no  reason,  provided  the  carbons  can  be  made 
to  stand,  why  the  number  of  candles  per  horse  power  might  not  be 
greatly  increased,  seeing  that  the  amount  which  can  be  obtained  from 
the  arc  is  from  1000  to  1500  candles  per  horse  power.  Provided  the 
lamp  can  be  made  either  cheap  enough  or  durable  enough,  there  is  no 
reasonable  doubt  of  the  practical  success  of  the  light,  but  this  point 
will  evidently  require  much  further  experiment  before  the  light  can  be 
pronounced  practicable. 

In  conclusion,  we  must  thank  Mr.  Edison  for  placing  his  entire 
establishment  at  our  disposal  in  order  that  we  might  form  a  just  and 
unbiased  estimate  of  the  economy  of  his  light. 


27 
ELECTEIC  ABSORPTION  OF  CRYSTALS 

BY  H.  A.  ROWLAND  AND  E.  L.  NICHOLS  ' 

[Philosophical  Magazine  [5],  XI,  414-419,  1881;  Proceedings  of  the  Physical  Society,  IV, 

215-221,  1881] 


The  theory  of  electric  absorption  does  not  seem  to  have  as  yet 
attracted  the  general  attention  which  its  importance  demands;  and 
from  the  writings  of  many  physicists  we  should  gather  the  impression 
that  the  subject  is  not  thoroughly  understood.  Nevertheless  the  sub- 
ject has  been  reduced  to  mathematics;  and  a  more  or  less  complete 
theory  of  it  has  been  in  existence  for  many  years.  Clausius  seems  to 
have  been  the  first  to  give  what  is  now  considered  the  best  theory. 
His  memoir,  '  On  the  Mechanical  Equivalent  of  an  Electric  Discharge/ 
&c.,  was  read  at  the  Berlin  Academy  in  1852.2  In  an  addition  to  this 
memoir  in  1866  he  shows  that  a  dielectric  medium  having  in.  its  mass 
particles  imperfectly  conducting  would  have  the  property  of  electric 
absorption.  Maxwell,  in  his  '  Electricity,'  art.  325,  gives  this  theory 
in  a  somewhat  different  form,  and  shows  that  a  body  composed  of  layers 
of  different  substances  would  possess  the  property  in  question.  One 
of  us,  in  a  note  in  the  '  American  Journal  of  Mathematics/  No.  1, 
1878,  put  the  matter  in  a  somewhat  different  form,  and  investigated 
the  conditions  for  there  being  no  electric  absorption. 

All  these  theories  agree  in  showing  that  there  should  be  no  electric 
absorption  in  a  perfectly  homogeneous  medium.  A  mass  of  glass  can 
hardly  be  regarded  as  homogeneous,  seeing  that  when  we  keep  it 
melted  for  a  long  time  a  portion  separates  out  in  crystals.  Glass 
can  thus  be  roughly  regarded  as  a  mass  of  crystals  with  their  axes  in 
different  directions  in  a  medium  of  a  different  nature.  It  should 
thus  have  electric  absorption.  Among  all  solid  bodies,  we  can  select 

1  Communicated  by  the  Physical  Society,  having  been  read  May  14th,  1881. 

2 1  have  obtained  my  knowledge  of  this  memoir  from  the  French  translation,  en- 
titled Tkeorie  Mecanique  de  la  Chaleur,  par  R.  Clausius,  translated  into  French  by  F. 
Folie:  Paris,  1869.  The  'Addition'  does  not  appear  in  the  memoir  published  in 
Pogg.  Ann.,  vol.  Ixxxvi,  p.  337,  but  was  added  in  1866  to  the  collection  of  memoirs. 


ELECTRIC  ABSORPTION  OF  CRYSTALS  205 

none  which  we  can  regard  as  perfectly  homogeneous  along  any  given 
line  through  them,  except  crystals.  The  theory  would  then  indicate 
that  crystals  should  have  no  electric  absorption;  and  it  is  the  object  of 
this  paper  to  test  this  point.  The  theory  of  both  Clausius  and  Max- 
well refers  only  to  the  case  of  a  condenser  made  of  two  parallel  planes. 
In  the  '  Note '  referred  to,  one  of  us  has  shown  that  in  other  forms 
of  condenser  there  can  be  electric  absorption  even  in  the  case  of  homo- 
geneous bodies.  Hence  the  problem  was  to  test  the  electric  absorp- 
tion of  a  crystal,  in  the  case  of  an  infinite  plate  of  crystal  with  parallel 
sides.  The  considerations  with  regard  to  the  infinite  plate  were 
avoided  by  using  the  guard-ring  principle  of  Thomson. 

The  crystals  which  could  be  obtained  in  large  and  perfect  plates 
were  quartz  and  calcite.  These  were  of  a  rather  irregular  form,  about 
35  millim.  across  and3  millim.  thick,  and  perfectly  ground  to  plane 
parallel  faces.  There  were  two  quartz  plates  cut  from  the  same  crystal 
perpendicular  to  the  axis,  and  two  cleavage-plates  of  Iceland  spar. 
There  were  also  several  specimens  of  glass  ground  to  the  same  thickness ; 
the  plates  were  all  perfectly  transparent,  with  polished  faces.  Exam- 
ined by  polarized  light,  the  quartz  plates  seemed  perfectly  homo- 
geneous at  all  points  except  near  the  edge  of  one  of  them.  This  one 
showed  traces  of  amethystine  structure  at  that  point;  and  a  portion 
of  one  edge  had  a  piece  of  quartz  of  opposite  rotation  set  in;  but  the 
portion  which  was  used  in  the  experiment  was  apparently  perfectly 
regular  in  structure.  The  fact  that  there  are  two  species  of  quartz, 
right-  and  left-handed,  with  only  a  slight  change  in  their  crystalline 
structure,  and  that,  as  in  amethyst,  they  often  occur  together,  makes 
it  not  improbable  that  most  pieces  of  right-handed  quartz  contain 
some  molecules  of  left-handed  quartz,  and  vice  versa.  In  this  case 
quartz  might  possess  the  property  of  electric  absorption  to  some 
degree.  But  Iceland  spar  should  evidently  more  nearly  satisfy  the 
conditions.  It  is  unfortunate  that  the  two  pieces  of  quartz  were  not 
cut  from  different  crystals. 

This  reasoning  was  confirmed  by  the  experiments,  which  showed 
that  the  quartz  had  about  one-ninth  the  absorption  of  glass;  but  that 
the  Iceland  spar  had  none  whatever,  and  is  thus  the  first  solid  so  far 
found  having  no  electric  absorption.  Some  crystals  of  mica,  &c.,  were 
tried;  but  calc  spar  is  the  only  one  which  we  can  say,  a  priori,  is  per- 

s  [There  is  a  gap  in  the  printed  article.  On  examination  of  the  various  plates  if 
the  Physical  Laboratory  of  the  Johns  Hopkins  University,  some  have  been  found  on 
about  2  mm.  thickness,  which  are  probably  those  used  in  this  research.] 


206  HENKY  A.  EOWLAND 

fectly  homogeneous.  Thus  mica  and  selenite  are  so  very  lamellar  in 
their  character,  that  few  specimens  ever  appear  in  which  the  lamina 
are  not  more  or  less  separated  from  one  another;  and  thus  they  should 
have  electric  absorption. 

II 

In  the  ordinary  method  of  experimenting  with  the  various  forms  of 
Leyden  jar,  there  are,  besides  the  residual  discharge  due  to  electric 
absorption  in  the  substance  of  the  insulator,  two  other  sources  of  a 
return  charge.  The  surface  of  the  glass  being  more  or  less  conduct- 
ing, an  electric  charge  creeps  over  the  surface  from  the  edges  of  the 
tinfoil.  In  discharging  the  jar  in  the  usual  way  by  a  connecting  wire, 
this  surface  remains  charged,  and  the  electricity  is  gradually  con- 
ducted back  to  the  coatings,  and  thus  recharges  them.  If,  further- 
more, the  coatings  be  fastened  to  the  glass  with  shellac  or  other  cement, 
the  return  charge  may  be  partly  due  to  it;  for  we  have  between  the 
coatings  not  merely  glass,  but  layers  of  glass,  cement,  &c.,  which  the 
theory  shows  to  give  a  residual  discharge.  Besides  the  coatings  are 
not  planes;  and  hence,  as  one  of  us  has  shown,  there  may  be  a  return 
charge,  even  if  the  glass  gave  none  between  infinite  planes.  If  the 
plates  were  merely  laid  on  the  glass  without  cementing,  the  same 
result  would  follow,  since  the  insulator  would  then  consist  of  air  and 
glass  in  layers. 

In  the  present  research  these  were  sources  of  error  to  be  avoided, 
since  the  residual  discharge  due  to  the  insulating  plates  themselves 
were  to  be  compared.  The  condenser-plates  were  copper  disks.  These 
were  amalgamated,  so  that  there  was  a  layer  of  mercury  between  them 
and  the  dielectric,  which  excluded  the  air  and  conducted  the  electricity 
directly  to  the  surface  of  the  dielectric :  thus  the  condition  of  a  single 
substance  between  the  plates  was  fulfilled.  The  errors  due  to  the 
creeping  of  the  charge  over  the  surface  of  the  dielectric  and  that  due 
to  the  plates  not  being  infinite  were  avoided,  the  first  entirely  and  the 
second  partially,  by  the  use  of  the  guard-ring  principle  of  Sir  Win. 
Thomson. 

Plate  IV  represents  this  apparatus.  The  plate  of  crystal,  c,  was 
placed  between  two  amalgamated  plates  of  copper,  a  and  &,  over  the 
upper  one  of  which  the  guard-ring,  d,  was  carefully  fitted;  this  ring, 
when  down,  served  to  charge  and  discharge  the  surface  around  the 
plate,  a;  and  so  the  errors  above  referred  to  from  the  creeping  of  the 
charge  along  the  plate,  and  from  the  plate  not  being  infinite,  were 
avoided. 


PLATE   IV. 


208  HENEY  A.  KOWLAND 

The  charging  battery  consisted  of  six  large  Leyden  jars  of  nearly  a 
square  foot  of  coated  surface  each,  charged  to  a  small  potential. 
Although  accurate  instruments  were  at  hand  for  measuring  the  poten- 
tial in  absolute  measure,  it  was  considered  sufficient  to  use  a  Harris 
unit-jar  for  giving  a  definite  charge;  for  very  accurate  measurements 
were  not  desired,  and  the  Harris  unit-jar  was  entirely  sufficient  for  the 
purpose.  The  return  charge  was  measured  by  a  Thomson  quadrant- 
electrometer  of  the  original  well-known  form. 

The  apparatus  shown  in  Plate  IV  performs  all  the  necessary  opera- 
tions by  a  half  turn  of  the  handle  e.  By  two  half  turns  of  the  handle, 
one  forward  and  the  other  back,  the  crystal  condenser  could  be  succes- 
sively charged  from  the  Leyden  battery,  discharged,  the  guard-ring 
raised,  the  upper  plate,  a,  again  insulated,  and  the  connection  made 
with  the  quadrant-electrometer. 

The  copper  ring,  d,  was  suspended  by  three  silk  threads  from  the 
brass  disk,  /,  which  in  turn  could  be  raised  and  lowered  by  the  crank,  g. 
A  small  wire  connected  the  ring  with  the  rod  on  which  was  the  ball,  h. 
This  rod  was  insulated  by  the  glass  tube  i,  and  could  revolve  about  an 
axis  at  fc.  By  the  up-and-down  motion  of  the  rod  the  ball  came  into 
contact  with  the  ball  (Z)  connected  with  the  earth,  or  the  ball  (ra)  con- 
nected with  the  battery.  When  the  cranks  were  in  the  position  shown 
in  the  figure,  the  heavy  ball  n  caused  the  ball  h  to  rise  and  press 
against  I;  but  when  /  descended,  the  piece  o  pressed  on  the  rod  and 
caused  h  to  fall  on  m. 

Another  rod,  q,  also  more  than  balanced  by  a  ball,  r,  was  insulated  by 
a  glass  tube,  s,  and  connected  with  the  quadrant-electrometer  by  a 
very  fine  wire.  It  could  also  turn  around  a  pivot  at  t;  so  that  when 
the  ring  u  rested  upon  it,  it  fell  on  the  upper  condenser-plate  a,  and 
connected  with  the  electrometer;  when  the  weight  u  was  raised  by  the 
crank  v,  the  rod  rested  against  f,  and  so  connected  the  electrometer  to 
the  earth,  to  which  the  other  quadrants  were  already  connected. 

At  the  beginning  of  an  experiment,  the  insulating  plate  to  be  tested 
having  been  placed  between  the  condenser-plates  a  and  &,  the  handle 
was  brought  into  such  a  position  that  the  ring,  d,  rested  on  the  plate 
around  a.  The  lengths  of  the  threads  between  d  and  f  were  such  that  o 
for  this  position  of  the  handle  did  not  touch  w,  and  so  li  remained  in 
connection  with  the  earth;  and  so  d  was  also  connected  with  the  earth, 
and  thus  also  with  &.  On  now  turning  the  handle  further,  the  ball  li 
descended  to  the  ball  m,  and  thus  charged  the  condenser  for  any  time 
desired.  On  now  reversing  the  motion,  the  following  operations  took 
place : 


ELECTRIC  ABSORPTION  OF  CRYSTALS 


209 


First,  the  ball  h  rose  and  discharged  the  condenser. 

Second,  the  guard-ring  d  ascended. 

Third,  the  rod  q,  which  had  been  previously  in  contact  with  p,  thus 
bringing  the  quadrant-electrometer  to  zero,  now  moved  down  and  rested 
on  the  upper  condenser-plate  a.  Thus  any  return  charge  quickly  showed 
itself  on  the  electrometer.  The  amount  of  deflection  of  the  instru- 
ment depends  upon  the  character  of  the  dielectric,  its  thickness,  the 
charge  of  the  battery,  the  time  of  contact  with  the  battery,  and  upon 
the  length  of  time  of  discharging. 

Ill 

In  comparing  the  glass  with  the  crystal  plates,  the  electrometer  was 
rendered  as  little  sensitive  as  the  ordinary  arrangement  of  the  instru- 
ment without  the  inductor-plate  would  allow.  The  electric  absorption 
of  the  glass  plates  for  a  charge  in  the  battery  of  two  or  three  sparks 
from  the  Harris  unit-jar  then  sufficed,  after  20  or  30  seconds  contact 
with  the  battery  and  5  seconds  discharging  time,  to  give  a  deflection  of 
about  200  scale-divisions,  which  were  millimetres.  The  quartz  and 
calcite  plates  were  then  alternately  substituted  for  the  glass,  the  same 
charge  and  the  same  intervals  of  contact  being  used,  and  the  resulting 
deflections  noted — two  plates  of  each  substance  of  the  same  thickness 
being  used. 

The  results  of  the  measurements  are  given  in  the  following  Tables, 
the  effect  of  the  glass  being  called  100. 


TABLE  I. 


April  12,  1880. 

Charge  of  battery,  2  sparks. 

Contact,  30  seconds. 

Glass  (1st  plate) 100-0 

Quartz  (1st  plate) 17-1 

"       (2nd  plate). 20-0 

Calcite  (1st  plate) 0.0 

"       (2nd  plate) 0-0 

(b) 

April  13,  1880. 

Charge  of  battery,  3  sparks. 

Contact,  20  seconds. 

Glass  (1st  plate) 100-0 

Quartz  (1st  plate) 19-3 

Calcite  (1st  plate) 0-0 


14 


April  14,  1880. 
Charge,  3  sparks. 
Contact,  10  seconds. 
Plates  carefully  dried  by  being  in  desic- 
cator over  night. 

Glass  (1st  plate) 100-0 

Quartz  (1st  plate) 10-7 

Calcite  (1st  plate) 0-0 

(d) 

April  22,  1880. 

Charge,  2  sparks. 

Contact,  30  seconds. 

Plate  in  desiccator  since  April  14. 

Glass  (2nd  plate) 100-0 

"      (1st  plate) 96-3 

Quartz  (1st  plate) 13-4 

"       (2nd  plate) 12-1 

Calcite  (1st  plate) 0-0 

"       (2nd  plate) 0-0 


210 


HENKY  A.  ROWLAND 


TABLE  II. 

MAT  1. — RELATIVE  EFFECTS  FOR  DIFFERENT  INTENSITIES  OF  CHARGE  AND 
TIME  OF  CONTACT 


Charge  of 
Battery. 

Material. 

Deflections,  in  millimetres. 

Contact, 
5  seconds. 

Contact, 
10  seconds. 

Contact, 
30  seconds. 

One  spark.  .  .  J 

Glass  (1st)  
Quartz  (1st)... 
Calcite  (1st)... 

133-0 
13-0 
0-0 

189-3 
22-7 
0-0 

225-0 
34-3 
0-0 

Two  sparks.  .  J 

Glass  (1st)  
Quartz  (1st)... 
Calcite  (1st).  .  . 

Off  the  scale 
24-0 
0-0 

Off  the  scale 
35-0 
0-0 

Off  the  scale 
50-0 
0-0 

These  Tables  seem  to  prove  beyond  question  that  calcite  in  clear 
crystal  has  no  electric  absorption.  Quartz  seems  to  have  about  ^  that  of 
glass;  but  we  have  remarked  that  quartz  is  not  a  good  substance  to  test 
the  theory  upon. 

Some  experiments  were  made  with  cleavage-plates  of  selenite,  which 
are  always  more  or  less  imperfect,  as  the  laminae  are  very  apt  to  sepa- 
rate. These  gave,  however,  effects  about  -J  or  ^  those  of  glass. 

In  order  to  test  still  further  the  absence  of  electric  absorption  in 
calcite,  the  electrometer  was  rendered  very  sensitive,  and  the  calcite 
plates  were  tested  with  gradually  increasing  charges,  from  that  which 
in  glass  gave  200  millim.  after  1  second  contact,  up  to  the  maximum 
charge  (ten  sparks  of  the  unit-jar)  which  the  condensers  were  capable 
of  carrying.  In  these  trials,  the  calcite  still  showed  no  effect,  even 
with  30  seconds  contact.  During  these  experiments  glass  was  fre- 
quently substituted  for  the  calcite,  to  leave  no  question  but  that  the 
apparatus  was  in  working  order. 

It  is  to  be  noted  that  the  relative  effects  of  the  quartz  and  the  glass 
were  different  for  dried  plates  and  plates  exposed  to  the  atmosphere. 
This  was  possibly  due  to  the  glass  being  a  better  insulator,  and  thus 
retaining  its  charge  better  when  dry  than  in  its  ordinary  condition. 

IV 

Thus  we  have  found,  for  the  first  time,  a  solid  which  has  no  electric 
absorption;  and  it  is  a  body  which,  above  all  others,  the  theory  of 
Clausius  and  Maxwell  would  indicate.  The  small  amount  of  the  effect 


ELECTRIC  ABSORPTION  OF  CRYSTALS  211 

in  quartz  and  selenite  also  confirms  the  theory,  provided  that  we  can 
show  that  in  the  given  piece  of  quartz  some  molecules  of  right-handed 
quartz  were  mixed  with  the  left;  for  we  know  that  the  theoretical  con- 
ditions for  the  absence  of  electric  absorption  are  rarely  satisfied  by 
laminated  substances  like  selenite  or  mica.  If  the  theory  is  con- 
firmed, the  apparatus  here  described  should  give  the  only  test  we  yet 
have  of  the  perfect  homogeneity  of  insulating  bodies;  for  any  optical 
test  cannot  penetrate,  as  this  does,  to  the  very  structure  of  the 
molecule. 


28 


[Presented  to  the  Congress  of    Electricians,   Paris,   September  17,  1881,  and   here 
translated  from  their  Proceedings] 

[Johns  Hopkins  University  Circulars,  No.  19,  pp.  4,  5,  1882] 

Among  the  subjects  to  be  discussed  by  this  Congress  is  that  of  atmos- 
pheric electricity,  and  I  should  like,  at  this  point,  to  urge  the  import- 
ance of  a  series  of  general  and  accurate  experiments  performed  simul- 
taneously on  a  portion  of  the  earth's  surface  as  extended  as  possible. 
Here  and  there  on  the  globe,  it  is  true,  an  observer  has  occasionally 
performed  a  series  of  experiments,  extending  even  over  several  years: 
but  the  different  observers  have  not  worked  in  accordance  with  any  pre- 
concerted plan,  it  has  not  been  possible  to  compare  their  instruments, 
and  even  where  absolute  measurements  have  been  obtained,  the  exact 
meaning  of  the  quantity  measured  has  not  been  perceived.  Let  us 
take,  for  instance,  Sir  William  Thomson's  water  dropping  apparatus, 
which  is  used  at  the  Kew  Observatory.  This  apparatus  is  composed 
of  one  tube  rising  a  few  feet  above  the  building  and  of  another  tube 
near  the  ground,  so  that  it  is  in  the  angle  made  by  the  house  and  the 
ground.  This  apparatus  indicates  a  daily  variation  in  the  electricity 
of  the  atmosphere,  but  the  result  is  evidently  influenced  by  the  condi- 
tions of  the  experiment.  Another  observer  who  should  fit  up  an  appar- 
atus in  another  country  might  obtain  entirely  different  conditions,  so 
that  it  would  be  impossible  to  compare  the  results.  Hence  the  neces- 
sity of  having  a  system. 

The  principal  aim  of  scientific  investigation  is  to  be  able  to  under- 
stand more  completely  the  laws  of  nature,  and  we  generally  succeed  in 
doing  this  by  bringing  together  observation  and  theory.  In  science 
proper,  observations  and  experiments  are  valuable  only  in  so  far  as  they 
rest  on  a  theory  either  in  the  present  or  in  the  'future.  We  can  as  yet 
present  only  a  plausible  theory  of  atmospheric  electricity,  but  the  real 
way  of  arriving  at  the  truth  in  this  case  is  to  let  ourselves  be  guided  in 
our  future  experiments  by  those  which  have  hitherto  been  made  on 
this  subject. 


ON  ATMOSPHERIC  ELECTEICITY  213 

The  principal  facts  which  have  been  discovered  can  be  stated  in  a  few 
words.  In  clear  weather,  the  potential  increases  as  we  go  higher,  at 
least  for  certain  parts  of  Europe,  and  there  is  a  diurnal  and  annual 
variation  of  this  quantity  which  the  presence  of  fogs  causes  also  to  vary. 
The  first  observers  were  inclined  to  attribute  the  electricity  of  the 
atmosphere  to  the  evaporation  of  water,  and  an  old  experiment  which 
consisted  in  dropping  a  ball  of  red-hot  platinum  into  water  placed  on  a 
gold  leaf  electrometer,  was  supposed  to  confirm  this  view.  Even  re- 
cently a  distinguished  physicist  held  this  opinion  in  the  case  of  electric 
storms.  Now  when  a  ball  of  platinum  is  thus  dropped  into  water,  the 
excessive  commotion  thus  produced  will  certainly  give  rise  to  electricity; 
but  to  assert  that  this  electricity  is  due  to  evaporation  may  very  well 
be  an  error.  It  is  true  that  occasionally  a  red-hot  meteorite  may  fall 
into  the  sea,  reproducing  thus  the  laboratory  experiment;  but  most  of 
the  water  is  evaporated  quietly.  Eecently  one  of  my  students  used 
under  my  direction  a  Thomson  quadrant  electrometer  in  order  to  inves- 
tigate this  question,  and  although  he  evaporated  large  quantities  of 
different  liquids,  he  did  not  find  any  trace  of  electrization.  I  hope  to 
prove  thus  conclusively  that  the  electricity  of  the  atmosphere  cannot 
be  the  result  of  evaporation. 

Sir  William  Thomson  thinks  that  the  experiments  which  have  been 
made  hitherto  indicate  that  the  earth  is  charged  negatively.  This  con- 
clusion would  certainly  explain  all  the  experiments  hitherto  performed 
in  Europe ;  but  the  only  method  of  reaching  certainty  on  this  point  is  to 
execute  a  series  of  experiments  on  the  whole  surface  of  the  globe,  and 
it  is  this  method  that  I  propose  to-day.  This  series  of  experiments 
would  furnish  data  for  determining  not  only  the  fact  of  terrestrial 
magnetism,  but  also  by  the  aid  of  Gauss's  theorem  the  amount  of  the 
charge  on  the  solid  portion  of  the  earth;  however,  this  amount  cannot 
be  determined  for  the  upper  atmosphere.  What  we  want  to  know  is 
the  law  according  to  which  the  electric  potential  varies  as  we  ascend 
on  the  whole  surface  of  the  globe  and  at  the  same  instant  of  time,  so 
that  it  may  be  possible  to  obtain  the  surface  integral  of  the  rate  of 
variation  of  the  potential  over  the  whole  globe.  If  the  earth  were  ever 
to  receive  an  increase  of  charge  coming  either  from  the  exterior  or  from 
the  upper  atmosphere,  this  increase  would  be  known.  When,  in  the 
London  Physical  Society,  I  criticized  the  theory  of  Profs.  Ayrton  and 
Perry  on  terrestrial  magnetism,  I  gave  at  the  end  of  my  paper  a  brief 
outline  of  a  recent  theory  on  auroras  and  storms,  which  was  built  on 
the  hypothesis  of  the  electrization  of  the  earth.  After  mature  reflec- 


214  HENKY  A.  ROWLAND 

tion  I  still  wish  to  present  to  you  this  theory,  which  deserves  to  be 
thought  of  in  mapping  out  a  system  of  international  experiments  on 
atmospheric  electricity. 

Suppose  Sir  William  Thomson's  explanation  is  correct  and  that  the 
earth  is  charged  with  electricity,  let  us  examine  what  would  then 
happen.  If  the  earth  were  not  exposed  to  disturbing  causes,  a  portion 
of  the  electricity  of  the  globe  would  discharge  itself  into  the  atmosphere 
and  would  distribute  itself  nearly  as  uniformly  as  the  resistance  of  the 
air  would  allow.  The  exterior  atmosphere  thus  charged  would  set  itself 
in  motion,  and  we  should  have  winds  produced  by  the  electric  repul- 
sions, and  this  would  last  until  the  electricity  had  been  distributed  in  a 
uniform  manner  on  the  earth  and  in  the  exterior  strata  of  the  atmos- 
phere ;  when  all  would  be  still  once  more.  An  observer  stationed  on  the 
earth  would  have  no  idea  of  the  charge  of  the  exterior  atmosphere;  but 
he  would  discover  the  charge  of  the  earth  by  means  of  the  ordinary 
instruments  used  in  experiments  on  the  electricity  of  the  atmosphere, 
such  as  Becquerel's  arrows  and  Thomson's  water  dropping  apparatus. 
There  would  be  another  result  which  however  could  not  be  measured  by 
observers  situated  on  the  earth,  namely,  the  extension  of  the  atmos- 
phere beyond  the  limits  determined  by  calculation.  The  rarefied  air 
being  electrified  would  repel  itself,  and  possibly  there  would  be  then  in 
the  exterior  atmosphere  a  region  in  which  the  pressure  would  vary  sTery 
slightly  for  a  great  difference  of  elevation.  We  have  learned  from 
auroras  and  meteors  that  the  atmosphere  extends  to  a  much  greater 
distance  than  that  indicated  by  Newton's  logarithmic  formula,  but  I 
think  that  what  I  have  said  is  the  first  rational  explanation  of  this  fact. 

Observe  now  what  would  happen  if  the  earth  of  which  we  speak  were 
subject  to  the  disturbing  causes  which  exist  on  our  globe;  the  most 
important  of  these  disturbing  factors  are  the  winds  and  the  general 
atmospheric  circulation.  This  circulation  constantly  carries  the  atmo- 
sphere from  the  equator  to  the  two  poles,  but  with  very  little  uni- 
formity. However,  near  the  poles  there  must  be  many  points  at  which 
the  air  comes  down  towards  the  earth  and  thus  shapes  its  course  towards 
the  equator.  Now  a  body  which  is  a  bad  conductor,  like  air,  when  it  is 
charged  tends  to  carry  its  charge  along  with  it  wherever  it  goes,  and 
thus  the  air  carries  its  charge  until  the  moment  when  it  descends 
towards  the  earth;  then  it  will  leave  it  behind  in  the  exterior  atmo- 
sphere, in  accordance  with  the  tendency  of  electricity  to  remain  at  the 
surface  of  charged  bodies.  The  charge  will  therefore  accumulate  in  the 
exterior  atmosphere,  until  there  is  a  great  tension;  the  atmosphere 


ON  ATMOSPHERIC  ELECTRICITY  215 

will  then  discharge  itself  either  towards  the  earth  or  through  the  rare- 
fied air  in  the  shape  of  an  aurora.  At  these  points  the  rarefied  air 
probably  heaps  itself  up  to  a  greater  height  than  elsewhere,  which 
would  explain  the  great  height  at  which  auroras  are  sometimes  observed. 

The  equilibrium  which  existed  previously  at  the  equator  would  also 
be  destroyed  by  the  absence,  at  this  point,  of  the  primitive  charge  in 
the  exterior  atmosphere,  and  the  earth  would  have  a  tendency  to  dis- 
charge itself  towards  the  exterior  atmosphere.  Owing  to  the  difference 
in  the  conditions  at  this  point,  this  tendency  will  be  apt  to  show  itself 
by  the  storms  which  arise  oftenest  in  the  equatorial  region.  Thus  the 
electricity  of  the  earth  would  tend  to  circulate  in  the  same  way  as  the 
air  from  the  equator  to  the  poles  and  conversely. 

But  I  do  not  intend  to  insist  upon  this  theory  here;  I  wish  simply 
through  it  to  bring  out  the  importance  of  establishing  on  the  whole 
surface  of  the  globe  a  system  of  general  observations  on  atmospheric 
electricity.  Even  if  the  theory  is  false,  it  is  only  by  observation  that 
the  truth  can  be  attained.  In  my  opinion,  it  is  almost  unworthy  of  the 
advanced  state  of  our  sciences  to-day,  that  it  should  be  at  present  impos- 
sible for  us  to  indicate  accurately  the  origin  of  the  energy  which  mani- 
fests itself  in  auroras  and  storms.  For  I  have  pointed  out  above  that 
it  is  necessary  to  give  up  explaining  these  phenomena  by  the  hypothesis 
of  the  production  of  electricity  by  evaporation. 

I  propose  therefore  that  from  this  section  of  the  Congress  a  com- 
mittee be  formed  to  examine  what  is  to  be  done  in  order  to  establish 
on  the  whole  earth,  and  especially  in  the  polar  regions,  a  systematic 
series  of  observations  on  atmospheric  electricity. 

EDITORIAL  NOTE. — International  Commission  of  Electricians 

[Professor  Rowland  sailed  from  New  York,  October  14,  to  attend  an 
international  commission  of  electricians,  then  about  to  assemble  in 
Paris.  Professor  John  Trowbridge  of  Cambridge  sailed  about  the  same 
date.  These  two  gentlemen  were  selected  to  represent  the  United 
States  government  by  the  Department  of  State — Congress  having  made 
provision  for  the  appointment  of  two  civilian  commissioners. 

This  official  commission  is  the  outgrowth  of  the  congress  of  electri- 
cians which  was  held  a  year  ago  in  Paris.  That  body  requested  the 
French  government  to  invite  other  nations  to  unite  in  constituting 
three  international  commissions  for  the  study  of  certain  specified 
problems,  namely: 

I.  A  re-determination  of  the  value  of  the  ohm. 


216  HENRY  A.  ROWLAND 

II.  (a)  atmospheric  electricity. 

(&)  protection  against  damage  from  telegraphic  and  telephonic 
wires — (pa  ratonn  erres) . 

(c)  terrestrial  currents  on  telegraphic  lines. 

(d)  the   establishment   of   an  international   telemeteorographic 

line. 

III.  Determination  of  a  standard  of  light. 

The  study  of  atmospheric  electricity  was  proposed  to  the  congress  by 
Mr.  Rowland.  After  hearing  his  paper  on  this  subject,  the  section  to 
which  he  belonged  adopted  on  his  motion  the  following  resolution  which 
was  subsequently  approved  by  the  entire  congress. 

Resolved  that  an  international  commission  be  charged  with  determin- 
ing the  precise  methods  of  observation  for  atmospheric  electricity,  in 
order  to  generalize  this  study  on  the  surface  of  the  globe. 

As  Mr.  Eowland  did  not  retain  his  manuscript,  the  foregoing  trans- 
lation of  the  paper  as  it  is  printed  in  the  Comptes  Rendus  of  the  con- 
gress has  been  made  b}r  Mr.  P.  B.  Marcou  and  is  printed  here  with  the 
author's  consent.] 


34 
THE  DETEEMINATION  OF  THE  OHM 

EXTKAIT    P'UNE    LETTKE    DE    M.    HENKY  A.   ROWLAND 

[Conference  Internationale  pour  la  Determination   des   Unites  Electriques.     Proces-Ver- 
baux,  Deuxieme  Session,  p.  37,  Paris,  1884] 

Les  experiences  relatives  a  la  determination  de  1'ohm  ont  ete  pre- 
parees  a  Baltimore  au  moyen  d'une  partie  du  credit  de  12,500  dollars 
alloue  dans  ce  but,  1'annee  derniere,  par  le  Congres  des  Etats-Unis. 

Apres  une  etude  preliminaire,  les  appareils  destines  a  ces  exper- 
iences ont  ete  mis  en  construction  en  juin  1883.  Les  autorites  de 
1'Universite  Johns  Hopkins  ont  bien  voulu  mettre  a  ma  disposition 
une  construction  qui  est  situee  en  dehors  de  la  ville,  a  1'endroit  appele 
Clifton,  et  qui  a  ete  transformed  en  laboratoire. 

La  source  d'electricite  qui  servira  aux  experiences  est  une  pile 
secondaire  du  systeme  Plante,  chargee  par  une  machine  dynamo-elec- 
trique  actionnee  par  une  machine  a  vapeur  d'environ  5  chevaux  de  force. 

Trois  methodes  au  moins  seront  employees  pour  la  determination 
de  1'ohm.  La  premiere  repose  sur  1'induction  mutuelle  de  deux  circuits ; 
j'ai  deja  fait  usage  de  cette  methode  en  1878,  mais  dans  les  nouvelles 
experiences  les  dimensions  des  appareils  seront  considerablement  aug- 
mentees;  les  bobines  auront  un  metre  de  diametre. 

La  deuxieme  methode  est  basee  sur  1'echauffement  d'un  conducteur 
par  le  courant  electrique,  le  meme  fil  etant  echauffe  successivement  par 
le  courant  et  par  des  moyens  mecaniques.  Les  appareils  employes 
seront  ceux  qui  m'ont  servi,  en  1879,  pour  determiner  1'equivalent 
mecanique  de  la  chaleur.  Afin  d'eviter  les  pertes,  le  calorimetre  sera 
rempli  d'un  liquide  non  conducteur  au  lieu  d'eau.  Pour  mesurer 
1'energie  electrique,  on  a  construit  un  electrodynamometre  ayant  des 
bobines  d'un  metre  de  diametre. 

La  troisieme  methode  est  celle  de  Lorenz.  Pour  determiner  la 
vitesse  du  disque,  il  sera  f-ait  usage  d'un  diapason  mu  par  un  mecanisme 
d'horlogerie,  construit  par  Kb'nig,  de  Paris. 

La  comparison  de  1'unite  de  FAssociation  Britannique  avec  1'unite 
mercurielle  est  pies  d'etre  terminee;  en  dehors  de  cela,  aucun  resultat 


218  HENRY  A.  EOWLAND 

n'a  ete  obtenu  jusqu'a  present,  mais  je  crois  pourvoir  donner  mes  re- 
sultats  definitifs  en  novembre. 

Comme  ces  experiences  seront  faites  avec  les  precautions  les  plus 
grandes  et  dans  des  conditions  tres  favorables,  grace  a  la  generosite  du 
Congres,  il  est  a  esperer  qu'aucune  decision  concernant  la  valeur  defi- 
nitive de  1'ohm  ne  sera  prise  avant  cette  epoque;  de  cette  maniere,  les 
Etats-Unis  et  d'autres  pays  pourront  accepter  1'etalon  arrete. 

HENEY  A.  KOWLAND. 


35 

THE  THEOKY  OF  THE  DYNAMO 

[Report  of  the  Electrical  Conference  at  Philadelphia  in  November,  1884,  pp.  72-83,  90,  91, 
104-107,  Washington,  18S6  ;  Electrical  Review  (N.  Y.),  November  1,  8,  15,  22, 1884] 

I  will  now  proceed  with  the  discussion  of  '  The  Theory  of  the 
Dynamo-Electric  Machine.'  I  only  claim  in  the  skeleton  of  the  theory 
which  I  have  here  prepared  to  give  a  few  points  which  may  be  of  inter- 
est and  possibly  of  value  to  those  who  are  constructing  these  machines. 

The  principal  losses  of  the  machine  I  put  down  under  the  following 
heads:  (1)  Mechanical  friction;  (2)  Foucault  currents  in  the  armature; 
(3)  energy  of  the  current  used  in  sustaining  the  magnet;  (4)  self-induc- 
tion of  the  coils;  (o)  heating  of  the  armature. 

Of  course  the  efficiency  of  the  machine  would  be  equal  to  the  whole 
work  of  the  machine  minus  the  different  losses  divided  by  the  work, 
namely :  , 

JJT      w  —  L—L  —  efc. 

£/  —  — 

w 

Thus,  when  the  losses  are  known,  the  efficiency  of  the  machine  is 
known. 

The  mechanical  friction  I  shall  not  discuss. 

With  respect  to  Foucault  currents  in  the  armature,  by  dividing  up 
the  armature  in  the  proper  way,  we  can  get  rid  of  most  of  these.  It  is 
very  often  effected  in  the  Siemens  armature  by  dividing  up  the  arma- 
ture into  discs. 

I  have  purposely  omitted  the  loss  due  to  change  of  magnetism  in  the 
armature  as  the  armature  revolves.  1  drew  attention  to  this  fact  sev- 
eral years  ago.  It  has  been  recently  experimented  upon  and  found 
that,  although  there  is  some  heating  effect,  it  is  very  small  indeed. 

With  respect  to  the  energy  used  in  sustaining  the  magnet,  if  the 
magnet  were  of  steel  there  would,  of  course,  be  no  loss.  The  only 
reason  for  not  using  a  steel  magnet  is  that  the  field  is  comparatively 
weak.  The  field  of  a  steel  magnet  is,  I  suppose,  less  than  one-third  of 
the  field  due  to  a  good  electro-magnet;  the  two  could  not  be  made 
equal  by  any  possible  means.  Therefore,  in  most  dynamo  machines, 
the  magnet  is  produced  by  the  current. 


220  HENRY  A.  KOWLAKD 

It  is  a  question  what  the  form  of  the  magnet  and  the  position  of 
these  coils  should  be  in  order  to  get  the  greatest  field  with  the  least 
•xpenditure  of  energy.  I  have  one  or  two  propositions  to  make  on  this 
subject  which  I  think  are  of  some  interest. 

The  first  proposition  I  have  to  make  is  that  a  round  magnet  is  better 
than  one  of  elongated  cross-section.  If  the  coils  are  long,  and  they 
are  usually  long  enough  for  the  purpose,  although  the  theory  assumes 
an  infinite  length,  the  magnetic  force  at  any  time  acting  on  a  round 
iron  core  is  exactly  the  same  as  on  an  elongated  core.  But  the  area 
of  a  circular  section  is  much  greater  than  that  of  an  elongated  section 
of  the  same  circumference,  and  therefore  the  same  amount  of  wire 
which  would  be  used  to  go  around  the  elongated  magnet,  would,  if 
extended  on  a  circular  section  of  the  same  circumference,  surround 
much  more  iron. 

The  principal  object  of  making  an  elongated  magnet  is  that  it  may 
include  the  whole  length  of  the  armature.  Most  makers  who  adopt 
this  form  think  it  better  to  elongate  the  cross-section  than  to  have  a 
long  pole  piece.  But  we  have  seen  that  the  round  form  is  more  efficient 
in  general  than  the  elongated  form,  and  the  only  question  is  whether  it 
will  be  more  efficient  in  this  particular  case.  I  shall  proceed  in  this 
theory  upon  the  known  fact  that  we  can  consider  lines  of  force  as  if 
they  were  conducted  by  the  iron  and  the  air  outside.  The  conductivity 
of  the  iron  for  the  lines  of  force  is  very  great,  much  greater  than  that 
of  air.  I  experimented  on  it  many  years  ago,  and  my  idea  is  that  it 
Varies  (according  to  the  degree  of  magnetization)  from  several  hundred 
up  to  5,000  times  that  of  air.  The  conductivity  for  iron  is  very  great, 
especially  for  wrought  iron;  for  cast  iron  it  is  probably  less.  Therefore 
the  lines  of  force  will  be  conducted  down  through  the  iron  from  any 
point  over  a  circular  cross-section  very  nearly  as  easily  as  they  are  from 
an  elongated  cross-section,  and  the  saving  in  the  wire  will  be  con- 
siderable. 

I  have  another  proposition  to  make  with  respect  to  the  magnet,  and 
that  is  that  one  circuit  of  the  lines  of  force  is  better  than  a  number. 
There  is  a  loss  from  having  a  number  of  electro-magnets,  even  if  they 
are  round.  For  this  reason,  that  the  same  magnetic  force  is  acting  in 
each  of  these  coils  provided  there  is  the  same  number  of  wires  per  unit 
of  length;  and  the  same  wire  will  go  more  times  around  the  same  iron 
concentrated  in  one  magnet  than  when  subdivided  into  several,  and 
will,  therefore,  act  upon  it  with  more  magnetizing  force. 

That  proposition  not  only  applies  to  this  form  of  magnet  (Fig.  1), 


THE  THEORY  OF  THE  DYNAMO 


but  it  also  applies  to  the  form  where  we  have  the  armature  revolving 
between  two  magnets  like  this  (Fig.  2),  because  we  can  turn  this  lower 
magnet  over  and  bring  the  two  together.  The  circuits  of  the  lines  of 
force  are  around  in  this  direction  and  in  this  (arrows,  Fig.  2).  So  that 
there  are  two  circuits  of  the  lines  of  force  instead  of  one.  The  energy 
expended  for  a  given  amount  of  work  will  be  less  with  this  form  (Fig.  1) 
than  with  this  (Fig.  2).  That  is  of  very  great  value  to  makers  of 
machines. 

The  theorem  applies  to  a  number  of  those  old  machines  where  there 


FIG.  i. 


Fio.  2. 


was  a  very  large  number  of  little  magnets  revolving  around  other  little 
magnets.  More  work  is  used  in  sustaining  the  magnets  in  that  form 
of  machine  than  in  the  more  modern  form  where  we  have  only  a  few 
circuits. 

I  had  a  number  of  drawings  made  of  magnets  in  the  Electrical  Exhi- 
bition, and  I  find  very  great  difference  in  this  respect;  more  difference 
where  Siemens  armatures  are  used  than  in  any  other  kind.  In  dis- 
cussing these  drawings  I  do  not  give  any  names,  nor  say  whether  one 
machine  as  a  whole  is  better  or  worse  than  another. 

First,  I  will  discuss  the  general  forms  of  the  magnet,  and  then  I  wish 
to  say  something  in  respect  to  the  form  of  the  pole  pieces  that  inclose 


222 


HENRY  A.  KOWLAND 


the  armature.  Of  course  this  form  belongs  both  to  the  Gramme  ring 
and  the  Siemens  armature.  Most  modern  machines  are  of  this  nature, 
either  Gramme  or  Siemens,  and  we  may  consider  them  both  one  if 
we  wish. 

We  will  now  proceed  with  respect  to  the  field  in  this  form  of  magnet 
(Fig.  3).  The  lines  of  force  proceed  down  the  magnet,  and  are  sup- 
posed to  go  across  here  (a  &),  where  wires  wound  around  the  revolving 
armature  cut  them,  and  so  produce  a  current.  It  is  evident  that  any 
lines  which  escape  across  this  open  space  (arrows)  are  lost.  If  there 


FIG.  a. 


FIG.  4. 


was  any  leakage  of  the  wire  around  the  magnet,  the  current,  instead  of 
going  around  the  magnet,  would  go  off  somewhere  else,  and  we  should 
consider  the  machine  defective  because  there  was  a  loss  of  the  current. 
Sq  if  any  of  these  lines  of  force,  instead  of  going  directly  across  there 
(a  &),  go  across  the  open  space  (arrows),  as  they  naturally  would  do,  all 
those  lines  of  force  are  lost,  and  we  would  have  to  add  so  much  more 
current  in  order  to  make  up  for  this  outside  loss.  I  have  an  illustra- 
tion of  such  losses  of  lines  of  force  from  a  drawing,  which  I  will  give 
you  (Fig.  4). 

This  machine  has  two  magnets — one  above  and  one  below.     The  lines 


THE  THEORY  OF  THE  DYNAMO 


223 


of  force  pass  up  through  here  (abed)  and  then  out  and  around  through 
here  (e  e),  &c.,  to  complete  the  circuit.  As  I  saw  the  machine  in  the 
exhibition  these  outside  pieces  (ee)  were  closer  to  the  poles  of  the 
magnets  than  I  have  drawn  them.  If  they  are  put  too  near,  some  lines 
of  force,  instead  of  passing  across  the  field  of  force,  where  the  wires 
revolve,  as  they  ought  to  do,  pass  off  at  these  openings,  the  circuits 
going  around  in  this  way  (arrows  f  f).  In  this  case  there  is  a  loss  due 
to  leakage  of  the  lines  of  force,  and  we  shall  therefore  have  to  expend 


FIG.  5. 


FIG.  6. 


more  energy  in  keeping  up  the  magnet.  There  is  energy  expended  in 
keeping  up  the  field  outside  as  well  as  in  keeping  up  the  field  through 
the  armature.  It  is  important  that  this  point  should  be  considered. 
These  questions,  '  How  many  lines  of  force  go  across  this  opening  and 
are  effective  in  producing  the  current,  and  how  many  escape  off  without 
passing  through  the  opening  and  are  lost?'  are  just  as  important  as 
the  question  of  the  leakage  of  the  current  in  the  wire.  There  are 
defects  in  many  of  these  machines  in  that  respect.  In  this  form  of 
machine  (Fig.  1),  where  there  is  a  simple  circuit,  this  magnet  has  to  be 


224:  HENKY  A.  KOWLAND 

attached  somewhere.  Very  often  the  magnet  is  turned  vertically,  poles 
downward,  and  attached  to  a  cast-iron  bench.  I  have  no  doubt  that 
some  lines  of  force  are  lost  (not  much  perhaps)  in  passing  across  from 
the  magnet  to  this  iron  bench.  The  makers  of  the  machine,  I  suppose, 
considered  this  to  some  extent,  but  what  is  needed  is  measurement  on 
that  point. 

Here  is  another  form  of  magnet  (Fig.  5).  That  machine  would  be 
defective.  It  has  two  magnets  and  two  magnetic  circuits  in  the  place 
of  one,  and  many  of  the  lines  of  force  probably  make  little  private  cir- 
cuits of  their  own  around  in  that  way  (arrows).  Those  lines  of  force 
are  of  course  lost,  and  it  is  more  or  less  defective  in  that  respect.  It 
would  be  better  to  diminish  the  number  of  magnetic  circuits  to  one. 

(I  am  only  giving  a  general  idea  of  the  principle  of  these  machines, 
and  I  do  not  refer  to  any  in  particular.) 

It  is  also  important  that  these  lines  of  magnetic  induction  shall  find 
easy  passage  around  in  order  to  produce  the  most  intense  field.  Thus 
the  opening  between  the  armature  and  pole  pieces  must  be  made  as 
small  as  possible,  in  order  that  the  lines  of  force  may  find  easy  passage 
across  it.  Everybody  recognizes  that.  Suppose  we  had  a  machine  made 
in  the  following  manner  (Fig.  6),  in  which  there  is  a  magnet  with 
a  Gramme  ring  here  (a),  and  pole  piece  here  (&),  a  ring  here  (c),  and 
pole  piece  here  (d),  but  no  pole  pieces  opposite  these.  How  are  the 
lines  of  force  to  pass  around  ?  I  do  not  know  that  it  would  be  easy  to 
see  how.  They  evidently  go  around  here  (arrows)  and  get  to  the  other 
side  the  best  way  they  can.  There  is  no  easy  passage  around  for  the 
lines  of  force  in  this  case. 

A  MEMBER.     May  they  not  to  some  extent  follow  the  shaft  ? 

Professor  EOWLAND.  It  is  evident  that  if  the  shaft  is  made  large 
enough  some  go  along  the  shaft  in  that  way  (arrows),  but  there  is  no 
easy  way  for  them  to  get  around. 

I  have  here  a  formula  for  the  amount  of  work  which  one  has  to 
expend  upon  a  magnet  in  order  to  produce  a  certain  effect.  I  will  take 
the  case  which  I  have  considered  most  efficient,  where  there  is  one 
magnetic  circuit.  It  is  an  original  idea  of  Faraday  that  these  lines  of 
force  are  conducted.  We  suppose  the  lines  of  force  to  pass  through 
the  iron  and  across  the  opening  in  this  way  (arrows,  Fig.  1),  and  they 
are  caused  to  do  that  by  what  may  be  called  the  magneto-motive  force 
of  the  helix. 

I  will  just  obtain  an  expression  for  the  number  of  lines  of  force  B. 
This  is  not  the  quantity  which  Maxwell  considers,  but  it  includes  the 


THE  THEORY  OF  THE  DYNAMO  225 

whole  number  of  lines  of  force  which  pass  through  the  magnet.  We 
may  write  B,  proportional  to  N,  the  number  of  turns  of  the  wire  around 
the  magnet,  and  C,  the  current;  and  inversely  proportional  to  the  re- 
sistance to  these  lines  of  force  in  going  around  the  circuit.  The  resist- 
ance to  the  lines  of  force  is  proportional  to  L,  the  length  of  the  iron  of 
the  system,  divided  by  S,  the  cross-section  of  the  magnet,  supposing  it 
to  be  uniform,  into  //,  the  magnetic  permeability  of  the  iron  (or  the 
conductivity  of  the  iron  for  the  lines  of  force).  This  quantity  ft  varies 
with  the  current,  and  can  readily  be  obtained.  Some  years  ago  I  gave 
a  formula  for  it.  It  can  be  expressed  simply  as  dependent  upon  the 
magnetization  of  the  iron  and  a  constant  depending  upon  the  iron 
alone.  We  have  something  more  to  add: 

Let  I  be  twice  the  width  of  the  opening  between  armature  and  pole 
piece,  and  A  the  area  across  which  the  lines  of  force  flow;  then  we 

have  to  add  -i  and  another  quantity,  which  we  can  call  p,  which  depends 

^L 

upon  the  resistance  of  these  lines  of  force  which  escape  in  all  direc- 
tions and  represents  the  loss  due  to  that  escapement.  Thus  we  have 
the  final  value  for  the  number  of  lines  of  force  (or  rather  induction) 
in  the  magnet 

NC 


T>  


ti      A  +  p 


This  gives  us  an  equation  which  may  be  solved  with  respect  to  fi. 
The  curve  for  the  magnetic  permeability  is  of  this  nature  (Fig.  7).  It 
will  be  of  a  more  or  less  flat  form,  according  to  the  value  of  I  and  p. 
Therefore,  in  increasing  the  magnetic  force  upon  the  magnet,  it  becomes 
easier  and  easier  to  magnetize  it  until  a  certain  point  is  reached,  and 
after  that  it  becomes  harder  and  harder.  In  practice  the  core  should 
have  sufficient  cross-section  to  produce  a  very  strong  magnetic  field, 
but  not  so  great  as  to  require  too  much  wire  to  wind  it.  The  two  must 
be  balanced,  which  can  only  be  done  by  calculation  or,  better,  by  experi- 
ments on  the  machine.  By  examining  the  force  of  the  magnet  at  each 
point,  and  in  that  way  getting  an  idea  of  how  these  lines  of  force  go, 
we  can  see  whether  the  cross-section  of  the  core  is  large  enough  to 
produce  all  the  lines  of  force  necessary  for  our  purpose  or  not.  Of 
course,  in  order  to  have  sufficient  magneto-motive  force  to  send  lines  of 
force  across  the  opening  in  sufficient  quantity,  we  must  have  sufficient 
wire.  As  the  thickness  of  the  coil  is  increased,  we  have  to  use  more 
wire  in  proportion  for  a  certain  diameter  of  core,  which  is  a  disadvan- 
15 


226 


HEXRY  A.  BOWL  AND 


tage,  since  each  coil  acts  very  nearly  the  same  as  every  other  in  produc- 
ing force.  But  if  the  core  is  very  short  indeed,  wire  must  be  piled  on 
it  to  a  very  great  extent  in  order  to  get  sufficient  magneto-motive  force, 
and  as  iron  is  cheaper  than  copper  it  might  he  better  to  lengthen  out 
the  core.  I  do  not  know  where  the  lengthening  should  end,  but  I 
should  suppose  when  the  requisite  wire  on  the  magnet  makes  a  moder- 
ately thin  layer.  Of  course,  as  we  lengthen  out  the  magnet,  the  resist- 
ance of  the  circuit  to  magnetization  becomes  greater;  but  that  is  a  very 
small  quantity.  I  do  not  suppose  the  increase  is  very  much  for  a 
considerable  lengthening  of  the  magnet.  As  I  said  before,  the  magnetic 
conductivity  of  iron  is  many  times  greater  than  that  of  air,  and  we  can 
lengthen  out  the  cores  without  producing  much  loss  on  account  of  that 
lengthening. 

Some  persons  have  suggested  that  there  might  be  a  slight  gain  from 


FIG.  7. 

the  fact  that  iron,  after  it  has  been  magnetized  a  great  number  of  times 
in  the  same  direction,  rather  likes  to  be  magnetized  in  the  same  direc- 
tion afterwards.  If  the  core  is  made  of  any  material  similar  to  steel, 
such  as  wrought  iron  or  anj'thing  of  that  sort,  it  might  be  possible  to 
have  some  gain  from  the  coercive  power  of  the  magnet.  There  would 
be  loss  from  that  cause  at  first;  but  from  the  continual  use  of  the 
machine  I  think  it  very  likely  the  iron  might  get  a  set  in  the  direction 
of  the  force.  If  the  core  were  of  steel,  for  instance,  it  might  be  that 
one  could  send  a  strong  current  through  at  first  and  magnetize  the  steel, 
and  then  be  able  to  diminish  the  current  considerably  and  still  keep  up 
a  very  large  magneto-motive  force.  I  do  not  know  how  practical  that 
would  be,  but  it  seems  to  me  that  one  could  produce  a  very  strong  field 
in  that  way.  In  the  commencement  of  the  operation  of  the  machine, 
we  would  have  to  send  a  powerful  current  to  magnetize  the  steel,  and 
then,  without  stopping  the  current,  to  diminish  it.  Then  the  set  of 


THE  THEORY  OF  THE  DYNAMO 


227 


the  steel  would  be  in  the  same  direction  with  the  current  and  produce 
the  field  with  less  expenditure  of  energy  than  if  it  were  simply  iron. 

There  is  no  difference  between  a  shunt  and  a  series  machine.  The 
magnetizing  force  on  the  magnet  I  have  set  down  as  proportional  to  the 
number  of  turns  multiplied  by  the  current;  that  is,  proportional  to  the 
cross-section  of  the  coils  multiplied  by  the  current  per  unit  of  cross- 
section,  so  that  the  magnetizing  action  can  be  the  same  either  from  a 
strong  current  or  a  weak  current.  Therefore,  if  the  exterior  dimen- 
sions of  the  coils  are  the  same  in  both  cases,  the  same  energy  is  ex- 
pended in  each  in  order  to  produce  the  same  force,  so  that  there  is  no 


FIG.  8. 

difference  between  a  shunt  machine  and  a  series  machine  as  far  as  the 
economy  of  the  magnet  is  concerned. 

I  do  not  wish  to  take  up  too  much  of  your  time,  and  will  go  on  to 
the  heating  of  the  armature.  Of  course  the  amount  of  energy  expended 
in  the  heating  of  the  armature  will  be  dependent  on  the  resistance  of 
the  armature.  It  is  well  known  that  the  efficiency  of  the  circuit  will 
merely  depend  upon  the  relation  between  the  resistance  of  the  arma- 
ture and  the  exterior  circuit. 

There  is  one  other  point  in  regard  to  losses ;  '  dead  wire,'  I  think,  is 
the  technical  term  for  it;  I  mean  that  portion  of  the  wire  which  does 
not  cut  the  lines  of  force.  In  the  Gramme  pattern  the  armature  is 


228 


HEXKY  A.  EOWLAXD 


inside  of  the  rings.  In  the  Siemens  pattern  the  coils  are  around  the 
ends  of  the  armature.  In  a  section  of  the  Gramme  ring  (Fig.  8),  the 
outside  portion  of  the  wire  (a)  is  active,  since  the  lines  of  force  follow 
the  core  and  the  outside  of  the  ring  around;  but  the  lines  of  force  do 
not  go  through  the  core  of  the  ring,  so  that  the  inside  portion  (6)  is 
dead,  so  that  we  can  say  nearly  half  the  wire  is  dead  wire.  In  the 
Siemens  armature  one  cannot  see  immediately  how  much  dead  wire 
there  will  be,  because  it  depends  upon  the  length  of  the  armature.  The 
wire  is  wound  around  in  that  way  (Fig.  9),  and  this  portion  (a  a)  is 
active,  and  this  portion  (6  &)  is  dead.  If  the  armature  is  very  thick  we 
would  have  more  dead  wire  than  when  it  is  simply  long.  I  cannot  say 
which  has  the  more  dead  wire,  but  I  dare  say  the  Gramme  has  more 


I     1     I     I 


J 4_l 


i    1    i     1     i 


FIG.  9. 

than  the  Siemens.  Furthermore,  either  in  the  Gramme  ring  or  the 
Siemens  armature  (Fig.  10)  we  have  the  lines  of  force  running  across 
here  (arrows) ;  that  portion  is  active ;  but  these  portions  (a  a)  in  between 
the  poles  are  dead,  and  when  the  armature  revolves  we  have  the  lines 
of  force  turning  around,  and  I  think  that  would  add  more  dead  wire. 
I  believe  an  attempt  has  been  made  to  throw  out  these  coils. 

There  is  no  necessity  to  go  further.  As  I  have  said,  the  efficiency  of 
the  circuit  depends  upon  the  ratio  of  the  resistance  of  the  armature  to 
the  resistance  of  the  wires,  and  therefore,  as  far  as  this  point  is  con- 
cerned, any  machine  can  be  made  as  efficient  as  one  pleases  by  putting 
in  greater  and  greater  external  resistance.  But  as  the  magnet  remains 
the  same,  we  would  find  a  point  where  the  efficiency  as  a  whole  would 
not  increase  for  an  increase  of  external  resistance,  but  would  actually 
diminish.  There  are  other  things  to  be  taken  account  of,  such  as  losses 


THE  THEORY  OF  THE  DYNAMO 


229 


due  to  the  self  induction  of  the  coils  which  produce  sparks  in  them. 
I  have  requested  Professor  Fitzgerald  to  take  up  that  point,  and  will 
leave  it  for  him  to  consider. 

There  is  another  point  with  regard  to  the  dynamo  which  can  be 
treated  in  this  simple  manner  with  no  use  of  the  calculus.  This  is 
very  simple  reasoning  if  you  only  know  the  principles.  I  shall  con- 
sider two  machines  similar  in  all  respects,  except  that  one  is  larger  than 
the  other,  or  rather  consider  one  machine,  and  see  what  the  effect  will 
be  when  that  machine  gradually  changes  in  size. 

The  point  from  which  we  start  shall  be  that  the  magnetic  field  is  con- 
stant in  the  two  machines.  For,  owing  to  the  fact  that  there  is  a  limit 
in  the  magnetization  of  a  magnet,  we  cannot  have  a  field  with  more 


FIG.  10. 

than  certain  strength  produced  by  iron,  and  I  will  suppose  that  the 
strength  is  reasonably  near  that  maximum  for  iron.  It  cannot  be  up 
to  the  maximum  strength,  of  course,  but  somewhere  near  it.  I  made 
some  experiments  many  years  ago  upon  an  ordinary  magnet,  the  results 
of  which  were  published  in  Silliman's  Journal,  by  means  of  what  I  call 
the  magnetic  proof  plane.  (Am.  J.  Sci.,  vol.  10,  1875,  p.  14.)  It 
applies  beautifully  to  dynamo  machines,  and  I  obtained  everything  with 
it  that  I  have  referred  to  here.  If  I  remember  right,  I  found  in  that 
magnet  about  one-third  of  the  field  that  an  iron  magnet  could  pos- 
sibly have. 

It  is  theoretically  possible  to  get  a  force  equal  to  the  magnetizability 
of  the  iron,  but  practically,  I  suppose  that  instance  is  about  the  case 
of  the  ordinary  dynamo  machine.  We  start,  then,  with  the  supposition 
that  the  field  of  force  in  the  two  machines,  one  of  which  is  larger  than 


230  HEXEY  A.  KOWLAKD 

the  other,  is  constant.  That  is  to  say,  the  magnetizing  force  at  any 
point  of  one  machine  is  equal  to  that  at  a  similar  point  in  the  other 
machine.  In  making  a  drawing  of  the  machines.,  it  would  not  matter 
about  the  scale  of  dimensions;  the  force  at  a  certain  point  is  a  certain 
amount  whatever  the  scale. 

Next  consider  what  must  be  the  current  through  the  wire  in  the  two 
machines.  There  are  the  same  numbers  of  turns  of  wire  around  the 
magnet,  and  everything  is  the  same  except  the  dimensions.  Consider 
the  current  passing  around  the  coil  of  a  tangent  galvanometer.  If  the 
galvanometer  grow,  in  order  to  produce  the  same  effect  at  the  centre 
(and  not  only  at  the  centre  but  at  every  point),  the  current  must  in- 
crease in  direct  proportion  to  the  radius  of  the  coil.  When  the  coil  is 
twice  as  large  the  current  must  be  twice  as  large,  in  order  to  produce 
the  same  force  at  every  point.  Thus,  if  there  is  no  difference  in  the 
material  of  the  two  machines,  we  have  their  currents  in  direct  propor- 
tion to  their  linear  dimensions.  Make  a  machine  twice  as  large  and 
the  current  in  the  coils  must  be  twice  as  great  to  produce  the  same 
magneto-motive  force.  Of  course  the  wire  has  increased  in  size;  if 
the  machine  has  increased  to  twice  its  original  size  the  cross-section 
of  the  wire  has  increased  four  times.  In  other  words,  from  that  cause 
the  current  per  unit  of  area  will  vary  inversely  as  the  square  of  I,  the 
linear  dimensions;  and  since  we  have  found  the  current  to  vary  directly 
as  I,  in  order  to  retain  the  same  force  in  the  field,  by  a  combination  of 
the  two  results,  it  varies  inversely,  as  I.  Therefore,  so  far  as  the 
magnets  are  concerned,  the  heating  effect,  which  depends  upon  the 
current  per  unit  of  cross-section,  will  decrease  with  the  size,  while  the 
surface  will  increase  in  proportion  to  the  square  of  the  size.  There 
will,  therefore,  be  less  danger  of  heating  in  a  large  magnet  than  in  a 
small  magnet,  but  this  is  only  with  respect  to  the  magnet. 

The  resistance  of  any  part  of  the  machine  varies,  of  course,  directly 
as  the  length  of  the  wire,  and  inversely  as  the  cross-section.  The  cross- 
section  varies  as  Z2,  so  that  resistance  varies  inversely  as  I.  Therefore 
the  larger  the  machine  the  less  the  resistance ;  one  machine  being  twice 
as  large  as  the  other,  the  resistance  will  be  half  as  great.  This  applies 
not  only  to  the  work  of  the  magnets,  but  to  the  work  of  the  armature. 

I  will  now  consider  the  electro-motive  force.  The  electro-motive 
force  is  proportional  to  the  product  of  the  current  and  the  resistance, 
or  we  may  write  E  =  RC.  We  have  the  current  proportional  to  I,  and 
the  resistance  inversely  proportional  to  I;  therefore  the  electro-motive 
force  is  constant.  As  we  are  running  the  machine,  it  turns  out  that 


THE  THEORY  OF  THE  DYXAMO  231 

the  electro-motive  force  does  not  vary  with  the  size,  but  we  shall  pres- 
ently see  how  this  is  modified  so  as  to  get  greater  electro-motive  force 
for  the  larger  machine. 

The  work  done  is  C2R  in  any  part  of  the  machine,  or  in  the  whole 
machine,  just  as  you  please.  This  varies  directly  as  I.  Therefore  the 
one  machine  which  is  twice  as  large  as  the  other  requires  twice  as  much 
power  to  run  it,  and  twice  as  much  electrical  energy  comes  out  of  it. 
But  it  is  to  be  remembered  that  the  weight  of  the  machine  varies  as  Is, 
and  we  only  get  work  proportional  to  I  out  of  it. 

So  far  as  results  go,  we  have  constructed  two  machines  which  differ 
only  in  size.  The  efficiency  of  these  two  machines  is  a  constant  quan- 
tity. That  will  be  rather  startling  to  some,  who  think  a  large  machine 
is  more  efficient  than  a  small  one.  As  far  as  we  have  gone  in  any  two 
machines,  one  of  which  is  simply  larger  than  the  other,  the  efficiency  is 
the  same. 

But  if  we  calculate  the  angular  velocity  of  the  armature  to  keep  the 
proper  current  we  shall  find  that  it  varies  inversely  as  the  square  of  the 
linear  dimensions.  In  other  words,  in  one  machine  twice  as  large 
as  another  the  velocity  of  the  armature  must  be  only  one-fourth  as 
great  in  order  to  produce  the  proper  current  in  the  wires.  This  takes 
account,  I  think,  of  every  irregularity  in  the  machine.  The  two 
machines  are  exactly  the  same  in  every  respect.  I  have  not  added  the 
loss  for  the  self-induction  of  the  coil.  I  have  an  idea  that  this  also 
should  be  taken  into  account,  but  Mr.  Fitzgerald  will  consider  that 
point. 

ISfow  the  question  comes  up,  can  we  increase  the  velocity  of  the  arma- 
ture above  that  point?  Is  it  practically  necessary  that  we  should  run 
one  machine  at  one-fourth  of  the  angular  velocity  if  it  is  twice  as  large  ? 
It  is  a  practical  question;  but  I  should  certainly  think  the  velocity  was 
not  in  that  proportion.  I  should  think  it  would  be  more  nearly  in- 
versely as  the  size  and  not  inversely  as  the  square  of  the  size.  If  so, 
then  by  so  arranging  the  wire  of  the  armature  as  to  increase  the  pro- 
portion of  external  resistance  we  can  have  the  same  current  per  unit 
of  section  when  running  the  armature  faster  and  the  same  electro- 
motive force.  If  we  do  that,  this  whole  theory  applies;  but  we  shall 
have  increased  the  external  resistance  of  the  machine  in  comparison 
with  the  resistance  of  the  armature,  and  when  we  do  that  we  increase 
the  efficiency  of  the  machine. 

I  think  it  is  from  this  cause  that  we  find  large  machines  more  efficient 
than  smaller  ones;  but  it  is  also  evident  that  there  is  a  limit  to  this, 


232  HENRY  A.  KOWLAND 

which  can  only  be  obtained,  I  suppose,  from  practically  making  the 
machines  and  seeing  how  much  faster  they  may  be  run  without  flying 
to  pieces.  As  far  as  this  theory  goes,  the  increase  comes  not  from  the 
size  of  the  machine,  but  from  the  fact  that  we  can  get  a  greater  electro- 
motive force  with  the  same  angular  velocity,  and  so  can  reduce  the 
internal  resistance  in  proportion.  In  very  large  machines  we  can  make 
the  wire  with  one  turn,  not  several  turns — simply  bars  on  the  machines. 
We  thus  decrease  the  resistance  of  the  machine,  and  at  the  same  time, 
if  we  run  it  above  this  proportion  which  I  have  pointed  out,  we  obtain 
the  proper  electro-motive  force.  In  other  words,  the  proper  electro- 
motive force  is  more  easily  obtained  from  the  large  than  the  small 
machine,  because  it  is  not  practically  necessary  to  decrease  the  velocity 
so  as  to  keep  it  inversely  as  the  square  of  the  size. 

[Discussion  by  Professor  Elihu  Thomson  and  others.] 

With  respect  to  Mr.  Thomson's  remarks,  I  am  very  glad  to  see  the 
matter  taken  up  in  this  spirit  and  to  have  my  principles  intelligently 
criticised.  However,  there  was  one  remark  which  I  wish  to  state  imme- 
diately as  an  error,  of  course,  with  regard  to  the  steel.  Steel  can  be 
magnetized  to  exactly  the  same  degree  as  soft  iron.  There  is  no  differ- 
ence between  soft  iron  and  steel  in  that  respect,  except  that  we  require 
an  immensely  greater  force  to  magnetize  steel  to  the  same  extent  as 
iron.  There  are  some  old  papers  of  mine,  which  were  published  in  the 
'  Philosophical  Magazine/  I  believe,  in  1873,  relating  to  experiments 
where  I  took  iron  and  steel  and  several  other  metals,  and  showed  that 
the  maximum  magnetization  was  the  same  in  all  cases. 

But  with  respect  to  a  number  of  statements  with  regard  to  flat  mag- 
nets and  round  magnets  I  am  very  glad  to  see  my  remarks  criticised  in 
the  manner  that  they  were,  because  it  shows  the  need  of  exactly  what 
I  stated;  and  that  is  experiments  upon  this  subject.  The  question  is 
one  of  quantity.  My  reasoning  gave  results  in  one  direction,  and  Mr. 
Thomson  gave  reasons  for  making  the  magnet  in  another  way,  and  it  is 
a  quantitative  question  of  course  as  to  which  is  the  best;  and  for  that 
reason  I  want  very  much  to  see  experiments  made  in  the  manner  which 
I  have  described  by  means  of  this  '  magnetic  proof  plane/  so  as  to  find 
out  what  the  escape  of  the  lines  of  magnetic  force  in  all  cases  is. 

I  think  we  can  decide  on  one  point  that  was  brought  up  without  any 
trouble,  and  that  is  with  respect  to  the  dynamo  made  with  extended 
pole  piece  (Fig.  2),  where  it  was  assumed  that  the  lines  of  force  had  a 


THE  THEORY  or  THE  DYNAMO  233 

tendency  to  go  in  a  particular  direction,  that  it  was  a  sort  of  gun  shoot- 
ing the  lines  of  force  through  the  armature.  That  is  not  true,  because 
they  do  not  have  any  tendency  to  go  that  way  at  all,  and  we  would  only 
add  that  much  to  the  area  of  the  end  of  the  magnet.  Very  few  lines  of 
force  will  go  out  there,  and  by  putting  this  additional  magnet  on  we 
add  to  the  area  of  the  magnet.  The  lines  of  force  will  go  out  at  the 
sides  probably  in  greater  numbers  than  they  would  at  the  end,  so  that 
I  do  not  think  that  particular  objection  holds  in  that  particular  case. 
It  is  a  question  of  quantity;  the  thing  should  be  measured  and  found 
out.  I  see  very  plainly  in  my  own  mind  that  more  lines  of  force  would 
go  out  the  side  by  adding  this  iron  here  (Fig.  2)  than  would  go  out  at 
the  end  of  it  by  leaving  it  vacant,  as  in  Fig.  1.  But  it  is  a  matter  of 
mere  opinion.  Another  reason  for  having  fewer  magnets  is  that  the 
surface  is  greater  in  the  case  of  the  larger  number  than  of  the  smaller 
number  for  the  lines  of  force  to  escape  from. 

There  was  another  point  brought  up  here  with  respect  to  the  machine 
which  was  made  in  this  way  (Fig.  4).  It  was  stated  that  there  was 
some  gain  from  the  magnetic  action  of  this  coil  on  the  iron  outside. 
There  is  undoubtedly  a  gain:  the  question  is  how  much,  and  whether 
more  lines  do  not  escape  than  would  make  up  for  that.  With  no 
experiments  to  go  on,  it  is  a  case  of  judgment.  My  own  judgment 
would  be  that  there  would  be  very  little  gain ;  but,  as  I  said  before,  the 
thing  should  be  measured,  and  then  we  could  find  out  about  that  point. 

[Discussion  by  Professors  Sylvanus  Thompson  and  Anthony  and 
others.] 

I  am  very  glad  that  that  point  of  hollow  magnets  has  been  brought 
up,  as  I  think  that  the  question  of  hollow  magnets,  hollow  lightning 
rods,  and  a  great  many  similar  things,  causes  more  difficulty,  especially 
to  practical  men,  than  almost  anything  else.  It  can  be  explained  in 
a  very  few  words.  Take  a  hollow  bar  having  the  magnetizing  coil 
around  it  acting  to  send  lines  of  force  along  it.  They  have  got  to  go 
out  to  make  their  complete  circuit.  They  could  only  end  at  a  certain 
point  if  we  had  free  magnetism,  that  is,  a  separate  magnetic  fluid. 
I  speak  not  from  a  physical  sense  but  from  a  mathematical  point  of 
view.  The  principal  resistance  to  the  propagation  of  these  lines  of 
force  is  in  the  air  and  not  in  the  magnet.  If  we  take  away  a  large 
portion  of  the  interior  of  that  magnet  we  will  have  the  surface  the 
same  as  it  was  before,  and  consequently  the  external  resistances  are  the 


234  HENRY  A.  EOWLAND 

» 

same.  In  such  a  case  as  that  we  leave  the  magnet  about  as  strong  as 
it  was  before.  But  that  would  not  be  the  case  if  we  compress  magnet- 
ism until  we  get  it  up  to  the  point  of  magnetization  of  the  centre.  In 
that  case  we  should  need  the  whole  mass,  and  it  is  almost  impossible 
to  magnetize  to  any  extent  without  the  centre  coming  in.  It  depends 
on  the  length  of  the  bar.  If  we  bring  the  bar  around,  making  a  com- 
plete magnetic  circuit  of  the  thing,  so  that  the  lines  of  force  do  not 
have  to  pass  out  into  the  air  at  all  when  we  put  a  wire  around  it  so  as 
to  wind  it  like  a  ring  at  every  point,  in  that  case  the  whole  cross-section 
becomes  equally  magnetized,  if  it  is  not  bent  too  much.  If  it  is  a  large 
ring  of  small  cross-section,  it  is  perfectly  magnetized  across  from  side 
to  side.  We  know  that  perfectly  well;  it  is  a  result  of  the  law  of  con- 
servation of  energy.  The  case  of  dynamos  is  like  that.  We  require 
the  whole  cross-section  to  transmit  these  lines  around.  The  resistance 
to  the  magnetization  comes  partly  from  this  opening  and  partly  from 
the  iron.  We  have  no  gain  in  making  these  cylinders  hollow;  indeed 
we  rather  increase  the  outside  surface  to  let  lines  of  force  flow  into  the 
air.  In  the  case  of  a  dynamo  machine,  the  solid  form  is  not  only 
desirable,  but  by  far  the  most  efficient. 

I  have  thought  of  that  matter  a  great  deal,  and  experimented  upon 
it.  Indeed  this  closed  circuit  is  the  very  idea  from  which  the  permea- 
bility of  the  iron  is  determined.  All  the  calculations  upon  that  sub- 
ject are  based  upon  that  law.  I  think  there  can  be  no  doubt  that  in 
the  dynamo  the  solid  form  is  the  proper  form,  and  that  the  whole  cross- 
section  is  effective.  The  whole  cross-section  of  a  round  piece  is  just  as 
effective  as  the  whole  cross-section  of  a  flat  piece.  The  flat  piece  ex- 
poses more  surface  to  the  air,  and  there  is  more  surface  for  the  force 
to  escape  from.  That  is  another  reason  for  not  making  the  magnets 
flat.  The  round  form  is  that  in  which  there  is  the  least  surface,  and 
therefore  the  least  liability  of  the  lines  of  force  to  escape.  You  can 
conduct  the  lines  of  force  by  a  round  piece  to  any  point  you  desire  much 
better  than  by  a  flat  piece. 

[Discussion  by  Professor  Sylvanus  Thompson.] 

I  do  not  know  that  the  theory  bears  upon  the  solidity  of  the  core. 
Of  course,  the  more  iron  in  there  the  better  is  the  efficiency  of  the 
machine.  I  suppose  there  would  be  no  objection  to  dividing  that 
cylinder  up  into  a  number,  so  that  the  Foucault  currents  could  not 
exist,  if  the  exterior  form  was  round;  but  I  do  have  an  objection  to 


THE  THEORY  OF  THE  DYNAMO  235 

making  it  any  other  shape.  Indeed,  currents  could  be  more  thoroughly 
eliminated  by  dividing  up  the  cross-section  than  by  making  it  of  a 
very  elongated  form. 

[Discussion  by  Professor  Elihu  Thomson.] 

I  do  not  like  to  rise  so  often,  but  I  think  there  is  some  misapprehen- 
sion. I  have  not  said  anything  about  large  masses  of  iron.  There  are 
the  same  masses  of  iron  in  my  method  as  in  any  other.  The  only 
question  is  as  to  making  them  round  or  elongated.  Of  course  by 
dividing  this  core  up  it  becomes  similar  to  a  core  of  the  Euhmkorff 
coil,  and  the  currents  change  very  rapidly.  From  Professor  Sylvanus 
Thompson's  remarks,  I  thought  that  that  was  desirable.  One  cannot 
say  that  the  current  is  transferred  from  the  core  to  the  wires  outside. 
The  same  current  might  take  place,  and,  if  the  resistances  are  the 
same,  would  take  place  in  the  wires  outside  in  both  cases.  By  lengthen- 
ing the  time  of  action  one  decreases  the  electro-motive  force  or  de- 
creases the  external  current.  If  the  time  is  ten  minutes  one  would 
have  one  electro-motive  force  for  the  external  current:  if  it  is  five 
minutes,  the  electro-motive  force  would  be  somewhere  near  twice  as 
great  as  before,  the  whole  quantity  of  electricity  passing  being  the  same 
in  both  cases. 


36 


[Report  of  the  Electrical  Conference  at  Philadelphia  in  November,  1884,  pp.  172-17-t; 

Washington,  1886] 

As  this  is  an  important  question,  especially  in  some  of  the  Western 
States,  I  will  say  a  few  words. 

In  order  to  protect  buildings  from  lightning  we  must  have  a  space 
into  which  the  lightning  cannot  come,  and  have  the  house  situated  in 
that  space.  What  sort  of  a  space  do  we  know  in  electrical  science  into 
which  electricity  cannot  enter  from  the  outside  ?  It  is  a  closed  space — 
I  mean  a  space  inclosed  by  a  very  good  conducting  body.  All  the  light- 
ning in  the  world  might  play  around  a  hollow  copper  globe  and  it  would 
not  affect  in  the  slightest  degree  anything  inside  the  globe;  but  the 
the  walls  of  the  vessel  need  not  be  solid  metal.  Of  course,  if  solid,  it 
is  all  the  better ;  but  if  it  is  made  of  a  net-work  of  very  good  conducting 
material  it  would  protect  the  inside  from  lightning  strokes.  A  spark 
striking  on  one  side  of  such  wire  cage  would  find  it  easier  to  go  around 
through  the  wire  of  the  cage  to  the  other  side  than  it  would  to  go 
through  the  centre.  This  is  Maxwell's  idea,  with  reference  to  protec- 
tion of  houses  from  lightning,  viz.,  to  enclose  the  house  in  a  rough  cage 
of  conducting  material.  Suppose,  for  instance,  this  box  is  the  house, 
and  suppose  we  start  from  the  roof  and  run  a  rod  diagonally  to  each 
corner  and  thence  down  to  the  earth.  We  thus  make  a  rough  cage. 
Of  course  there  are  openings  on  the  sides;  and  if  we  wished  to  make  a 
better  protection  we  could  put  rods  down  the  sides  wherever  we  wished. 
Now,  there  is  ground  underneath  the  house,  and  the  lightning  might, 
by  jumping  across  the  centre,  find  a  good  conductor  through  the  middle 
of  the  house  and  go  down  to  the  earth  in  that  way.  How  do  we  prevent 
that?  By  running  the  lightning-rods  clear  across  underneath  the 
house.  Then  the  lightning  would  find  it  easier  to  go  around  the  house 
than  to  jump  across,  even  if  there  were  a  good  conductor  through  the 
middle.  A  house  inclosed  in  a  cage  of  that  sort  would  be  perfectly 
protected,  even  if  it  were  a  powder  magazine,  or  anything  of  that  sort. 
Of  course,  in  the  case  of  petroleum  storage  reservoirs,  where  fumes  are 
given  off,  there  would  be  danger  then,  as  the  stroke  might  ignite  the 


ON  LIGHTNING  PROTECTION  237 

fumes  of  the  petroleum.  That  would  not  be  the  case  of  a  powder 
magazine.  The  protection  in  that  case  could  be  made  perfect. 

It  is  not  necessary  to  have  lightning-rods  insulated.  Indeed  the 
question  is,  can  we  insulate  a  lightning-rod  ?  We  may  insulate  it  for  a 
small  potential,  but  lightning  coming  from  a  mile  or  two  to  strike  a 
house  is  not  going  to  pay  any  attention  to  such  an  insulator;  we  may 
just  as  well  nail  the  lightning-rod  directly  to  the  house  as  far  as  that 
goes. 

The  idea  of  having  the  lightning-rods  inclose  the  bottom  as  well  as 
the  sides  of  the  house  is  very  important,  because  we  do  not  know,  and 
we  have  no  right  to  assume,  that  the  earth  is  a  good  conductor.  We 
are  perfectly  certain  if  the  earth  forms  a  good  conductor  that  then  the 
lightning  could  go  down  at  the  sides  into  the  earth.  By  inclosing  the 
house  in  a  case  both  below  and  above  we  obviate  all  that  difficulty,  and 
it  makes  no  difference  whether  the  earth  is  a  good  conductor  or  not. 

I  am  glad  of  this  public  opportunity  to  say  something  with  regard  to 
a  peculiar  form  of  lightning-rod;  it  is  in  reference  to  a  form  of  a  rod 
shaped  like  the  letter  U.  I  think  the  idea  is  that  the  lightning  strikes 
on  one  side,  and  that  it  goes  down  and  has  inertia  and  flies  up  again. 
The  company  which  advocated  this  idea  had  the  impudence  to  bring  a 
lawsuit  against  a  scientific  man  who  said  it  was  a  humbug.  A  company 
of  course  can  make  a  great  deal  of  trouble  to  one  man;  but  when  there 
is  such  a  gross  humbug  as  that  around,  one  would  like  to  undergo  the 
danger  of  a  lawsuit.  There  is  nothing  scientific  about  it;  it  will  endan- 
ger life  in  any  house  in  which  it  is  placed. 

Mr.  SCOTT.  I  would  like  to  ask  whether  a  building  constructed  of 
iron  would  not  be  completely  protected  from  lightning  ? 

Professor  EOWLAND.  Yes,  if  it  has  a  floor  of  iron  too.  If  a  gas-pipe 
came  up  into  the  centre  the  lightning  might  find  it  easier  to  go  across 
to  the  pipe  than  to  go  around.  But  if  we  made  a  floor  of  iron  the 
lightning  would  find  it  easier  to  go  around  than  across  to  the  pipe.  It 
must  be  an  entirely  inclosed  house. 

Mr.  SCOTT.  Then  would  not  a  petroleum  tank  entirely  constructed 
of  iron  with  an  iron  bottom  be  the  safest  inclosure  possible  for  petro- 
leum? 

Professor  ROWLAND.  The  peculiarity  of  that  is  that  the  fumes  of 
petroleum  are  all  the  time  coming  out  from  the  cracks.  The  whole  out- 
side is  probably  covered  with  petroleum.  I  suppose  also  the  ground  is 
saturated  with  petroleum.  The  petroleum  as  far  as  the  inside  goes 
would  be  perfectly  safe. 


238  HENKY  A.  ROWLAND 

Lieutenant  FISKE.  I  would  like  to  ask  how  far  lightning  obeys  the 
ordinary  law  of  currents,  whether  it  takes  the  path  of  least  resistance 
or  not.  Do  high  potentials  always  do  that?  In  general  across  a  nar- 
row space  the  resistance  is  greater  than  going  around  by  the  iron,  and 
the  question  is,  to  what  extent  does  the  lightning  obey  the  law  of 
circuits  ? 

Professor  ROWLAND.  I  would  like  to  say  one  word  more  with  respect 
to  petroleum.  In  the  case  of  the  tank  you  have  a  mixture  of  the  petro- 
leum vapor  and  air  which  probably  would  explode.  Unless  the  tank  was 
a  very  good  conductor  there  might  be  also  a  little  spark  in  the  interior, 
not  enough  to  hurt  a  man  in  there;  but  the  smallest  spark  inside  the 
tank  would  cause  an  explosion.  I  am  not  certain  whether  the  iron  of 
the  tank  is  a  good  enough  conductor  to  prevent  every  trace  of  spark  in 
the  interior.  Indeed,  suppose  we  had  a  tank  with  a  cover  upon  it. 
That  is  supposed  to  be  a  closed  vessel,  yet  the  lightning  would  have  to 
pass  from  top  to  bottom  between  the  cover  and  the  tank,  and  perhaps 
a  little  spark  would  take  place  in  the  interior;  and  possibly  in  going 
from  one  of  the  plates  of  the  iron  tank  to  the  other  it  may  find  some 
resistance  and  jump  over  some  small  plate  in  the  interior  of  the  tank. 
It  would  be  a  most  difficult  thing  to  protect. 

With  regard  to  that  other  question,  lightning  in  the  air,  of  course, 
does  not  obey  Ohm's  law;  it  is  entirely  a  discontinuous  anomaly.  It  is 
like  the  breaking  of  a  metal.  A  piece  of  metal  is  supposed  to  break  at 
a  certain  strain;  but  it  does  not  always  break  then;  it  pulls  out  in 
strings  or  something  of  that  sort.  One  cannot  measure  the  distance 
and  say  the  lightning  is  going  to  jump  across  that  distance. 


37 
THE  VALUE  OF  THE  OHM 

[La  Lumieve  filectrique,  XXVI,  pp.  188,  189,  477,  1887] 

La  Yaleur  de  PTJnite  de  Besistance  de  1'Association  Britannique. 

A  la  derniere  reunion  de  1'  Association  britannique,  le  professeur 
H.  A.  Eowland  a  donne  la  valeur  definitive  de  1'unite  de  resistance 
electrique  de  1'Association,  telle  qu'elle  a  ete  determined  par  la  com- 
mission americaine.  La  valeur  donnee  en  1876  etait  :  unite  B.  A.  = 
0-9878  ohm. 

Dans  la  derniere  determination,  on  s'est  servi  des  methodes  de  Kirch- 
hoff  et  de  celle  de  Lorenz. 

La  premiere  a  donne  une  valeur  de  0-98646  ±  40  et  la  seconde  0-9864 
±  18;  son  erreur  probable  est  done  de  moins  de  la  moitie  de  celle  de  la 
premiere  methode. 

Le  professeur  Eowland  a  egalement  determine  la  resistance  d'une 
colonne  de  mercure  de  1  mm.2  de  section  et  de  100  centimetres  de  lon- 
gueur, et  a  trouve  0-95349  unites  B.  A. 

Valeur  de  1'Etalon  B.  A.  de  1'Ohm,  d'apres  les  Mesures  de  la  Com- 
mission, Americaine,  par  Eowland. 

Les  observations  ont  ete  terminees  en  1884  deja,  mais  les  calculs 
viennent  d'etre  termines  et  seront  publics  prochainement.  En  1786: 

Eowland  a  trouve  1  unite  B.  A.  =  0-9878  ohm. 

Kimball  a  trouve  1  unite  B.  J..  =  0-9870  ohm. 

Maintenant  Eowland  trouve  par  la  methode  de  Kirchhoff  et  a  1'aide 
de  73  observations 

1  unite  B.  A.  =  (0-98627  ±  40)  ohms 

et  Kimball  par  la  methode  de  Lorenz  et  au  moyen  de  43  observations 
1  unite  B.  A.  =  (0-98642  ±  18)  ohms. 

En  combinant  les  deux  resultats,  on  trouve  que  1'unite  mercurielle  est 
egale  a  0-95349  unites  B.  A.,  c'est-a-dire  que  1'ohm  de  mercure  cor- 
respond a  une  colonne  de  mercure  de  106-32  cm. 

Eappelons  ici  les  valeurs  obtenues  par  diiferents  physiciens  et  qui  se 
rapprochent  le  plus  du  resultat  ci-dessus : 


240  HENEY  A.  KOWLAND 

Lord  Eayleigh     106-25  cm. 

Glazebrook   106-29  cm. 

Wiedemann      106-19  cm. 

Mascart     106-37  cm. 

Weber  .  ,.106-16  cm. 


38 
ON  A  SIMPLE  AND  CONVENIENT  FOEM  OF  WATER  BATTERY 

[American  Journal  of  Science   [3],  XXXI21,   147,   1887 ;    Philosophical   Magazine   [5], 
XXIII,  303,  1887 ;  Johns  Hopkins  University  Circulars,  No.  57,  p.  80,  1887] 

For  some  time  I  have  had  in  use  in  my  laboratory  a  most  simple, 
convenient  and  cheap  form  of  water  battery  whose  design  has  been  in 
one  of  my  note-books  for  at  least  fifteen  years.  It  has  proved  so  useful 
that  I  give  below  a  description  for  the  use  of  other  physicists. 

Strips  of  zinc  and  copper,  each  two  inches  wide,  are  soldered  to- 
gether along  their  edges  so  as  to  make  a  combined  strip  of  a  little  less 
than  four  inches  wide,  allowing  for  the  overlapping.  It  is  then  cut 
by  shears  into  pieces  about  one-fourth  of  an  inch  wide,  each  composed 
of  half  zinc  and  half  copper. 

A  plate  of  glass,  very  thick  and  a  foot  or  less  square,  is  heated  and 
coated  with  shellac  about  an  eighth  of  an  inch  thick.  The  strips  of 
copper  and  zinc  are  bent  into  the  shape  of  the  letter  IT,  with  the 
branches  about  one-fourth  of  an  inch  apart,  and  are  heated  and  stuck 
to  the  shellac  in  rows,  the  soldered  portion  being  fixed  in  the  shellac, 
and  the  two  branches  standing  up  in  the  air,  so  that  the  zinc  of  one 
piece  comes  within  one-sixteenth  of  an  inch  of  the  copper  of  the  next 
one.  A  row  of  ten  inches  long  will  thus  contain  about  thirty  elements. 
The  rows  can  be  about  one-eighth  of  an  inch  apart  and  therefore  in  a 
space  ten  inches  square  nearly  800  elements  can  be  placed.  The  plate 
is  then  warmed  carefully  so  as  not  to  crack  and  a  mixture  of  beeswax 
and  resin,  which  melts  more  easily  than  shellac,  is  then  poured  on  the 
plate  to  a  depth  of  half  an  inch  to  hold  the  elements  in  place.  A  frame 
of  wood  is  made  around  the  back  of  the  plate  with  a  ring  screwed  to 
the  centre  so  that  the  whole  can  be  hung  up  with  the  zinc  and  copper 
elements  below. 

When  required  for  use,  lower  so  as  to  dip  the  tips  of  the  elements 
into  a  pan  of  water  and  hang  up  again.  The  space  between  the  ele- 
ments being  -fa  inch,  will  hold  a  drop  of  water  which  will  not  evaporate 
for  possibly  an  hour.  Thus  the  battery  is  in  operation  in  a  minute  and 
is  perfectly  insulated  by  the  glass  and  cement. 

This  is  the  form  I  have  used,  but  the  strips  might  better  be  soldered 
face  to  face  along  one  edge,  cut  up  and  then  opened. 
16 


40 

ON  AN  EXPLANATION  OF  THE  ACTION  OF  A  MAGNET  ON 
CHEMICAL  ACTION1 

BY  HENRY  A.  ROWLAND  AND  Louis  BELL 

[American  Journal  of  Science    [3],  XXXVI,  39-47,  1888;    Philosophical  Magazine  [5]. 

XXVI,  105-114,  1888] 

In  the  year  1881  Prof.  Eemsen  discovered  that  magnetism  had  a 
very  remarkable  action  on  the  deposition  of  copper  from  one  of  its  solu- 
tions on  an  iron  plate,  and  he  published  an  account  in  the  American 
Chemical  Journal  for  the  year  1881.  There  were  two  distinct  phe- 
nomena then  described,  the  deposit  of  the  copper  in  lines  approximat- 
ing to  the  equipotential  lines  of  the  magnet,  and  the  protection  of  the 
iron  from  chemical  action  in  lines  around  the  edge  of  the  poles.  It 
seemed  probable  that  the  first  effect  was  due  to  currents  in  the  liquid 
produced  by  the  action  of  the  magnet  on  the  electric  currents  set  up 
in  the  liquid  by  the  deposited  copper  in  contact  with  the  iron  plate. 
The  theory  of  the  second  kind  of  action  was  given  by  one  of  us,  the 
action  being  ascribed  to  the  actual  attraction  of  the  magnet  for  the 
iron  and  not  to  the  magnetic  state  of  the  latter.  It  is  well  known 
since  the  time  of  Faraday  that  a  particle  of  magnetic  material  in  a 
magnetic  field  tends  to  pass  from  the  weaker  to  the  stronger  portions 
of  the  field,  and  this  is  expressed  mathematically  by  stating  that  the 
force  acting  on  the  particle  in  any  direction  is  proportional  to  the  rate 
of  variation  of  the  square  of  the  magnetic  force  in  that  direction. 
This  rate  of  variation  is  greatest  near  the  edges  and  points  of  a  mag- 
netic pole,  and  more  work  will  be  required  to  tear  away  a  particle  of 
iron  or  steel  from  such  an  edge  or  point  than  from  a  hollow.  This 
follows  whether  the  tearing  away  is  done  mechanically  or  chemically. 
Hence  the  points  and  edges  of  a  magnetic  pole,  either  of  a  permanent 
or  induced  magnet,  are  protected  from  chemical  action. 

One  of  Prof.  Remsen's  experiments  illustrates  this  most  beautifully. 
He  places  pieces  of  iron  wire  in  a  strong  magnetic  field,  with  their 
axes  along  the  lines  of  force.  On  attacking  them  with  dilute  nitric 
acid  they  are  eaten  away  until  they  assume  an  hour-glass  form,  and  are 

1  Read  at  the  Manchester  meeting  of  the  British  Association,  September,  1887. 


ACTION  OF  A  MAGNET  ox  CHEMICAL  ACTION  243 

furthermore  pitted  on  the  ends  in  a  remarkable  manner.  On  Prof. 
Remsen's  signifying  that  he  had  abandoned  the  field  for  the  present, 
we  set  to  work  to  illustrate  the  matter  in  another  manner  by  means 
of  the  electric  currents  produced  from  the  change  in  the  electrochemical 
nature  of  the  points  and  hollows  of  the  iron. 

The  first  experiments  were  conducted  as  follows:  Two  bits  of  iron 
or  steel  wire  about  1  mm.  in  diameter  and  10  mm.  long  were  imbedded 
side  by  side  in  insulating  material,  and  each  was  attached  to  an  insulated 
wire.  One  of  them  was  filed  to  a  sharp  point,  which  was  exposed  by 
cutting  away  a  little  of  the  insulation,  while  the  other  was  laid  bare  on 
a  portion  of  the  side.  The  connecting  wires  were  laid  to  a  reflecting 
galvanometer,  and  the  whole  arrangement  was  placed  in  a  small  beaker 
held  closely  between  the  poles  of  a  large  electromagnet,  the  iron  wires 
being  in  the  direction  of  the  lines  of  force.  When  there  was  acid  or 
any  other  substance  acting  upon  iron  in  the  beaker,  there  was  always  a 
deflection  of  the  galvanometer  due  to  the  slightly  different  action  on 
the  two  poles.  When  the  magnet  was  excited  the  phenomena  were 
various.  When  dilute  nitric  acid  was  placed  in  the  beaker  and  the 
magnet  excited,  there  was  always  a  strong  throw  of  the  needle  at  the 
moment  of  making  circuit,  in  the  same  direction  as  if  the  sharp  pointed 
pole  had  been  replaced  by  copper  and  the  other  by  zinc.  This  throw 
did  not  usually  result  in  a  permanent  deflection,  but  the  needle  slowly 
returned  toward  its  starting  point  and  nearly  always  passed  it  and 
produced  a  reversed  deflection.  This  latter  effect  was  disregarded  for 
the  time  being,  and  attention  was  directed  to  the  laws  that  governed 
the  apparent  '  protective  throw,'  since  the  reversal  was  so  long  delayed 
as  to  be  quite  evidently  due  to  after  effects  and  not  to  the  immediate 
action  of  the  magnet. 

With  nitric  acid  this  throw  was  always  present  in  greater  or  less 
degree,  and  sometimes  remained  for  some  minutes  as  a  temporary 
deflection,  the  time  varying  from  this  down  to  a  few  seconds.  The 
throw  was  independent  of  direction  of  current  through  the  magnet,  and 
apparently  varied  in  amount  with  the  strength  of  acid  and  with  the 
amount  of  deflection  due  to  the  original  difference  between  the  poles. 
This  latter  fact  simply  means  that  the  effect  produced  by  the  magnet 
is  more  noticeable  as  the  action  on  the  iron  becomes  freer. 

When  a  pair  of  little  plates  exposed  in  the  middle  were  substituted 
for  the  wires,  or  when  the  exposed  point  of  the  latter  was  filed  to  a 
flat  surface,  the  protective  throw  disappeared,  though  it  is  to  be  noted 
that  the  deflection  often  gradually  reversed  in  direction  when  the  cur- 


244  HENRY  A.  EOWLAND 

rent  was  sent  through  the  magnet;  i.  e.,  only  the  latter  part  of  the 
previous  phenomenon  appeared  under  these  circumstances. 

When  the  poles,  instead  of  being  placed  in  the  field  along  the  lines 
of  force,  were  held  firmly  perpendicular  to  them,  the  protective  throw 
disappeared  completely,  though  as  before  there  was  a  slight  reverse 
after-effect. 

Some  of  Professor  Eemsen's  experiments  on  the  corrosion  of  a  wire 
in  strong  nitric  acid  were  repeated  with  the  same  results  as  he  obtained, 
viz.:  the  wire  was  eaten  away  to  the  general  dumb-bell  form,  though 
the  protected  ends  instead  of  being  club-shaped  were  perceptibly  hol- 
lowed. When  the  wire  thus  exposed  was  filed  to  a  sharp  point  the 
extreme  point  was  very  perfectly  protected,  while  there  was  a  slight 
tendency  to  hollow  the  sides  of  the  cone,  and  the  remainder  of  the 
wire  was  as  in  the  previous  experiments.  In  both  cases  the  bars  were 
steel  and  showed  near  the  ends  curious  corrugations,  the  metal  being 
left  here  and  there  in  sharp  ridges  and  points.  In  one  case  the  cylinder 
was  eaten  away  on  sides  and  ends  so  that  a  ridge  of  almost  knife-like 
sharpness  was  left  projecting  from  the  periphery  of  the  ends. 

These  were  the  principal  phenomena  observed  with  nitric  acid. 
Since  this  acid  is  the  only  one  which  attacks  iron  freely  in  the  cold,  in 
Prof.  Eemsen's  experiment,  this  was  the  one  to  which  experiments  were 
in  the  main  confined.  With  the  present  method,  however,  it  was  pos- 
sible to  trace  the  effect  of  the  magnet  whenever  there  was  the  slightest 
action  on  the  iron,  and  consequently  a  large  number  of  substances,  some 
of  which  hardly  produce  any  action,  could  be  used  with  not  a  little  facility. 

In  thus  extending  the  experiments  some  difficulties  had  to  be 
encountered.  In  many  cases  the  action  on  the  iron  was  so  irregular 
that  it  was  only  after  numerous  experiments  under  widely  varying 
conditions  that  the  effect  of  the  magnet  could  be  definitely  determined. 
Frequently  the  direction  of  the  original  action  would  be  reversed  in  the 
course  of  a  series  of  experiments  without  any  apparent  cause,  but  in 
such  case  the  direction  of  the  effect  due  to  the  magnet  remained  always 
unchanged,  uniformly  showing  protection  of  the  point  so  long  as  the 
wires  remained  parallel  to  the  lines  of  force.  When,  however,  the 
original  action  and  the  magnetic  effect  coincided  in  direction,  the  repe- 
tition of  the  latter  showed  a  decided  tendency  to  increase  the  former. 

When  using  solutions  of  various  salts  more  or  less  freely  precipitated 
by  the  iron,  it  frequently  happened  that  the  normal  protective  throw 
was  nearly  or  quite  absent,  but  showed  itself  when  the  magnet  circuit 
was  broken  as  a  violent  throw  in  the  reverse  direction,  showing  that  the 
combination  had  been  acting  like  a  miniature  storage  batterv  which 


ACTION  OF  A  MAGNET  ON  CHEMICAL  ACTION 


245 


promptly  discharged  itself  when  the  charging  was  discontinued  by 
breaking  the  current  through  the  magnet.  The  gradual  reversal  of 
the  current  some  little  time  after  exciting  the  magnet  was  noted  fre- 
quently in  these  cases,  as  before.  Owing  to  this  peculiarity  and  their 
generally  very  irregular  action,  the  various  salts  were  disagreeable  sub- 
stances to  experiment  with,  though  as  a  rule  they  gave  positive  results. 

Unless  the  poles  were  kept  clean  experimenting  became  difficult  from 
the  accumulation  of  decomposition  products  about  them  and  oxidation 
of  their  surfaces.  A  few  experiments  showed  how  easily  the  original 
deflection  could  be  modified,  nearly  annulled  or  even  reversed  in  direc- 
tion by  slight  differences  in  the  condition  of  the  poles.  These  difficul- 
ties of  the  method  are,  however,  more  than  counterbalanced  by  its 
rapidity  and  delicacy  when  proper  precautions  are  taken. 

Xearly  thirty  substances  were  tested  in  the  manner  previously  de- 
scribed; but  comparatively  few  of  them  gave  very  decided  effects  with 
the  magnet,  though,  as  later  experiments  have  shown,  the  protective 
action  is  a  general  one.  The  substances  first  tried  were  as  follows. 
The  table  shows  the  various  acids  and  salts  tried,  and  their  effects  as 
shown  by  the  original  apparatus: 


Substances. 


Effect  due  to 
Magnet. 


Notes. 


Nitric         acid 

Sulphuric    "    

Hydrochloric  acid. 

Acetic 

Formic 

Oxalic 

Tartaric 

Chromic 

Perchloric 

Chloric 

Bromic 

Phosphoric 

Permanganic 

Chlorine  water 

Bromine       (l     

Iodine  " 

Copper  sulphate 

"       nitrate 

"       acetate 

"       chloride 

"       tartrate 

Mercuric  bromide 

"         chloride 

Mercurous  nitrate 

Ferric  chloride 

Silver  nitrate 

Platinum  tetrachloride. 


Strong. 

Little  or  none. 
n  « 

None. 


Some  effect. 
K 

None. 


Slight  effect. 
Decided     " 


Some. 


Slight. 
Some. 


Decided. 
Some. 


Always  powerful  protective  throw. 
Does  not  act  very  readily  on  the  iron. 


Sometimes  quite  distinct  throw,  irregular. 
Much  less  marked  than  with  chromic. 


Hardly  any  effect  on  iron. 
More  than  with  perchloric. 


Mainly  showing  as  throw,  on  breaking. 


Throw,  on  breaking. 

Very  slight  solution,  weak. 

Mainly  as  throw  on  breaking,     [breaking. 

Both  protective  throw,  and  sometimes  on 

Action  very  irregular. 


246  HEXKY  A.  EOWLAND 

Several  things  are  worthy  of  note  in  this 'list.  In  the  first  place 
those  solutions  of  metallic  salts  which  are  precipitated  by  iron  all  show 
distinct  signs  of  protective  action  when  the  current  is  passed  through 
the  magnet.  Of  the  various  acids  this  is  not  generally  true ;  only  those 
show  the  magnetic  effect,  which  act  on  iron  without  the  evolution  of 
hydrogen,  and  are  powerful  oxidizing  agents.  In  general,  substances 
which  acted  without  the  evolution  of  hydrogen  gave  an  effect  with  the 
magnet. 

From  these  experiments  it  was  quite  evident  that  the  protective 
action,  whatever  its  cause,  was  more  general  than  at  first  appeared  and 
steps  were  next  taken  to  extend  it  to  the  other  magnetic  metals.  Small 
bars  were  made  of  nickel  and  cobalt  and  tried  in  the  same  manner  as 
before.  These  metals  are  acted  on  but  very  slightly  by  most  acids,  and 
the  range  of  substances  which  could  be  used  was  therefore  very  small, 
but  all  the  substances  which  gave  the  magnetic  effects  with  iron  poles 
gave  a  precisely  similar,  though  much  smaller  effect,  whenever  they 
were  capable  of  acting  at  all  on  the  nickel  and  cobalt.  This  was  notably 
the  case  with  nitric  acid,  bromine  water,  chlorine  water,  and  platinum 
tetrachloride,  which  were  the  substances  acting  readily  on  the  metals  in 
question.  Even  with  these  powerful  agents,  however,  the  magnetic 
action  was  very  much  less  than  with  iron,  and  experimentation  on 
metals  even  more  weakly  magnetic  was  evidently  hopeless. 

As  a  preliminary  step  toward  ascertaining  the  cause*  of  the  magnetic 
action  and  its  non-appearance  where  the  active  substance  evolved  hydro- 
gen, it  now  became  necessary  to  discover  and  if  possible  eliminate  the 
cause  of  the  reversal  of  the  current  which  regularly  followed  the  protec- 
tive throw.  Experiments  soon  showed  that  it  could  not  be  ascribed  to 
accumulation  of  decomposition  products  around  the  electrodes,  and 
polarization,  while  it  could  readily  neutralize  the  original  deflection, 
could  not  reverse  its  direction.  Whatever  the  cause,  it  was  one  which 
did  not  act  with  any  great  regularity,  and  it  was  soon  found  that  stirring 
the  liquid  while  the  magnet  was  on,  uniformly  produced  the  effect  ob- 
served. Since  one  pole  was  simply  exposed  over  a  small  portion  of  its 
side  while  the  other  had  a  sharp  projecting  point,  it  was  the  latter  which 
was  most  freely  attacked  when  there  were  currents  in  the  liquid,  whether 
these  were  stirred  up  artificially  or  were  produced  by  the  change  in  gal- 
vanic action  due  to  the  presence  of  the  magnet.  AVhen  the  poles  were 
placed  in  fine  sand  saturated  with  acid  this  reversing  action  was  much 
diminished,  and  in  fact  anything  which  tended  to  hinder  free  circulation 
of  the  liquid  produced  the  same  effect.  Several  materials  were  tried  and 


.Acxiox  OF  A  MAGNET  ox  CHEMICAL  ACTION  247 

of  these  the  most  successful  was  an  acidulated  gelatine  which  was 
allowed  to  harden  around  the  poles.  In  this  case  the  protective  throw 
was  not  nearly  as  large  as  in  the  free  acid,  since  the  electrodes  tended 
to  become  polarized  while  the  gelatine  was  hardening,  and  only  weakly 
acid  gelatine  would  harden  at  all;  but  the  reversing  action  completely 
disappeared,  so  that,  when  the  magnet  was  put  on,  a  permanent  deflec- 
tion was  produced  instead  of  a  transitory  throw. 

This  point  being  cleared  up  attention  was  next  turned  to  the  negative 
results  obtained  with  acids  which  attack  iron  with  evolution  of  hydro- 
gen. The  galvanometer  was  made  much  more  sensitive  and  removed 
from  any  possible  disturbing  action  due  to  the  magnet;  and  with  these 
precautions  the  original  experiments  were  repeated,  it  seeming  probable 
that  even  if  the  magnetic  effect  were  virtually  annulled  by  the  hydrogen 
evolved,  some  residual  effect  might  be  observed. 

This  residual  effect  was  soon  detected,  first  with  hydrobromic  acid, 
and  then  with  hydrochloric,  hydriodic,  sulphuric  and  others.  The 
strongest  observed  effect  was  with  hydriodic  acid,  but  as  this  may  pos- 
sibly have  contained  traces  of  free  iodine  it  may  be  regarded  as  some- 
what doubtful.  The  effect  in  all  these  cases  was  very  small,  and  though 
now  and  then  suspected  in  the  previous  work,  could  not  have  been 
definitely  determined,  much  less  measured. 

Some  rough  measurements  were  made  on  the  electromotive  forces 
involved  in  this  class  of  phenomena  by  getting  the  throw  of  the  galvano- 
meter for  various  small  known  values  of  the  E.  M.  F.  The  values  found 
varied  greatly,  ranging  from  less  than  0-0001  volt  in  case  of  the  acids 
evolving  hydrogen,  up  to  0-02  or  0-03  volts  with  nitric  acid  and  certain 
salts.  These  were  the  changes  produced  by  the  magnet,  while  the 
initial  electromotive  forces  normally  existing  between  the  poles  would 
be,  roughly  speaking,  from  0-0001  to  nearly  0-05  volts,  never  disappear- 
ing and  rarely  reaching  the  latter  figure. 

From  these  experiments  it  therefore  appears  that  the  protective 
action  of  the  magnetic  field  is  general,  extending  to  all  substances  which 
act  chemically  on  the  magnetic  metals.  While  this  is  so,  the  strongest 
effect  is  obtained  with  those  substances  which  act  without  the  evolution 
of  hydrogen.  But  the  series  is  really  quite  continuous,  perchloric  acid 
for  instance  producing  but  little  more  effect  than  hydrobromic,  while 
this  in  turn  differs  less  from  perchloric  than  from  an  acid  like  acetic. 
It  seems  probable  that  the  action  of  the  hydrogen  evolved  is  partially 
to  shield  the  pole  at  which  it  is  evolved,  and  lessen  the  difference  be- 
tween the  poles  produced  by  the  magnet.  It  probably  acts  merely 


248  HENRY  A.  BOWLAND 

mechanically,  for  it  is  to  be  noted  that  those  acids  which  evolve  a  gas 
other  than  hydrogen  (perchloric  acid,  for  instance),  which  is  not  ab- 
sorbed by  the  water,  tend  to  produce  little  magnetic  effect  compared 
with  those  which  act  without  the  evolution  of  any  gas. 

As  to  the  actual  cause  of  the  protective  action  exercised  by  the  mag- 
netic field,  all  these  experiments  go  to  show  that  it  is  quite  independent 
of  the  substance  acting,  with  the  exception  above  noted,  and  is  probably 
due  to  the  attractive  action  of  the  magnet  on  the  magnetic  metals 
forming  the  poles  subjected  to  chemical  action,  as  we  have  before 
explained. 

In  the  first  place,  whenever  iron  is  acted  upon  chemically  in  a  mag- 
netic field  those  portions  of  it  about  which  the  magnetic  force  varies 
most  rapidly  are  very  noticeably  protected,  and  this  protection  as  nearly 
as  can  be  judged  varies  very  nearly  with  the  above  quantity.  Wherever 
there  is  a  point  there  is  almost  complete  protection,  and  wherever  there 
is  a  flat  surface,  no  matter  in  how  strong  a  field,  it  is  attacked  freely. 
Whenever  in  the  course  of  the  action  there  is  a  point  formed,  the  above 
condition  is  satisfied  and  protection  at  once  appears.  Thus,  in  the 
steel  bars  experimented  on,  whenever  the  acid  reached  a  spot  slightly 
harder  than  the  surrounding  portions  it  produced  a  little  elevation  from 
which  the  lines  of  force  diverged,  and  still  further  shielding  it  produced 
a  ridge  or  point,  sharp  as  if  cut  with  a  minute  chisel.  Mckel  and 
cobalt  tend  to  act  like  iron,  though  they  are  attacked  with  such  diffi- 
culty that  the  phenomena  are  much  less  strongly  marked.  With  the 
non-magnetic  metals  they  are  completely  absent.  Now,  turning  to  the 
experiments  with  the  wires  connected  with  a  galvanometer,  the  same 
facts  appear  in  a  slightly  different  form. 

When  the  poles  were  placed  perpendicular  to  the  lines  of  force  instead 
of  parallel  to  them,  the  magnet  produced  no  effect  whatever,  showing, 
first,  that  the  effect  previously  observed  depended  not  merely  on  the 
existence  of  magnetic  force  but  on  its  relation  to  the  poles,  and,  sec- 
ondly, that  when  the  poles  were  so  placed  as  to  produce  little  deflection 
of  the  lines  of  force  the  protective  effect  disappeared. 

When  the  pointed  pole  was  blunted  the  effect  practically  disappeared, 
the  poles  remaining  parallel  to  the  lines  of  force,  and  when  plates  were 
substituted  for  the  wires  no  effect  was  produced  in  any  position,  show- 
ing that  the  phenomena  were  not  due  to  the  directions  of  magnetization 
but  to  the  nature  of  the  field  at  the  exposed  points.  In  short,  whatever 
the  shape  or  arrangement  of  the  exposed  surfaces,  if  at  any  point  or 
points  the  rate  of  variation  of  the  square  of  the  magnetic  force  is 


ACTION  OF  A  MAGNET  ox  CHEMICAL  ACTION  249 

greater  than  elsewhere,  such  points  will  be  protected,  while  if  the  force 
is  sensibly  constant  over  the  surfaces  exposed  there  will  be  no  protection 
at  any  point.  With  all  the  forms  of  experimentation  tried  this  law 
held  without  exception.  It  therefore  appears  that  the  particles  of 
magnetic  material  on  which  the  chemical  action  could  take  place  are 
governed  by  the  general  law  of  magnetic  attraction  and  are  held  in 
place  against  chemical  energy  precisely  as  they  would  be  held  against 
purely  mechanical  force.  To  sum  up: 

When  the  magnetic  metals  are  exposed  to  chemical  action  in  a 
magnetic  field  such  action  is  decreased  or  arrested  at  any  points  where 
the  rate  of  variation  of  the  square  of  the  magnetic  force  tends  toward 
a  maximum. 

It  is  quite  clear  that  the  above  law  expresses  the  facts  thus  far 
obtained,  and  while  in  any  given  case  the  action  of  the  magnet  is  often 
complicated  by  subsidiary  effects  due  to  currents  or  by-products,  the 
mechanical  laws  of  motion  of  particles  in  a  magnetic  field  hold  here  as 
elsewhere  and  cause  the  chemical  action  to  be  confined  to  those  points 
where  the  magnetic  force  is  comparatively  uniform. 

The  effect  of  currents  set  up  in  the  liquid  during  the  action  of  the 
magnet  cannot  be  disregarded  especially  in  such  experiments  as  those 
of  Xichols  (this  Journal,  xxxi,  272,  1886)  where  the  material  acted  on 
was  powdered  iron  and  the  disturbances  produced  by  the  magnet  would 
be  particularly  potent.  The  recent  experiments  of  Colardeau  (Journal 
de  Physique,  March,  1887)  while  perhaps  neglecting  the  question  of 
direct  protection  of  the  poles,  have  furnished  additional  proof  of  the 
purely  mechanical  action  of  the  magnet  by  reproducing  some  of  the 
characteristic  phenomena  where  chemical  action  was  eliminated  and 
the  only  forces  acting  were  the  ordinary  magnetic  attractions. 

An  attempt  was  made  to  reverse  the  magnetic  action,  i.  e.  to  deposit 
iron  in  a  magnetic  field  and  increase  its  deposition  where  there  was  a 
sharp  pole  immediately  behind  the  plate  on  which  the  iron  was  being 
deposited.  This  attempt  failed.  The  action  was  very  irregular  and  the 
results  not  decisive.  The  question  of  stirring  effect  was  also  examined. 
Usually  stirring  the  liquid  about  one  pole  increased  the  action  on  that 
pole,  but  sometimes  produced  little  effect  or  even  decreased  it.  This 
however  is  in  entire  agreement  with  the  irregular  action  sometimes 
observed  in  the  case  of  the  after-effect  in  the  original  experiments. 

An  excellent  method  of  experiment  is  to  imbed  an  iron  point  in  wax 
leaving  the  minute  point  exposed:  imbed  a  flat  plate  also  in  wax  and 
expose  a  point  in  its  centre.  Place  the  point  opposite  to  the  plate,  but 


250  HENRY  A.  EOWLAND 

not  too  near  and  place  in  the  liquid  between  the  poles  of  a  magnet  and 
attach  to  the  galvanometer  as  before. 

There  is  a  wide  field  for  experiment  in  the  direction  indicated  above, 
for  it  is  certainly  very  curious  that  the  effect  varies  so  much.  If  hydro- 
gen were  as  magnetic  as  iron,  of  course  acids  which  liberated  it  would 
have  no  action.  But  it  is  useless  to  theorize  blindly  without  further 
experiment;  and  we  are  drawn  off  by  other  fields  of  research. 

In  this  Journal  for  1886,  (1.  c.)  Professor  E.  L.  Nichols  has  investi- 
gated the  action  of  acids  on  iron  in  a  magnetic  field.  He  remarks  that 
the  dissolving  of  iron  in  a  magnetic  field  is  the  same  as  removing  it  to 
an  infinite  distance  and  hence  the  amount  of  heat  generated  by  the 
reaction  should  differ  when  this  takes  place  within  or  without  the 
magnetic  field.  Had  he  calculated  this  amount  of  heat  due  to  the 
work  of  withdrawing  it  from  the  field,  he  would  probably  have  found 
his  method  of  experiment  entirely  too  rough  to  show  the  difference,  for 
it  must  be  very  small.  He  has  not  given  the  data,  however,  for  us  to 
make  the  calculation.  The  results  of  the  experiments  were  inconclu- 
sive as  to  whether  there  was  greater  or  less  heat  generated  in  the  field 
than  without. 

In  the  same  Journal  for  December,  1887,  he  describes  experiments 
on  the  action  of  the  magnet  on  the  passive  state  of  iron  in  the  magnetic 
field.  In  a  note  to  this  paper  and  in  another  paper  in  this  Journal  for 
April,  1888,  he  describes  an  experiment  similar  to  the  one  in  this  paper 
but  without  our  theory  with  regard  to  the  action  of  points.  Indeed 
he  states  that  the  ends  of  his  bars  acted  like  zinc,  while  the  middle  was 
like  platinum,  a  conclusion  directly  opposite  to  ours.  The  reason  of  this 
difference  has  been  shown  in  this  paper  to  be  probably  due  to  the  cur- 
rents set  up  in  the  liquid  by  the  reaction  of  the  magnet  and  the  electric 
currents  in  the  liquid. 

In  conclusion  we  may  remark  that  our  results  differ  from  Professor 
Nichols  in  this:  First,  we  have  given  the  exact  mathematical  theory 
of  the  action  and  have  confirmed  it  by  our  experiments,  having  studied 
and  avoided  many  sources  of  error,  while  Professor  Nichols  gives  no 
theory  and  does  not  notice  the  action  of  points.  Secondly,  our  experi- 
ments give  a  protective  action  to  the  points  and  ends  of  bars,  while 
Professor  Nichols  thinks  the  reverse  holds  and  that  these  are  more 
easily  dissolved  than  unmagnetized  iron. 


43 

ON  THE  ELECTROMAGNETIC  EFFECT  OF  CONVECTION- 
CURRENTS 

BY  HENRY  A.  ROWLAND  AND  CABY  T.  HUTCHINSOX 
[Philosophical  Magazine  [5],  XXVII,  445-460,  1889] 

The  first  to  mention  the  probable  existence  of  an  effect  of  this  kind 
was  Faraday/  who  says : — "  If  a  ball  be  electrified  positively  in  the 
middle  of  a  room  and  then  be  moved  in  any  direction,  effects  will  be 
produced  as  if  a  current  in  the  same  direction  had  existed."  He  was 
led  to  this  conclusion  by  reasoning  from  the  lines  of  force. 

Maxwell,  writing  presumably  in  1872  or  1873,  outlines  an  experi- 
ment, similar  to  the  one  now  used,  for  the  proof  of  this  effect. 

The  possibility  of  the  magnetic  action  of  convection-currents  occurred 
to  Professor  Rowland  in  1868,  and  is  recorded  in  a  note-book  of  that 
date. 

In  his  first  experiments,  made  in  Berlin  in  1876,  Prof.  Rowland  used 
a  horizontal  hard  rubber  disk,  coated  on  both  sides  with  gold,  and 
revolving  between  two  glass  condenser-plates.  Each  coating  of  the 
disk  formed  a  condenser  with  the  side  of  the  glass  nearer  it;  the  two 
sides  of  the  disk  were  charged  to  the  same  potential.  The  needle  was 
placed  perpendicular  to  a  radius,  above  the  upper  condenser-plate,  and 
nearly  over  the  edge  of  the  disk.  The  diameter  of  the  hard  rubber 
disk  was  21  cm.,  and  the  speed  61  per  second. 

The  needle  system  was  entirely  protected  from  direct  electrostatic 
effect.  On  reversing  the  electrification,  deflexions  of  from  5  to  7-5 
mm.  were  obtained,  after  all  precautions  had  been  taken  to  guard 
against  possible  errors.  Measurements  were  made,  and  the  deflexions 
as  calculated  and  observed  agreed  quite  well;  but  it  was  not  possible  to 
make  the  measurements  with  as  great  accuracy  as  was  desired,  and 
hence  the  present  experiment. 

Helmholtz,2  in  1875  and  later,  carried  out  some  experiments  bearing 

i  Experimental  Researches,  vol.  i,  art.  1644.  *Wiss.  Abh.  i,  p.  778. 


252  HEXRY  A.  EOWLAXD 

on  this  subject.  According  to  the  "  potential  theory "  of  electrody- 
namics which  he  wished  to  test,  unclosed  circuits  existed.  The  end  of 
one  of  these  open  circuits  would  exert  an  action  on  a  close  magnetic  or 
electric  circuit.  So  the  following  experiment  was  made  by  M.  Schiller,3 
under  his  direction. 

A  closed  steel  ring  was  uniformly  magnetized,  the  magnetic  axis  coin- 
ciding with  the  mean  circle  of  the  ring.  This  was  hung  by  a  long  fibre 
and  placed  in  a  closed  metal  case.  A  point  attached  to  a  Holtz  machin.j 
was  fixed  near  the  box,  and  a  brush-discharge  was  kept  up  from  this 
point.  If  the  point  acted  as  a  current-end,  a  deflexion  would  be  ex 
pected,  on  the  potential  theory.  No  deflexion  was  observed,  although 
the  calculated  deflexion  was  23  scale-divisions.  The  inference  is  tha', 
either  the  potential  theory  is  untrue,  or  else  that  there  is  no  unclosed 
circuit  in  this  case,  i.  e.  that  the  convection-currents  completing  the 
circuit  have  an  electromagnetic  effect. 

Schiller's  further  work,  not  bearing  directly  upon  convection-cur- 
rents, leads  him  to  the  conclusion  that  all  circuits  are  closed,  and  that 
displacement-currents  have  an  electromagnetic  effect. 

Dr.  Lecher  is  reported  to  have  repeated  Professor  Eowland's  experi- 
ment, with  negative  results.  His  paper  has  not  been  found. 

Rontgen*  has  discovered  a  similar  action;  he  rotates  a  dielectric  disk 
between  the  enlarged  plates  of  a  horizontal  condenser  and  gets  a  de- 
flexion of  his  needle.  He  apparently  guards  against  the  possibility  of 
this  being  due  to  a  charge  on  his  disk.  A  calculation  of  the  force  he 
measures  shows  it  to  be  almost  one-eighth  of  that  in  the  Berlin  experi- 
ment. His  apparatus  is  not  symmetrically  arranged,  the  disk  being 
much  closer  to  the  upper  condenser-plate;  the  distances  from  the  upper 
and  lower  plates  are  0-14  and  0-25  cm.  respectively.  He  uses  a 
difference  of  potential  corresponding  to  a  spark-length  of  0-3  cm. 
in  air  between  balls  of  2  cm.  diameter,  i.  e.  about  33  electrostatic 
units,  equal  to  the  sparking  potential  between  plane  surfaces  :  t  0-26 
cm.  The  disk  is  an  imperfect  conductor,  and  altogether  it  does  not 
seem  clear,  in  spite  of  the  precautions  taken,  that  this  is  not  diu-  to 
convection-currents. 

In  the  Berlin  apparatus,  as  stated  above,  the  needle  is  near  the  edge 
of  the  disk;  the  magnetic  effect  produced  is  assumed  to  be  proportional 
to  the  surface-density  multiplied  by  the  linear  velocity;  hence  the  force 
will  be  much  greater  at  the  edge  of  the  disk  than  near  the  centre :  but 

3Pogg.  Ann.  clix,  p.  456.  * Sitzb.  d.  Berl.  Akad.,  Jan.  19,  1888. 


PLATE  V 


ELECTROMAGNETIC  AFFECT  OF  COXVECTIOX-CURREXTS         253 

the  iield  will  be  more  irregular,  and  so  make  accurate  measurements 
more  difficult. 

In  the  present  apparatus  a  uniform  field  is  secured  by  using  two 
vertical  disks  rotating  about  horizontal  axes  in  the  same  line;  the  needle 
sy.-tcin  is  placed  between  the  disks,  opposite  their  centres.  The  disk? 
are  in  the  meridian;  they  are  gilded  on  the  faces  turned  towards  the 
needle.  Between  the  disks  are  placed  two  glass  condenser-plates  gilded 
on  the  surfaces  near  the  disk;  and  between  these  glasses  is  the  needle. 
The  whole  apparatus  is  symmetrical  about  the  lower  needle  of  the 
astatic  system. 

Each  disk  is  surrounded  by  a  gilded  hard  rubber  guard-plate  in  order 
to  keep  the  density  of  the  charge  uniform  at  the  edges.  The  guard- 
plates  are  provided  with  adjusting-screws  to  enable  them  to  be  put 
accurately  in  the  plane  of  the  disks;  and  the  glass  plates  in  turn  have 
adjusting-screws  for  securing  parallelism  with  the  guard-plates.  The 
glass  was  carefully  chosen  as  being  nearly  plane.  Disks,  glass  plates, 
and  guard-plates  all  have  radial  scratches,  to  prevent  conduction-cur- 
rents from  circulating  around  the  coatings. 

In  the  periphery  of  the  disk  are  set  eight  brass  studs  which  pene- 
trate radially  for  about  5  centim.,  then  turning  off  at  a  right  angle  run 
parallel  to  the  axis  until  they  come  out  on  the  surface  of  the  disks. 
They  there  make  contact  with  the  gold  foil.  Metal  brushes  set  in  the 
guard-plate  bear  on  these  studs,  and  in  this  way  the  disks  are  electrified. 

The  figure  (PI.  V,  Fig.  1)  gives  a  vertical  projection  of  the  entire 
disk-apparatus : — D  D  are  the  disks ;  G  G  G  G  the  guard-rings ;  Y  Y  Y  Y 
the  condenser-plates ;  R  R  R  R  hard  rubber  rings  fitting  on  the  should- 
ers A  A;  X  X  X  X  bearing-boxes  for  the  axle;  P  P  P  P  supporting- 
standards  ;  E  E  metal  bases  sliding  in  the  bed  B  B,  and  held  in  any 
position  by  screws  Z ;  F  F  the  bases  carrying  the  glass  plates,  sliding  in 
the  same  way  as  the  others.  S  S  S  8  are  the  adjusting-screws  for  the 
guard-plates,  and  1 1  for  the  glass  plates.  L  L  L  L  are  collars  for  catch- 
ing the  oil  from  the  bearings;  C  C,  C'  C'  are  speed-counters,  C  C  gear 
with  the  axle,  and  C'  C'  with  C  C  in  the  manner  shown;  each  has  200 
teeth,  and  speed-reading  is  taken  every  40,000  revolutions. 

The  needle  system  is  enclosed  in  the  brass  tube  T,  ending  in  the 
larger  cylindrical  box  in  which  are  the  mirror  and  upper  needle.  This 
is  closed  in  by  the  conical  mouth-piece  Q,  across  the  opening  of  which 
is  ] daced  a  wire  grating.  The  mirror  is  shown  at  M,  the  upper  needle 
at  y  and  the  lower  at  N.  The  system  is  hung  by  a  fibre-suspension 
about  30  <?m.  in  length,  protected  by  a  glass  tube.  The  needle- 


25-1  HENEY  A.  EOWLAND 

system  is  made  by  fitting  two  small  square  blocks  of  wood  on  an  alumi- 
nium wire;  on  two  sides  of  each  of  the  wooden  blocks  are  cemented 
small  scraps  of  highly  magnetized  watch-spring.  The  needle  thus  made 
is  about  1  X  1  X  10  mm. 

The  mirror  is  fixed  just  below  the  upper  needle,  and  is  read  by  a 
telescope  200  cm.  distant.  The  plane  of  the  mirror  is  at  an  angle 
of  45°  with  the  plane  of  the  disks  for  convenience.  The  whole  is  sup- 
ported by  the  board  00  attached  to  a  wall -bracket. 

Two  controlling  magnets  (W  W)  with  their  poles  turned  in  opposite 
directions  are  used.  By  means  of  the  up  and  down  motion  of  either 
magnet,  any  change  in  the  sensitiveness  can  be  attained;  and  by  the 
motion  in  azimuth,  the  zero  point  is  controlled.  The  advantage  of  its 
use  lies  in  the  extremely  delicate  means  it  affords  of  changing  the 
sensitiveness,  much  more  delicate  than  with  a  single  magnet. 

The  bed-plate  B  is  screwed  to  one  end  of  a  table,  at  the  other  end  of 
which  a  countershaft  is  placed  (Fig.  2).  This  is  run  by  an  electric 
motor  in  the  next  room,  the  belt  running  through  the  open  doorway. 
The  motor  is  14  metres  from  the  needle. 

Although  the  disks  and  countershaft  were  carefully  balanced  when 
first  set  up,  and  the  table  braced  and  weighted  by  a  heavy  stone  slab, 
yet  at  the  speed  used,  125  per  second,  the  shaking  of  the  entire  appar- 
atus was  considerable;  the  needle  was  so  unsteady  that  it  could  not  be 
read.  This  was  seen  to  be  due  to  vibrations  of  the  telescope  itself  and 
not  to  the  needle.  To  prevent  it,  each  leg  of  the  table  on  which  the 
telescope  rested  was  set  in  a  box  about  30  cm.  deep  filled  with  saw- 
dust, and  a  heavy  stone  slab  was  placed  on  top  of  this  table.  This 
entirely  did  away  with  the  trouble;  the  swing  of  the  needle  was  as 
regular  when  the  apparatus  was  revolving  as  when  it  was  at  rest. 

The  two  hard  rubber  rings  (RR)  mentioned  above  have  grooves  cut 
in  their  peripheries ;  in  these  grooves  wires  are  wound.  These  serve  as 
a  galvanometer  for  determining  the  needle-constant.  When  not  in  use 
they  are  held  in  the  position  shown  in  the  figure,  but  when  it  is  desired 
to  determine  the  needle-constant  they  are  slipped  on  the  shoulders 
(AAAA)  and  pushed  up  in  contact  with  the  back  of  the  disks.  Each 
has  two  turns:  this  arrangement  will  be  referred  to  as  the  disk- 
galvanometer. 

If  a  known  current  is  sent  through  the  disk-galvanometer,  and  the 
geometrical  constant  be  known,  the  part  of  the  constant  depending  on 
the  field  and  needle  is  determined. 

The  current  is  measured  by  a  sine-galvanometer,  placed  in  another 


ELECTRON AGXETIC  EFFECT  OF  COXYECTIOX-CURREXTS         •.*•'>•"> 

part  of  the  room.  To  determine  H  at  the  sine-galvanometer  a  metre 
brass  circle  is  put  around  the  sine-galvanometer,  and  the  needle  of  the 
latter  used  as  the  needle  of  the  tangent-galvanometer  thus  made. 
I- ing  this  tangent-glavanometer  in  connection  with  a  Weber  electro- 
dynamometer,  H  at  the  sine-galvanometer  is  measured. 

The  charging  was  by  a  Holtz  machine  connected  to  a  battery  of  six 
gallon  Leyden  jars.  These  latter  are  in  circuit  with  a  reversing-key, 
an  electrostatic  gauge,  and  the  disks. 

The  potential  was  measured  by  a  large  absolute  electrometer;  all 
previous  observers  have  used  spark-length  between  balls,  with  Thom- 
son's formula.  Greater  accuracy  is  claimed  for  this  work,  largely  on 
this  account. 

In  this  instrument  the  movable  plate  is  at  one  end  of  a  balance-arm, 
from  the  other  end  of  which  hangs,  on  knife-edges,  a  balance-pan. 
This  movable  plate  is  surrounded  by  a  guard-ring. 

The  lower  plate  is  fixed  by  an  insulating  rod  to  a  metal  stem,  which 
slides  up  and  down  in  guides.  The  distances  are  read  off  on  a  scale  on 
the  metal  stem.  The  zero  reading  is  got  by  inserting  a  piece  of  plane 
parallel  glass  whose  thickness  has  been  measured.  The  lower  plate  and 
<riiard-ring  have  a  diameter  of  35  cm.,  and  the  movable  disk  a  diameter 
of  10  cm. 

The  routine  of  the  observations  was  as  follows: — A  determination 
of  H  and  the  needle-constant  (/?)  was  first  made.  The  electrostatic 
gauge  was  then  set  at  a  certain  point,  and  readings  of  difference  of 
potential  were  taken.  The  disks  were  now  started,  electrified,  and  a 
series  of  three  elongations  of  the  needle  taken;  the  electrification  re- 
versed and  three  more  elongations  taken,  &c. 

About  every  five  minutes  speed-readings  had  to  be  noted,  and  at  each 
reversal  it  was  necessary  to  replenish  the  charge  in  order  to  keep  the 
gauge-arm  just  at  the  mark.  In  this  way  a  '  series '  of  readings  con- 
sisting of  about  25  reversals  was  made.  After  the  series,  electrometer 
readings  were  again  taken;  the  conditions  were  then  changed  in  some 
way.  and  another  series  begun. 

The  circumstances  to  be  changed  are : — distance  of  disks  from  needle ; 
distance  of  glass  plates  from  needle;  electrification;  and  direction  of 
rotation. 

The  calculation  of  the  deflexion  is  based  on  the  assumption  that  the 
magnetic  effect  of  a  rotating  charge  is  proportional  to  the  quantity  of 
electricity  passing  any  point  per  second,  just  as  with  a  conduction- 
current.  Below  are  the  formulae  used. 


256  HEXEY  A.  ROWLAND 

In  the  equations  the  letters  have  the  following  meanings.     All  quan- 
tities are  given  in  terms  of  C.  G.  S.  units. 

X=  Distance  from  centre  of  disk  to  lower  needle. 
r  =  Distance  from  centre  of  disk  to  upper  needle. 
c  =  Radius  of  disk. 
I  =  Distance  between  needles. 
a  =  Radius  of  windings  of  disk-galvanometer. 
i  =  Distance,  centre  of  disk-galvanometer  to  lower  needle. 
p  =  Distance,  centre  of  disk-galvanometer  to  upper  needle. 
N  =  Number  of  revolutions  per  second. 

a  =  Surface-density  of  electrification  in  electrostatic  measure. 
V=  Ratio  of  the  units. 

a  =  Angle  of  torsion  of  the  electro-dynamometer. 
<f>  =  Angle  of  deflexion  of  sine-galvanometer. 
8  =  Angle  of  deflexion  of  tangent-galvanometer. 
J  =  Change  of  zero-point  on  electrifying  the  disks  =  half  the  charge 

on  reversing. 

*  =  Scale-reading  for  disk-galvanometer. 
w  =  Weight  on  pan  of  electrometer. 
D  =  Distance  of  glass  plates  and  disks. 
^  =  Electrometer  reading, 
z  =  Condenser  distance. 

Force,  in  the  direction  of  the  axis,  due  to  a  circular  current  of  radius 
c,  at  a  distance  x  on  the  axis 


Strength  of  convection-current 

NT 

.'.  total  force  due  to  the  disk  of  radius  c 


_4 ^  _  _- 

~       ~V 


and  for  the  two  disks  acting  in  the  same  direction,  total  force 

T_Q_2  Na  A 
V  A' 

This  gives  the  force  on  the  lower  needle. 


ELECTROMAGNETIC  EFFECT  OF  CONVECTION-CURRENTS         257 

Correction  for  the  upper  needle  : 

Potential  at  any  point  due  to  a  circular  current, 

V'=  Cldw, 
equals  the  solid  angle  subtended  at  the  point  by  the  circle 


Substituting  the  value  of  /,  we  have  as  the  potential  of  the  disk 

'*  * 


a.  4..  .81      1M 

/_v  1.3...(2i-l)    p      /c\"l 

(   ;a.4...2Ha*+2)       W  J 

But 


and 

8  p  _»' 

&ft 

.'.  The  force 


f  _atc". 
\      ~^^ 


and  for  the  two, 


where  the  sign  of  the  entire  expression  has  been  changed,  since  the 
poles  of  the  upper  and  lower  needles  are  opposite. 
Or 


X_Q_»         *    Z? 
i  —  or.  —  ^. 


17 


258  HENRY  A.  KOWLAND 

Needle  —  constant. 

The  disk-galvanometer  windings  have  in  the  same  way,  for  the  lower 
needle,  the  force  due  to  current  I  in  one  turn 


For  the  four  turns, 

X'=8-/<7. 

Upper  needle.  —  The  force  is  got  in  the  same  way  as  for  the  disk,  omit- 
ting the  integration,  i.  e.  we  must  multiply  the  general  term  of  B  by 


_       and  replace  2*        by  /.    This  gives 

CL  V 

yfil.3...(a»-l)2»Y«\Mp   1. 

"       2.4  ...  at     7  W  ^  /  ' 


a  replacing  c,  and  p,  r. 
For  the  total  force, 


,_8^/rp/av_3p/«Y      n 

l  -    -  r  1  \~  \  —  •J-f^4  I  ~   I  T«.»  • 

p  L    w          \^/        J 


or 


Forces  acting  on  the  needle  system:  — 

Let  M  =  moment  of  lower  needle, 
Let  M'  =  moment  of  upper  needle, 
then 

Couple  on  lower  needle  due  to  field  =      H  M  sin  6, 

Couple  on  upper  needle  due  to  field  =  —  H'M'  sintf. 

Total  couple  =  (EM  —H'M')  sin  6. 

Due  to  disk-galvanometer: 

Couple  on  lower  needle  =  MX'  cos  6, 
Couple  on  upper  needle  =  M'  X^'  cos#. 

Total  couple     =  {  MX'  +  M'XJ  }cos  6, 

=  S7iI\MC  +  M'D  \cos0. 
.:  for  equilibrium, 

S-I\MO  +  M'D\  cos  6  =  \HM-  H'M'}  sin  fl, 
or 

__  (HM-  H'M'}  tan  e 


ELECTROMAGNETIC  EFFECT  OF  CONVECTION-CURRENTS         259 

n  ]u-t 

But  =,  =  0-03  nearly,  and  -^  is  approximately  unity.  . 

.   I==(HM-H'_M^^0 

8nM(C  +  Z>) 
or 

-f '-  •=.  -—± 1 1—  3  (say) . 

M  tan  o 

Similarly,  for  the  revolving  disks, 


=  /?  tan  J. 

8    ,  ^    ^ 

^_  O'<-     —  T^~    —  '  -  <  —  • 

F     /?.  J 


For  the  sine-galvanometer: 


TT 

I  =  —  sin  <p. 


/.  7=10-*  5-46  ZTsin  f, 
and 

/5  =  10-*.  5-46 


tan  P 

For  measurement  of  H  :  — 
Electrodynamometer, 


ls=0-zjr   V  sin  a. 

^  =  constant  of  windings  =  10~3.  6'454. 
K-  moment  of  inertia       =  102.  8-266. 
T=  time  of  one  swing        =2-441. 
.-.    i  =  10~2.  7-59  Vsin  «. 

Tangent  galvanometer:  — 

i  =  |C  tan  d  =  ^  tan  8  . 
0  2-w 

n  =  no.  turns       =  10. 
b  =  radius  turns  =  49-98. 
.-.    t  =  0-795  JJ  tan  d, 

and,  substituting  the  value  of  t, 

JI=10-'.  9-55  £***. 
tan  d 


260  HENRY  A.  KOWLAND 

Surface  density  (a): — 

a  is  obtained  from  electrometer-readings. 

V 


V  —  *-f  i/  — 

A 

A  =  corrected  area  of  movable  plate 
f=*r{5im 


.:   V  =  10  X  1'756  D  iJ~uT, 

and  ff  =  1-397  -  VaT. 

e  ' 

As  soon  as  the  attempt  was  made  to  electrify  the  apparatus,  diffi- 
culties of  insulation  were  met  with.  The  charged  system  was  quite 
extensive,  and  the  opportunity  for  leakage  was  abundant;  in  addition, 
the  winter  here  has  been  very  damp.  Most  of  the  trouble  of  this  kind 
has  been  due  to  the  glass  in  the  apparatus;  in  no  case  where  glass  was 
used  as  an  insulator  has  it  proved  satisfactory,  not  even  when  the  air 
was  dry.  First,  the  stand  with  glass  legs,  on  which  the  Ley  den- jar 
battery  was  placed,  was  found  to  furnish  an  excellent  earth-connection. 

Paraffin  blocks  interposed  stopped  this.  The  reversing-key  had 
three  glass  rods  in  it,  all  of  which  were  found  to  leak ;  six  different  spec- 
imens of  glass,  some  bought  particularly  for  this  as  insulating  glass, 
were  all  found  to  allow  great  leakage.  Shellacing  had  no  effect.  Hard 
rubber  was  finally  substituted  for  glass ;  and  after  that  the  key  insulated 
very  well,  even  in  damp  weather. 

On  charging  the  glass  plates,  the  disks  being  earthed,  it  seemed 
almost  as  if  there  was  a  direct  earth-connection,  so  rapid  was  the  fall  of 
the  charge.  This  was  not  regarded  at  the  time,  as  the  plates  were 
always  kept  earthed ;  but  later,  when  it  became  necessary  to  charge  the 
plates,  the  insulation  had  to  be  made  good. 

Investigation  showed  that  this  was  caused  by  leakage  directly  through 
the  substance  of  the  glass  to  the  brass  back-pieces  (H  H).  Hard  rubber 
pieces  were  substituted,  and  the  trouble  was  entirely  removed. 

There  was  at  first  a  deflexion  in  reversing  the  electrification  while 
the  disks  were  at  rest.  This  was  of  course  due  to  direct  electrostatic 
effect;  but  it  was  not  for  some  time  clear  where  the  point  of  weakness 
in  the  electrostatic  screen  lay.  It  was  found  to  be  the  faulty  contact 
between  the  tinfoil  covering  of  the  glass  tube  and  the  brass  collar;  the 
brass  had  been  lacquered.  After  this  was  corrected  there  was  never 


ELECTROMAGNETIC  EFFECT  OF  COXVECTION-CUKRENTS         261 

again  any  deflexion  on  reversing  the  charge,  although  the  precaution 
was  taken  of  testing  it  every  day  or  so. 

The  currents  induced  in  the  axle  by  the  rotation  caused  no  incon- 
venience; if  the  disks  are  rotated  in  the  same  direction  their  effect  is 
added,  while  the  effect  of  the  axles  is  in  opposite  directions.  Even 
when  the  disks  were  rotated  oppositely,  the  deflexion  due  to  the  axles 
was  only  3  or  4  cm.,  and  remained  perfectly  constant. 

On  running  the  disks,  unelectrified,  without  the  glass  plates  between 
them  and  the  needle,  a  deflexion  of  4  or  5  cm.  was  noticed.  This  was 
perfectly  steady  deflexion,  and  could  easily  be  shown  to  be  due  to  the 
presence  of  the  plate,  as  it  ceased  when  the  plates  were  replaced. 

This  was  very  troublesome  for  a  time,  especially  as  the  presence  of  a 
brass  plate  in  place  of  the  glass  was  found  to  diminish  the  deflexion, 
but  did  not  bring  the  needle  back  to  zero  as  the  glasses  did.  On  look- 
ing at  the  figure  (Plate  Y,  Fig.  1)  it  will  be  seen  that  there  is  a  brass 
plug  (/)  closing  the  bottom  of  the  tube  in  which  the  needle  is  placed. 
The  rapid  rotation  of  the  disks  caused  a  very  appreciable  exhaustion 
at  the  centre,  and  consequently  a  steady  stream  of  air  was  sucked  down 
the  tube  through  the  open  mouthpiece,  and  out  through  the  imperfect 
connection  of  the  plug.  Air-currents  were  not  at  first  suspected,  as  the 
deflexion  was  so  very  steady.  The  brass  plate  used  was  smaller  than 
the  glass,  and  hence  did  not  completely  shield  the  tube. 

After  the  brass  back-pieces  (H  H)  had  been  taken  out,  and  a  hard 
rubber  substituted,  it  was  found  that  with  one  direction  of  rotation  the 
needle  was  extremely  unsteady;  it  would  run  up  the  scale  for  several 
centimetres,  stop  suddenly,  &c. — evidently  a  forced  vibration.  This 
was  traced  to  air-currents  also.  Now,  the  air  blew  into  the  open  mouth 
of  the  cone.  The  apparatus  had  been  run  for  some  months  with  this 
open,  and  not  the  slightest  irregularity  had  been  seen.  But  the  hard 
rubber  pieces  were  very  much  larger  than  the  brass  ones  which  were 
removed ;  they  filled  up  the  lower  space  to  a  greater  extent,  and  deflected 
the  air  upwards  more  than  before,  causing  the  unsteadiness.  With  the 
opposite  rotation  the  air  was  thrown  down  instead  of  up,  and  conse- 
quently did  not  affect  the  needle. 

The  first  systematic  observations  were  made  in  January,  1889,  with 
the  disks  charged  and  plates  earthed.  The  deflexion  on  reversing  was 
got  without  difficulty,  and  it  was  in  the  direction  to  be  expected;  that 
is,  with  positive  electrification,  the  effect  was  equivalent  to  a  current  in 
the  direction  of  motion  of  the  disk.  A  number  of  series  were  taken  in 
the  next  two  months;  they  agreed  among  themselves  well  enough,  but 


262  HENEY  A.  EOWLAND 

did  not  follow  the  law  assumed.  The  deviation  can  best  be  explained 
in  this  way: — The  equations  above  show  that  for  a  fixed  position  of 

N~ D     N 

the  disks  J  oc  a-,  —  a-x.    If  then,  N  and  /9  being  constant,  the  con- 
p  e       p 

denser  plates  are  moved  up  to  the  disk,  step  by  step,  thus  varying  e, 
and  D  be  changed  at  the  same  time  so  as  to  keep  D/e  <xa,  a  constant, 
the  deflexions  should  be  constant. 

Such  was  not  found  to  be  the  case;  the  deflexions  were  directly 
proportioned  to  e  instead  of  being  constant :  that  is,  with  greater  differ- 
ence of  potential,  the  deflexions  were  greater,  although  the  surface 
density  remained  constant.  Finally  this  was  found  to  be  due  to  a 
charge  on  the  back  surface  of  the  gold  coating.  The  end  of  the  axle 
comes  nearly  up  to  the  surface  of  the  disk  and  taken  with  all  the  brass 
work  must  form  a  condenser  of  a  certain  capacity  with  the  inner  face 
of  the  gold  foil. 

This  made  a  change  necessary  in  the  method  of  working;  the  disks 
had  to  be  earthed  and  the  glasses  charged.  This  was  done;  but  now 
the  deflexions  were  found  always  to  be  greater  with  positive  rotation 
(Zenith,  North,  Nadir,  South)  then  with  negative. 

It  was  considered  possible  that  the  brushes  might  have  something 
to  do  with  this,  so  they  were  taken  off.  Earth  connection  with  the  disk 
was  made  by  drilling  through  to  the  surface  of  the  disk  in  the  line  of 
the  axle  and  setting  in  a  screw,  which  came  flush  with  the  surface  and 
also  made  contact  with  the  axle;  this,  however,  made  no  difference,  the 
deflexions  for  negative  rotation  were  always  smaller. 

Table  I  gives  the  results  of  a  number  of  observations.  All  were 
taken  with  the  plates  charged  and  the  disks  earthed  by  means  of  the 
axle.  • 

The  meaning  of  the  letters  has  been  given;  l//9is  directly  propor- 
tional to  the  needle  sensitiveness. 

The  sudden  variations  in  the  values  of  1//9  are  due  to  changes  pur- 
posely made  in  the  needle. 

The  last  column  gives  the  values  of  V.  This  work  is  not  intended 
as  a  determination  of  V,  but  the  calculation  is  made  merely  to  show  to 
what  degree  of  approximation  the  effect  follows  the  assumed  law. 

The  deflexions  are  about  the  same  as  those  obtained  in  the  Berlin 
experiments — 5  to  8  mm.  on  reversing.  The  force  measured  then 
was  1/50000  H;  now  it  is  1/125000  H.  The  sensitiveness  of  the  needle 
in  the  two  cases  was  almost  the  same.  In  the  former  experiment  a 
force  of  3  X  10~7  deflected  the  needle  1'  of  arc;  the  corresponding  num- 


ELECTROMAGNETIC  EFFECT  OF  CONVECTION-CURRENTS 


263 


ber  now  is  2-7  X  10~7r  slightly  more  sensitive.     The  scale  distances 
were  110  and  200  cm.  respectively.     So  this  experiment  gives  about 


TABLE  I. 


No. 

Rotation. 

X. 

e. 

N. 

<r. 

1//3. 

2A. 

V. 

mm. 

1 

+ 

2-54 

1-24 

122 

1-16 

1-50.  105 

5-3 

2-42.101° 

2 

+ 

2-57 

11 

125 

1-30 

3-11 

9-0 

3-38 

8 

+ 

II 

129 

1-23 

2-15 

6-94 

3-00 

4 

_ 

11 

129 

1-23 

ii 

5-58 

3-68 

5 

+ 

1-21 

127 

1-21 

2-25 

5-6 

3-74 

6 

— 

a 

133 

1-21 

u 

5-7 

3-74 

7 

+ 

Cl 

130 

1-47 

" 

8-4 

3-10 

8 

_ 

II 

133 

1-47 

u 

7-3 

3-64 

9 

+ 

1-24 

121 

1-32 

2-22 

9-4 

2-26 

10 

_ 

11 

130 

1-32 

ii 

7-2 

3-16 

11 

+ 

11 

125 

1-26 

2-17 

7-6 

2-70 

12 

_ 

11 

126 

1-26 

»< 

5-7 

3-64 

13 

+ 

2-85 

1-50 

125 

1-19 

2-23 

6-5 

2-82 

14 

— 

ii 

129 

1-19 

ii 

5-0 

3-78 

15 

— 

u 

125 

1-11 

2-19 

5-85 

2-82 

16 

+ 

1-43 

127 

1-08 

2-35 

7-3 

2-46 

17 

— 

u 

128 

1-08 

ti 

5-4 

3-32 

18 

— 

it 

129 

1-08 

u 

5-3 

3-42 

19 

+ 

3-22 

1-80 

123 

1-13 

2-44 

5-1 

3-30 

20 

— 

ii 

u 

124 

1-13 

11 

4-9 

3-48 

3-  19  x  ]0i° 

TABLE  II. 


#13. 

#14- 

mm. 

6-7 

5-1 

5-1 

4-9 

6-6 

3-9 

7-6 

5-3 

8-0 

5-0 

5-8 

5-2 

6-3 

4-9 

8-0 

5-0 

8  0 

5-0 

4-3 

4-4 

5-9 

6-6 

6-0 

5-0 

6-5 

5-0 

the  same  scale-deflexion  at  twice  the  distance  with  a  force  ^  as  great. 
The  agreement  between  the  two  is  seen  to  be  quite  good. 

The  observations,  except  Nos.  1,  2,  15,  and  18  given  above,  were  taken 


264  HENRY  A.  EOWLAND 

in  pairs — first  one  direction  of  rotation  and  the  other  immediately  after- 
wards, everything  except  the  rotation  being  kept  constant. 

The  table  shows  that,  in  every  case  except  one,  the  deflexion  for 
negative  rotation  is  appreciably  smaller  than  the  corresponding  positive. 

The  difference  is  too  great  to  be  due  to  accidental  errors  in  the  read- 
ings, as  the  following  table,  giving  the  successive  deflexions  in  the  case 
of  #13  and  #14  will  show. 

There  is  but  one  deflexion  in  #13  as  small  as  the  mean  of  #14,  and 
but  one  in  #14  as  large  as  the  mean  of  #13. 

This  is  a  fair  example  of  the  way  the  deflexions  run.  As  a  further 
illustration  of  this  take#17  and#18;  these  two  are  identical  in  arrange- 
ment, but  the  direction  of  rotation  is  in  one  case  got  by  crossing  the 
belts  from  the  countershaft  to  the  disks  and  leaving  the  main  bolt 
straight;  in  the  other  the  main  belt  is  crossed  while  the  auxiliary  belts 
are  straight.  The  deflexions  are  the  same.  This,  too,  shows  that  the 
difference  cannot  be  due  to  any  effect  of  the  countershaft.  The  cause 
of  this  has  not  yet  been  explained.  The  work  is  to  be  continued  with 
this  and  also  with  new  apparatus,  made  like  the  Berlin  apparatus,  but 
with  the  disk  much  larger,  30  cm.  in  diameter;  at  least  double  the 
speed  then  obtained  will  be  used.  This  ought  to  give  deflexions  on 
reversal  of  1-5  to  1-7  cm. 

The  values  of  V  do  not  agree  so  well  as  might  be  looked  for;  but. 
when,  in  addition  to  the  numerous  difficulties  already  mentioned,  the 
smallness  of  the  deflexion  is  considered,  and  the  possibility  of  the  needle 
being  affected  by  currents  or  magnets  in  other  portions  of  the  labora- 
tory, so  far  away  as  not  to  be  guarded  against,  and  which  might  well  be 
changed  between  the  time  of  taking  the  observation  and  the  determin- 
ation of  the  needle-constant,  and,  finally,  that  a  distubing  cause  of  some 
kind  is  still  undoubtedly  present,  the  agreement  is  seen  to  be  as  good 
as  could  justly  be  expected. 

Physical  Laboratory,  Johns  Hopkins  University, 
April  22,  1889. 


NOTE,  added  April  29 

There  seems  to  be  a  misunderstanding  in  certain  quarters  as  to  the 
nature  of  the  deflexion  obtained  in  Prof.  Eowland's  first  experiment. 
The  paper  reads : — "  The  swing  of  the  needle  on  reversing  the  electri- 
fication was  about  10  to  15  mm.,  and  therefore  the  point  of  equilibrium 
was  altered  5  to  7-5  mm/'  This  has  been  construed  to  mean  that  the 


ELECTROMAGNETIC  EFFECT  OF  CONVECTION-CURRENTS         265 

deflexion  was  merely  a  throw,  and  that  no  continuous  deflexion  was 
obtained.  This  is  entirely  erroneous;  there  was  always  a  continuous 
deflexion.  The  throw  was  read  merely  because  the  needle  was  always 
more  or  less  unsteady,  and  better  results  could  be  got  by  seizing  a 
favorable  moment  when  the  needle  was  quiet  and  reading  the  throw, 
than  by  attempting  to  take  the  successive  elongations,  or  waiting  for 
the  needle  to  come  to  rest.  In  the  experiment  described  above  the 
needle  was  very  steady  and  no  such  trouble  was  experienced.  On  elec- 
trifying, the  needle  would  take  up  a  certain  position  and  would  remain 
there  as  long  as  the  charge  was  kept  up ;  on  reversal,  it  would  move  off 
to  a  new  and  perfectly  definite  position  about  6  to  7  mm.  away,  and 
remain  there,  &c.  H.  A.  E. 

C.  T.  H. 


44 

ON  THE  RATIO  OF  THE  ELECTROMAGNETIC  TO  THE 
ELECTROSTATIC  UNIT  OF  ELECTRICITY 

Br  flcxKr  A.  ROWLAXD,  with  the  «*»UUnc<r  of  E.  H.  BALL  mud  L.  B.  FLETCMEK 


(PkitMipktrml  MmpuiHe  [5J,  XXVIII.  304-315,  1889;  4w«rfe«»  SOWTM/  «/  &*»«  [S], 

JTJTJT  K///,  299-998,  IMf] 

The  determination  described  below  was  made  in  the  laboratory  of 
the  Johns  Hopkins  University  about  ten  years  ago,  and  was  laid  aside 
for  further  experiment  before  publication.  The  time  never  arrived  to 
complete  it,  and  I  now  seize  the  opportunity  of  the  publication  of  a 
determination  of  the  ratio  by  Mr.  ROM  in  which  the  same  standard 
condenser  was  used,  to  publish  it.  Mr.  Rosa  has  used  the  method  of 
getting  the  ratio  in  terms  of  a  resistance.  Ten  years  ago  the  absolute 
resistance  of  a  wire  was  a  very  uncertain  quantity  and,  therefore,  I 
adopted  the  method  of  measuring  a  quantity  of  electricity  electro- 
statically and  then,  by  passing  it  through  a  galvanometer,  measuring  it 
electromagnet  ically. 

The  method  consisted,  then,  in  charging  a  standard  condenser,  whose 
geometrical  form  was  accurately  known,  to  a  given  potential  as  meas- 
ured by  a  very  accurate  absolute  electrometer,  and  then  passing  it 
through  a  galvanometer  whose  constant  was  accurately  known,  and 
measuring  the  swing  of  the  needle. 

DESCBIPTIOX  OF  IXSTBCTCEXTS 

Ekctrt/rnet«T.  —  This  was  a  very  fine  instrument  made  partly  according 
to  my  design  by  Edelmann,  of  Munich,  As  first  made,  it  had  many 
faults  which  were,  however,  corrected  here.  It  is  on  Thomson's  guard 
ring  principle  with  the  movable  plate  attached  to  the  arm  of  a  balance 
and  capable  of  accurate  adjustment.  The  disc  is  10-18  cm.  diameter 
in  an  opening  of  10-38  cm.  and  the  guard  plates  about  33-0  cm.  diam- 
eter. All  the  surfaces  are  nickel  plated  and  ground  and  polished  to 
optical  surfaces  and  capable  of  accurate  adjustment  so  that  the  dis- 
tance between  the  plates  can  be  very  accurately  determined.  The 
balance  is  sensitive  to  a  mg.  or  less  and  the  exact  position  of  the  beam 


RATIO  Of  ffx-JUxmrntaftLomtem^f.  10  TEr.m !'»»<iHi!if '^TH*  TTSTHT  Bfl 


:-   —:\  :          I'.-':.::        .::._-  '  -  :    :  '•    •    -•  :-.r    in  i     '  -.-:    -:   "   •    -,   .  ---   :;;   -/.:  - 

^  :£•.  iesiedi  throttgh- 

ovt  iis  attire  nnge  bjr  Tailing;  the  detracts  and  weights  to  give  the 

constant  puifnlial  of  a  standard  gaiager  and  fband  to  give  relative  icad- 

:r_-  '•    •":•:•;•:   1   in  ^  •     •-   '.^i.-:.      I'     -    :•---•;-:  --•:  ->.:  :-;^-::.  ;-;-   ;-    ->.-:• 

„..._.     ,'i-.|.,.i..      ,_    :      ..-.-..^  -'--.;     --.J.--.-7     I"'     ->  -;.     -.-  —  .-_•;  _-    -.;  —  .      -.  :  ,.     ,-      [ogfid 

.'-.  -  ".-  r  ;•.•":-?  ::".  "  .  "  "  "«r  i~  -iriil  "  "  :  ;  ~".  ""  !oin.bine<3  weigiit^  tnd 
dEctvartalK  fontty  it  ins  fbvnd  Dest  to  limit  its  swing'  to  a  -fa  nna.  OB. 
cadk  aide  of  its  normal  posrtiwm.  The  mean  of  two  meadin^R  of  the 

:;--,i-  :••-.   •-  r  -.:  r.:  •".:-•  -'-.  -  >..i:r  ;omp  up   md  the  >ther  lown.  •••---.-  ;-.-••: 
one  r 

The  ad  justm  -  :~  ~  -  :'  the  plates  parallel  to  each  0>ther  ami  o^f  the 
nwiainle  vlate  in  the  Diane  of  the  <nard  rin<r  could  be  made  to  almost 

IT  JT  ^  Ij 

i.~  -7'r7.  "••-   ~~  potential  "i  khe  ~~~. 


where  4  is  the  drnfanrr  of  the  plates,  w§  the  absolute  force  on  the 

_.  .  -;•-•_:  -\i-.-_   j.-  i    J_  •  -;    .  :^ -.;-.-•;   -.  -  •  \       According  "     iTaiw  ?I1 


where  ^  aia^  ^  are  the  iradn.  of  the  disc  anxi  the  openrng^  foe  it 
=    Rl     //  —  _-..        .':.-.   \i.i-    :orred  •   •    Ha^    Aaal   1 
nenee  we  kave^  finaEhrr 


F= 


Stmmioni  canaVvwr. — This  Terr  a«enate  instrument  was  made  from 

irsj--  '--  )[?     ".--•-,-    -'- .r    -,£  y..~  5Tork,   L~  :    :onsisted    'J   >ne 

knfflorw  baiL  vezy  acennateljr  ttnmeii  and  nickel  pW**^  in  which  two  bolls 

.-:   :  ---.-...       •     ,.'-;-._-"--,-    ,     •  -  :       /.-..-  '-;;;.-     •-:'_  i  be  -  ?rv 

IT        - 

;i  .     ,.r     .   .:._..:     .  .-.  .,      :'-"-.'-         -.-   •-.-.  -        ,-^-.\  -  wus  made 

ITT  two  wires  aftMrat  -J^T  ^^  dBanwteTy  one  of  which  was  protruded 

--  .      •_-:-     -  •  -..,    '-.,          .-.          -     -      .'-,.:     -  .--  ,-.     --  ,        ---     •.     .-;-.-.       - 

r  •     .--::     -  mm  Bam   niftaVav-    ••-.  :   -':-   -.•••-:    :~-  tntrodiBBBJ    ri 
aaiitan  nlni  in  iffiit  Iftn  iHimliii^i      Tins  eonld  be  efiected  five  times 

^-  -  -  .  .  -  -  :      7~-  ,    ;  .  ••    -    -.     -•--.".;.'-  -.  -  -.•-,--.-.-.   -.      .;-.-,,;-;  -^--. 

•ini  d  py  ••^aiing  in  water,  and  the  ckilioafadie  capacities  fiwmd  to  be 
50-00  and  29-556  e-g.  SL  mniteiw 

:- .-   V.~    7    -i  -  :  >;-:. 


268  HENRY  A.  KOWLAND 

Galvanometer  for  Electrical  Discharges. — This  was  very  carefully  m- 
sulated  by  paper  and  then  put  in  hot  wax  in  a  vacuum  to  extract  the 
moisture  and  fill  the  spaces  with  wax.  It  had  two  coils,  each  of  about 
70  layers  of  80  turns  each  of  No.  36  silk  covered  copper  wire.  They 
were  half  again  as  large  as  the  ordinary  coils  of  a  Thomson  galvano- 
meter. The  two  coils  were  fixed  on  the  two  sides  of  a  piece  of  vulcanite 
and  the  needle  was  surrounded  on  all  sides  by  a  metal  box  to  protect 
it  from  the  electrostatic  action  of  the  coils.  A  metal  cone  was  attached 
to  view  the  mirror  through.  The  insulation  was  perfect  with  the 
quickest  discharge. 

The  constant  was  determined  by  comparison  with  the  galvanometer 
described  in  this  Journal,  vol.  xv,  p.  334.  The  constant  then  given  has 
recently  been  slightly  altered.  The  values  of  its  constant  are 

By  measurement  of  its  coils 1832-24 

By  comparison  with  coils  of  electrodynamometer.  . .  .   1833-67 
By  comparison  with  single  circle 1832-56 

Giving  these  all  equal  weights,  we  have 

1832-82 

instead  of  1833-19  as  used  before. 

The  ratio  of  the  new  galvanometer  constant  to  this  old  one  was 
found  by  two  comparisons  to  be 

10-4167 
10-4115 


Mean,     10-4141 
Hence  we  have 

G  =  19087. 

Electrodynamometer.  —  This  was  almost  an  exact  copy  of  the  instru- 
ment described  in  Maxwell's  treatise  on  electricity  except  on  a  smaller 
scale.  It  was  made  very  accurately  of  brass  and  was  able  to  give  very 
good  results  when  carefully  used.  The  strength  of  current  is  given 
by  the  formula 


—  - 

T  —  ysin  a 

where  K  is  the  moment  of  inertia  of  the  suspended  coil,  t  its  time  of 
vibration,  a  the  reading  of  the  head,  and  C  a  constant  depending  on 
the  number  of  coils  and  their  form. 


RATIO  OF  ELECTROMAGNETIC  TO  ELECTROSTATIC  UNIT        269 

LARGE  COILS. 

Total  number  of  windings 240 

Depth  of  groove  -84     cm. 

Width  of  groove -76     cm. 

Mean  radius  of  coils    13-741  cm. 

Mean  distance  apart  of  coils 13-786  cm. 

SUSPENDED   COILS. 

Total  numher  of  windings 126 

Depth  of  groove  -41     cm. 

Width  of  groove  -38     cm. 

Mean  radius 2-760  cm. 

Mean  distance  apart    2-707  cm. 

These  data  give,  by  Maxwell's  formulae, 

(7  =  0-006457. 

In  order  to  be  sure  of  this  constant,  I  constructed  a  large  tangent 
galvanometer  with  a  circle  80  cm.  diameter  and  the  earth's  magnetism 
was  determined  many  times  by  passing  the  current  from  the  electro- 
dynamometer  through  this  instrument  and  also  by  means  of  the  ordi- 
nary method  with  magnets.  In  this  way  the  following  values  were 
found. 

Magnetic  Electrical 

method.  method. 

December  16,  1879  -19921  -19934 

January  3,  1879    -19940  -19942 

February  25,  1879    -19887  -19948 

February  28,  1879    -19903  -19910 

March  1,  1879   -19912  -19928 


Mean   -19912  -19933 

which  differ  only  about  1  in  1000  from  each  other.     Hence  we  have 
for  C: 

From  calculation  from  coils -006457 

From  tangent  galvanometer -006451 

Mean  -006454  c.  g.  s.  units. 

The  suspension  was  bifilar  and  no  correction  was  found  necessary  for 
the  torsion  of  the  wire  at  the  small  angles  used. 


270  HENRY  A.  EOWLAND 

The  method  adopted  for  determining  the  moment  of  inertia  of  the 
suspended  coil  was  that  of  passing  a  tube  through  its  centre  and  placing 
weights  at  different  distances  along  it.  In  this  way  was  found 

K  =  82Q-Q  c.  g.  s.  units. 

The  use  of  the  electrodynamometer  in  the  experiment  was  to  determine 
the  horizontal  intensity  of  the  earth's  magnetism  at  any  instant  in  the 
position  of  the  ballistic  galvanometer.  This  method  was  necessary  on 
account  of  the  rapid  changes  of  this  quantity  in  an  ordinary  building1 
and  also  because  a  damping  magnet,  reducing  the  earth's  field  to  about 
•J  its  normal  value,  was  used.  For  this  purpose  the  ballistic  galvano- 
meter was  set  up  inside  the  large  circle  of  80  cm.  diameter  with  one 
turn  of  wire  and  simultaneous  readings  of  the  electrodynamometer  and 
needle  of  ballistic  galvanometer  were  made. 

THEORY  OF  EXPERIMENT. 
We  have  for  the  potential 

v      8*?  ,  ,—         ,  /-[",   ,  -00021 

- •*  d  ^w  --  ed  V  w\  1  H g— 

For  the  magnetic  intensity  acting  on  the  needle 

TT__  2xnp"-c  V  1C  sin  a 
*(p2  +  J2)itan? 
For  the  condenser  charge 


Whence 

_  eGC  (p^  +  b^Z  Nt  i*l  wd     tan?    P..  >* 

'"*V      TV  sin  a  2  sin  £0[_     ~2 


but 

and  2  sin  $0  =  I  *  |~1  —  i  f  *  Y  ~|  nearly. 

ML        \  us  J  " 

So  that  finally 

=  eGC  _.__-__ 


A=0;  -0011;  -0030;  -0056;  -0090  for  1,  2,  3,  4,  5  discharges  as  inves- 
tigated below. 

1  This  experiment  was  completed  before  the  new  physical  laboratory  was  finished. 


EATIO  or  ELECTROMAGNETIC  TO  ELECTROSTATIC  UNIT        271 


-0002 


.Frrrz  -0013  for  first  ball  of  condenser  and  -0008  for  other,  as  investi- 

gated below. 

I  =  correction  for  torsion  of  fibre  =  0  as  it  is  eliminated. 
e  =  constant  of  electrometer  =  17-221. 
Q  =  constant  of  ballistic  galvanometer  =  19087. 
p  =  radius  of  large  circle  =  42-105  cm. 
w  =  number  of  coils  on  circle  =  1. 
c  =  constant  of  electrodynamometer  =  -006454. 
K  =.  moment  of  inertia  of  coil  of  electrodynamometer  =  826  -6. 
b  =  distance  of  plane  of  large  circle  from  needle  —  1-27. 
C  =  capacity  of  condenser  =  50-069  or  29-556. 
D  =  distance  of  mirror  from  scale  =  170-18  cm. 
w  =  weight  in  pan  of  balance. 
t  =  time  of  vibration  of  suspended  coil. 
7*=  time  of  vibration  of  needle  of  ballistic  galvanometer. 
,3  =  deflection  of  needle  on  scale  when  constant  current  is  passed. 
a  =  reading  of  head  of  electrodynamometer  when  constant  current 

is  passed. 

o  =  swing  caused  by  discharge  of  condenser. 
A  =  distance  of  plates  of  electrometer. 
IV  =  number  of  discharges  from  condenser. 
X  =  logarithmic  decrement  of  needle. 
A  =  correction  due  to  discharges  not  taking  place  in  an  instant. 

The  principal  correction,  requiring  investigation  is  A.     Let  the  posi- 
tion and  velocity  of  the  needle  be  represented  by 

x  =  v0  sin  U  and  v  =  f0b  cos  bt,  where  b  =  /1. 

At  equal  periods  of  time  tt,  2/r  3tt,  etc.,  let  new  impulses  be  given  to 
the  needle  so  that  the  velocity  is  increased  by  v0  at  each  of  these  times. 
The  equations  which  will  represent  the  position  and  velocity  of  the 
needle  at  any  time  are,  then, 


272  HENRY  A.  EOWLAND 

between  0  and  tt         x  =.  a0  sin  bt  v  =  a0b  cos  bt 

"        tt  and  2tt      x  =  a'  sin  b(t  +  t'}      v  =  a'b  cos  b(t  +  /') 
"        2^  and  3*,    x  =  a"  sin  b(t  +  I")   v  =  a"b  cos  b(t  +  t") 

At  the  times  0,  tt,  2t,,  etc.,  we  must  have 

x  =  0  v0  =  a0b 

a0  sin  W,  =  a'  sin  *(*,  +  *')  v0  +  a0b  cos  W,  =  a'b  cos  £(/,  +  t  ) 

a'  sin  &(2f,  +  t'}  =  a"  sin  b(2t,  +  t")     v.a'b  cos  b(2t,  +  t") 

etc.  =  a"b  cos  *(3f,  +  J") 

etc. 

Whence  we  have  the  following  series  of  equations  to  determine  a',  a", 
etc.,  and  t',  t",  etc. 


afib*  =  «02i2  +  v*  +  2r0a0b  cos  Ut\  sin  b(tt  +  t'}  =  |?  sinW, 

«"2*2  =  a'252  4-  Vo2  +  2y0a'i  cos  b(2t,  -  t')  ;  sin  b(2tt  +  t")  =  ^sin  i(2/,  +  /') 


S^  +  i!");  sin  4(3^  +  /'")=      °sin  J(3/4  +  r') 
etc.  etc. 

"When  t,  is  small  compared  with  the  time  of  vibration  of  the  magnet, 
we  have  very  nearly  t'  —  —  \tt\  t"  =  —  i  fl  t'"  =  —  f  t  fl  etc. 

a"  =  2a0\l  +  cos  btt)  =  4<(1  -  t  (W,)2) 

fl'"  -9a02(l-f(^)2) 

a'"*  =  16a0\l-$(btty) 

aiv2  =  25a02(l  —  2  (&,)*) 

«T2  = 
Whence 

a'  =  2a0(l  -  4  (&,)') 

a"  =3-/0(l  -*(«,)') 

a'"  =K(1-|(*O*). 

aiT  =5fl0(l-     (d/,)«) 

Now  a0,  a',  a",  a'"  and  a"  are  the  values  of  3  with  1,  2,  3,  4  and  5 
discharges  and  a0,  2a0,  3a0,  4a0  and  5a0  are  the  values  provided  the 
discharges  were  simultaneous. 

This  correction  is  quite  uncertain  as  the  time,  £,,  is  uncertain. 

In  assuming  that  the  impulses  were  equal  we  have  not  taken  account 
of  the  angle  at  which  the  needle  stands  at  the  second  and  subsequent 
discharges,  nor  the  magnetism  induced  in  the  needle  under  the  same 
circumstances.  One  would  diminish  and  the  other  would  increase  the 


EATIO  OF  ELECTROMAGNETIC  TO  ELECTROSTATIC  UNIT         273 

effect.     I  satisfied  myself  by  suitable  experiments  that  the  error  from 
this  cause  might  be  neglected. 

The  method  of  experiment  was  as  follows:  The  store  of  electricity 
was  contained  in  a  large  battery  of  Leyden  jars.  This  was  attached 
to  the  electrometer.  The  reading  of  the  potential  was  taken,  the 
handle  of  the  discharger  was  turned  and  the  momentary  swing  observed 
and  the  potential  again  measured.  The  mean  of  the  potentials  ob- 
served, with  a  slight  correction,  was  taken  as  the  potential  during  the 
time  of  discharge.  This  correction  came  from  the  fact  that  the  first 
reading  was  taken  before  the  connection  with  the  condenser  was  made. 
The  first  reading  is  thus  too  high  by  the  ratio  of  the  capacities  of  the 
condenser  and  battery  and  the  mean  reading  by  half  as  much.  Hence 
we  must  multiply  d  by  1  —  F  where  F=  -0013  for  first  ball  of  con- 
denser and  -0008  for  other.  This  will  be  the  same  for  1  or  5  dis- 
charges. From  10  to  20  observations  of  this  sort  constituted  a  set,  and 

the  mean  value  of  -,  which  was  calculated  for  each  observation  sepa- 
rately, was  taken  as  the  result  of  the  series. 

Before  and  after  each  series  the  times  of  vibration,  t  and  T,  and  the 
readings,  /9  and  a,  were  taken.  The  logarithmic  decrement  was  ob- 
served almost  daily. 

EE  STILTS 

The  table  on  the  following  page  gives  the  results  of  all  the  observa- 
tions. 

These  results  can  be  separated  according  to  the  number  of  discharges 
as  follows: 

1. 

300-59 
300-17 
296-72 
297-84 
298-90 
298-57 
299-05 
300-80 
296-56 


2. 

3. 

4. 

5. 

298-37 

295-73 

296-43 

296-50 

298-61 

296-40 

297-24 

296-37 

297-43 

298-75 

301-82 

297-38 

297.78 

298-66 

295-02 

296-87 

300-19 

296-75 

295-22 

296-31 

298-80     298-48     297-26     29715     296-69 
18 


CO 

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X 

tt 

EATIO  OF  ELECTROMAGNETIC  TO  ELECTROSTATIC  UNIT        275 

In  taking  the  mean,  I  have  ignored  the  difference  in  the  weights  due 
to  the  number  of  observations,  as  other  errors  are  so  much  greater  than 
those  due  to  estimating  the  swing  of  the  needle  incorrectly. 

It  will  be  seen  that  the  series  with  one  discharge  is  somewhat  greater 
than  with  a  larger  number.  This  may  arise  from  the  uncertainty  of 
the  correction  for  the  greater  number  of  discharges,  and  I  think  it  is 
best  to  weight  them  inversely  as  this  number.  As  the  first  series  has, 
also,  nearly  twice  the  number  of  any  other,  I  have  weighted  them  as 
follows : 

Wt.  vxlO-8 

8  298-80 

4  298-48 

3  297-26 

2  297-15 

1  296-69 


Mean  298-15 

Or  v  =  29815000000  cm.  per  second. 

It  is  impossible  to  estimate  the  weight  of  this  determination.  It  is 
slightly  smaller  than  the  velocity  of  light,  but  still  so  near  to  it  that 
the  difference  may  well  be  due  to  errors  of  experiment.  Indeed  the 
difference  amounts  to  a  little  more  than  half  of  one  per  cent.  It  is  seen 
that  there  is  a  systematic  falling  off  in  the  value  of  the  ratio.  This  is 
the  reason  of  my  delaying  the  publication  for  ten  years. 

Had  the  correction,  A,  for  the  number  of  discharges  been  omitted, 
this  difference  would  have  vanished;  but  the  correction  seems  perfectly 
certain,  and  I  see  no  cause  for  omitting  it.  Indeed  I  have  failed  to  find 
any  sufficient  cause  for  this  peculiarity  which  may,  after  all,  be  acci- 
dental. 

As  one  of  the  most  accurate  determinations  by  the  direct  method  and 
made  with  very  elaborate  apparatus,  I  think,  however,  it  may  possess 
some  interest  for  the  scientific  world. 


47 
NOTES  ON  THE  THEORY  OF  THE  TRANSFORMER 

[Johns  Hopkins  University  Circulars,  No.  99,  pp.  104,  105,  1892;  Philosophical 
Magazine  |51,  XXXIV,  54-57,  1892  ;  Electrical  World,  XX,  20,  1892] 

As  ordinarily  treated  the  coefficient  of  self  and  mutual  induction  of 
transformers  is  assumed  to  be  a  constant  and  many  false  conclusions 
are  thus  drawn  from  it. 

I  propose  to  treat  the  theory  in  general,  taking  account  of  the  hyster- 
esis as  well  as  the  variation  in  the  magnetic  permeability  of  the  iron.1 

The  quantity  p  as  used  by  Maxwell  is  the  number  of  lines  of  magnetic 
induction  enclosed  by  the  given  conductor.  This  will  be  equal  to  the 
number  of  turns  of  the  wire  into  the  electric  current  multiplied  by  the 
magnetic  permeability  and  a  constant.  But  the  magnetic  permeability 
is  not  a  constant  but  a  function  of  the  magnetizing  force,  and  hence  we 
must  write 

p  —  Bny  +  C(nyY  +  D(ny}b  +  etc. 

Where  B,  C,  etc.,  are  constants,  n  is  the  number  of  turns  and  y  the 
strength  of  current. 

In  this  series  only  the  odd  powers  of  y  can  enter  in  order  to  express 
the  fact  that  reversal  of  the  current  produces  a  negative  magnetization 
equal  in  amount  to  the  direct  magnetization  produced  by  a  direct  cur- 
rent. This  is  only  approximately  true,  however,  and  we  shall  presently 
correct  it  by  the  introduction  of  hysteresis.  It  is,  however,  very  nearly 
true  for  a  succession  of  electric  waves. 

To  introduce  hysteresis,  first  suppose  the  current  to  be  alternating  so 
that  y  =  c  sin  (bt  -f-  e)  where  t  is  the  time  and  e  the  phase.  The  intro- 
duction of  a  term  A  cos  (U  -\-  e)  into  the  value  of  the  number  of  lines 
of  induction  will  then  represent  the  effect  very  well.  But  the  current 
is  not  in  general  a  simple  sine  curve  and  so  we  must  write 

y  =  ax  sin  (bt  +  e^  +  a2  sin  (2bt  +  e2)  +  as  sin  (3bt  +  e3)  +  . 


1  The  problem  is  treated  by  the  method  of  magnetic  circuit  first  applied  by  me  to 
iron  bars  in  my  paper  on  'Magnetic  Distribution'  (Pliil.  Mag.,  1875),  and  afterwards 
to  the  magnetic  circuit  of  dynamos  at  the  Electrical  Conference  at  Philadelphia  in 
1884.  I  also  used  the  same  method  in  my  paper  on  magnetic  permeability  in  1873. 


NOTES  ON  THE  THEORY  OF  THE  TRANSFORMER  277 

In  this  case  it  is  much  more  difficult  to  express  the  hysteresis  empir- 
ically. In  most  cases  the  first  term  in  the  value  of  y  is  the  largest.  A 
term  of  the  same  nature  as  before  will,  in  this  case,  suffice  to  express 
the  hysteresis  approximated.  We  can  then  write  for  the  total  flux  of 
magnetic  induction 

p  =  A  cos  (U  +  ei)  +  Buy  +  Cn3y*  +  Dtfy5  +  etc. 

Problem  1.  —  To  find  the  electromotive  force  necessary  to  make  the 
electric  current  a  sine  curve  in  a  transformer  without  secondary.  Let 
the  resistance  be  E,  and  make  y  =  c  sin  (bt).  Then  Maxwell's  equation 
becomes 


*= 

Substituting  the  value  of  y  we  have 

E=  (Rc—Abn}  sin  (bt}  +  Bncb  cos  (bt}  +  3  Cn3  sin  2(bt)  cos  bt  +  etc. 
But 

Sin  *bt  cos  bt  =  \  (cos  bt  —  cos  3  U} 
Sin  *bt  cos  U  =  jig.  (cos  5  bt  —  3  cos  3  U  +  2  cos  bt) 
Si  n6^  cos  bt  =  etc. 

Hence  the  electromotive  force  that  must  be  given  to  the  circuit  must 
contain  not  only  the  given  frequency  of  the  current  but  also  frequencies 
of  3,  5,  7,  etc.,  times  as  many.  In  other  words,  the  odd  harmonics. 

Problem  2.  —  Transformer  without  secondary,  the  electromotive  force 
being  a  sine  curve. 

E  sin  U  =  Ry  +  n  §  . 
ct  t 

First  it  is  to  be  noted  that  when  we  place  in  this  equation  the  general 
value  of  y  and  make  the  coefficients  of  like  functions  of  bt  zero,  all  the 
even  harmonics  will  strike  out. 

Hence  the  value  of  the  electric  current  will  be 

y  =  a1sin(W  +  «i)  +«3  sin  (3  bt  +  e3)+a6  sin  (5bt  +  et)+. 
Substituting  this  value  in  the  value  for  p,  the  equation  is  theoretically 
sufficient  to  determine  av  az,  etc.,  and  elf  e3)  etc.  The  equations  are 
cubic  or  of  higher  order  and  the  solution  can  only  be  approximate  and  I 
have  not  thought  it  worth  while  to  go  further  with  the  calculation. 
However,  it  is  easy  to  draw  the  following  conclusion: 

1.  A  simple  harmonic  current  through  an  iron  transformer  will  pro- 
duce a  secondary  electromotive  force  and  current,  or  both,  which  con- 
tain not  only  the  fundamental  period  but  the  higher  odd  harmonics. 


278  HENRY  A.  HOWL  AND 

2.  This  effect  is  not  due  to  hysteresis  but  to  the  variation  in  the  mag- 
netic permeability. 

3.  The  harmonics  increase  with  the  increase  in  magnetization  of  the 
iron  and  nearly  vanish  as  the  magnetization  decreases,  although  it  is 
doubtful  if  they  ever  quite  vanish.     Hence,  an  increase  of  resistance 
will  decrease  the  harmonics. 

4.  In  the  method  of  introducing  the  hysteresis  into  the  equations,  it 
enters  as  an  addition  to  the  resistance  in  the  term  Ra{  -f-  Anb,  where 
R  is  the  resistance,  a^  the  maximum  current,  A  the  coefficient  of  hyster- 
esis, which  is  dependent  upon  the  amount  of  magnetization  of  the  iron, 

n  the  number  of  turns  of  wire,  and  b=  —is  2-  divided  by  the  time  of 

a  complete  period. 

The  introduction  of  the  hysteresis  into  the  ordinary  equations,  there- 
fore, presents  little  or  no  difficulty. 

Many  observers  have  noted  that  the  current  curve  in  a  transformer 
was  not  a  sine  curve  and  Prof.  Ayrton  has  shown  the  presence  of  the 
odd  harmonics  but  gives  no  explanation.  Mr.  Fleming  has  attributed 
them  to  hysteresis,  but  I  believe  the  present  paper  gives  the  first  true 
explanation. 

Problem  3. — To  find  the  work  of  hysteresis.  Let  the  .resistance,  R, 
be  zero.  The  work  done  will  then  be  the  integral  of  the  current  times 
the  electromotive  force,  or 

(1P  fit 
dta 

the  integral  to  be  taken  for  one  period  of  the  current. 

27T 

f***  I  d*u  dii        1 

w=    I-     bA  sin  (bt  +  e,}  y  +  Bny   •/  +  (7ns3 y2 -7f-  +   \dt 

I II  \         '      if  a  J  fjf  -J     fit 

«/  V    |_  Ui  J 

w  =  A  ~a\. 
o 

All  the  other  terms  are  zero. 

In  a  unit  of  time  the  energy  absorbed  is 


Steinmetz  has  found  by  experiment  that  this  varies  as  the  1-6  power 
of  the  magnetic  induction.  Of  course  the  present  theory  gives  nothing 
of  this  but  only  suggests  a  way  of  introducing  the  hysteresis  into  cal- 
culations of  this  nature.  For  this  purpose  replace  A  by  A1^-6  and  the 


NOTES  ON  THE  THEOBY  OF  THE  TRANSFORMER  279 

work  of  hysteresis  becomes  -=-  a™  which  is  thus  the  formula  of  Stein- 

</ 

metz. 

In  the  case  where  a  secondary  exists  the  number  of  turns  of  wire 
being  n1  and  the  current  y1,  we  have  simply  to  replace  ny  in  the  above 
formula  by  ny  -}-  n^y1  and  change  the  phase  of  the  hysteresis  term  so 
as  to  be  90°  from  the  combined  magnetizing  force,  ny  -f-  n^y1.  The 
equations  of  the  currents  will  then  be,  by  Maxwell's  formula, 

E=Ry    +  n 


which  suffice  to  determine  both  y  and  y1.  The  result  is  too  complicated 
to  be  attractive.  The  equations  show,  however,  that  the  odd  harmonics 
must  appear  in  either  the  electromotive  forces  or  the  primary  or  second- 
ary currents,  if  not  in  all  of  them  at  once.  The  exact  distribution  is 
only  a  case  of  complicated  calculation. 

It  is  to  be  specially  noted  that  all  formulae  by  which  self  induction  is 
balanced  by  a  condenser  will  not  be  correct  when  applied  to  an  iron 
transformer  but  only  to  an  air  transformer.  They  will,  however,  apply 
approximately  to  iron  transformers  in  which  the  magnetization  is  small 
and  thus  probably  will  apply  better  to  transformers  with  an  open 
magnetic  circuit  than  with  a  closed  one. 

Also  an  iron  transformer  should  not  be  compared  with  an  air  trans- 
former or  two  iron  transformers  with  different  magnetizations  with 
each  other. 

In  conclusion  I  may  add  that  the  mathematical  difficulties  might  be 
overcome  by  another  mode  of  attack  but  other  work  draws  me  in 
another  direction  and  I  leave  the  matter  to  be  worked  up  further  by 
others. 


48 

NOTES  ON  THE  EFFECT  OF  HARMONICS  ON  THE  TRANS- 
MISSION OF  POWER  BY  ALTERNATING  CURRENTS 

[Electrical  World,  XX,  368,  1892;   La  Lumiere  Electrique,  XL  VII,  42-44,  1893] 

In  a  recent  number  of  The  Johns  Hopkins  University  Circular  and 
the  Phil.  Mag.  for  July,  1892, x  I  have  shown  that  an  iron  transformer 
introduces  harmonics  of  the  periods  3,  5,  7,  etc./  times  the  fundamental 
period  into  the  currents  and  electromotive  forces  both  primary  and 
secondary  of  a  transformer  and  that  these  increased  in  value  as  the 
iron  was  more  and  more  magnetized. 

It  is  my  present  object  to  call  attention  to  the  effect  of  these  har- 
monics on  the  transmission  of  power  and  its  measurement.  For  light- 
ing purposes  they  are  evidently  of  very  little  significance,  as  currents 
of  all  periods  are  equally  efficient  in  producing  heat.  There  is  a  loss, 
however,  in  the  fact  that  they  cause  more  loss  of  heat  in  the  wires  and 
the  iron  of  the  transformers.  But  for  the  transmission  of  power  the 
case  is  very  different.  Here  the  motors  are  designed  to  run  at  speeds 
dependent  on  the  period;  if  there  is  more  than  one  period  the  adjust- 
ment fails,  and  there  is  a  loss.  The  harmonics  are  thus  useless  in  the 
transmission  of  power  by  synchronous  motors,  and  are  of  very  little  use 
in  motors  with  revolving  fields.  In  these  cases  the  harmonics  travel 
around  the  circuits,  heating  the  wires  and  the  iron  without  producing 
valuable  work.  They  then  represent  an  almost  complete  loss  in  the 
transmission  of  power,  and  as  they  may  contain  10,  20  or  even  30  or  40 
per  cent  of  the  current,  according  to  the  magnetization  of  the  trans- 
former, they  are  probably  responsible  for  some  loss  of  efficiency  in  many 
cases,  as  will  be  shown  further  on. 

Indeed,  I  believe  they  are  the  explanation  of  many  seeming  mysteries 
in  the  working  of  alternating  current  motors. 

Special  arrangements  of  condensers  and  coils  can  be  made  to  pick 
out  these  harmonics  so  that  they  become  more  important  than  the 

1  See  also  the  Electrical  World  of  July  9,  1892. 

2  The  periods  2,  4,  6,  etc.,  can  evidently  be  introduced  by  magnetizing  the  iron  of 
the  transformer  in  one  direction  by  a  constant  current,  or  having  it  originally  with 
an  asymmetrical  magnetic  set. 


EFFECT  OF  HARMONICS  ON  THE  TRANSMISSION  OF  POWER     281 

original  period.  This  may  occur  accidentally  and  cause  many  curious 
results  in  the  working  of  motors. 

It  is,  then,  of  the  first  importance  in  the  transmission  of  power  that 
the  curves  shall  be  pure  sine  curves,  and  dynamos,3  transformers  and 
motors  must  be  designed  in  the  future  with  reference  to  this  point. 
It  would  seem,  also,  that  most  calculations  on  the  efficiency  of  power 
transmission  by  alternating  currents  must  be  at  fault  unless  they 
include  the  action  of  the  harmonics. 

As  to  the  amount  of  loss  from  this  cause  it  is  difficult  to  decide  in 
general.  With  synchronous  motors  the  harmonics  simply  flow  around 
the  wires  without  producing  useful  current  of  any  kind.  But  this  may 
not  cause  great  loss  if  the  resistance  is  small.  Indeed,  considerable 
distortion  may  represent  small  loss  of  power  in  certain  cases  and  great 
loss  in  others,  according  to  the  difference  of  phase  of  the  current  and 
electromotive  force  in  the  harmonics. 

In  the  case  of  motors  with  rotary  fields  the  harmonics  produce  fields 
revolving  with  velocities  3,  5,  7,  etc.,  times  the  primary  field.  Now  it 
is  essential  for  the  efficiency  of  these  motors  that  the  armature  shall 
revolve  nearly  as  fast  as  the  field,  and  hence  the  efficiency  for  the 
harmonics  must  be  very  small  indeed,  and  this  must  decrease  the  effi- 
ciency of  the  apparatus  as  a  whole. 

As  to  the  heating  of  the  wires  by  the  harmonics,  it  is  easy  to  see  that 
the  total  heating  due  to  all  the  currents  of  different  periods  will  simply 
be  the  sum  of  the  heatings  due  to  each  of  the  currents  separately. 

The  effect  of  harmonics  on  the  hysteresis  is  much  more  complicated 
and  can  hardly  be  calculated  without  further  experiment.  However, 
the  following  hypotheses  may  give  some  idea  of  the  action.  Let  the 
primary  electromotive  force  be  considered  unity,  and  let  a3,  a5,  etc.,  be 
the  electromotive  forces  of  the  harmonics.  If  these  acted  separately 
on  the  hysteresis  the  total  would  be  : 


Again,  if  they  all  combined  so  that  the  maximum  electromotive  force 
is  equal  to  the  sum  of  them  all,  the  hysteresis  will  be  nearly: 


3  Dynamos  and  motors  introduce  the  odd  harmonics  on  account  of  the  variations 
of  the  self-induction  of  the  machine,  which  becomes  very  apparent  when  a  strong 
current  is  flowing.  The  armature  reactions  may  also  introduce  the  harmonics. 


282  HENRY  A.  EOWLAND 

However,  it  is  hardly  probable  that  this  last  condition  would  be  often 
satisfied,  in  which  case  this  formula  would  give  too  great  a  value. 
When  the  harmonics  are  small  this  last  formula  can  be  written  nearly 


As  an  example,  suppose  a3=-3  and  a5—  -2  and  a7  =  1,  these  two 
formula  give  an  increase  of  10  and  24  per  cent  in  the  loss  due  to 
hysteresis. 

The  current  heating  is  only 

l  +  a\  +  a\  +  etc. 4 
Or,  in  the  example, 

1  +  -09  +  -04  +  -01  ==  1-14. 

It  would  seem,  then,  that  the  losses  due  to  hysteresis  and  current 
heating  may  be  much  increased  by  the  harmonics. 

I  believe  the  statement  has  been  made  that  the  form  of  the  curve 
does  not  influence  the  hysteresis.  This  is  evidently  incorrect,  unless 
we  take  the  top  of  the  curve  to  reckon  from,  in  which  case  the  statement 
agrees  with  the  second  hypothesis  given  above  if  the  harmonics  are  of 
the  proper  phase. 

To  estimate  the  influence  on  the  efficiency  of  a  plant,  assume  the 
efficiency  of  the  dynamo  and  synchronous  motor  with  primary  currents 
as  each  equal  to  90  per  cent,  and  of  the  two  transformers  equal  to  93 
per  cent,  and  assume  that  all  the  currents  have  the  same  harmonics  as 
given  above.  The  total  efficiency  will  be  70  per  cent.  If  the  harmonics 
are  now  added,  the  30  per  cent  loss  will  become  about  35  per  cent,  the 
efficiency  will  be  decreased  to  65  per  cent  nearly,  a  loss  of  5  per  cent. 
There  is  too  much  assumption  about  this  calculation  to  warrant  full 
belief,  and  the  figures  are  given  more  as  a  challenge  to  further  investi- 
gation than  as  facts.  That  there  is  a  decrease  of  efficiency  is  certain, 
but  the  amount  must  be  determined  by  further  experiment  and  mathe- 
matical investigation.  But,  however  small  the  loss,  provided  it  occurs 
in  the  transformers  or  the  dynamos  and  motors,  it  may  be  of  great 
consequence  on  account  of  its  heating  effect,  because  the  output  of 
these  is  limited  by  the  amount  of  the  heat  generated. 

The  practical  conclusion  seems  to  be  that  transformers  and  the  arma- 
tures of  dynamos  to  be  used  in  the  transmission  of  power  must  be 
designed  for  low  magnetizations.  By  experiment  with  transformers, 

4  This  formula  assumes  that  the  resistance  is  the  same  for  the  harmonics,  whereas 
it  is  greater  on  account  of  the  '  skin '  effect. 


EFFECT  OF  HARMONICS  ox  THE  TRANSMISSION  OF  POWER     283 

made  by  Dr.  Duncan  in  this  laboratory,  immense  distortion  of  the 
curves  has  been  found  when  the  induction  exceeds  12,000  lines  per 
square  centimetre,  while  the  curves  are  comparatively  smooth  with  only 
5000;  hence  I  scarcely  think  it  advisable  to  use  more  than  5000  for 
transformers,  even  though  low  frequency  were  used.  As  to  dynamos 
and  motors  the  limit  will  depend  on  the  variety  of  machine  used  and 
will  not  influence  the  better  class  very  much. 

The  fixing  of  the  limit  of  magnetization  of  transformers  at  5000 
causes  the  output  with  given  current  to  vary  inversely  as  the  frequency. 
As  the  hysteresis  with  slow  frequency  will  be  less,  we  may  increase  the 
current  somewhat  to  make  up  for  it.  As  to  the  exact  law,  it  depends 
on  the  relative  dimensions  of  wire  and  iron.  Practically  we  might 
estimate  for  an  ordinary  transformer  that  the  output  varied  inversely 
as  the  eight-tenth  power  of  the  frequency. 

The  law  that  the  output  varies  inversely  as  the  four-tenth  power  of 
the  frequency  assumes  that  the  magnetization  increases  with  decrease 
of  frequency  and  thus  distorts  the  curves  as  shown  above. 

The  immense  increase  of  the  size  and  cost  of  transformers  when  dis- 
tortion of  the  curve  is  avoided  precludes  the  use  of  very  low  frequencies 
even  were  it  otherwise  desirable. 

It  is  to  be  noted  that  the  action  of  the  iron  in  producing  harmonics 
is  directly  on  the  electromotive  force,  and  the  amount  of  current  flow- 
ing will  depend  on  the  resistance  and  the  self-induction  of  the  circuit. 
The  resistance,  owing  to  so-called  '  skin '  effect,  will  be  greater  for  the 
harmonics  than  for  the  fundamental  period.  Self-induction  depending 
on  the  air  will  always  diminish  the  harmonics,  while  if  it  is  due  to  iron 
it  may  either  increase  or  decrease  them  according  to  their  phase. 

The  measurement  of  the  energy  supplied  by  an  alternating  current  is 
also  much  complicated  by  the  presence  of  harmonics. 

Let  the  current  be 

C  =  A^  sin  (bt  +  <i)  +  As  sin  (3  U  -f  ?>3)  +  A&  sin  (5  bt  +  ? s)  + 
and  electromotive  force 

E  =  B,  sin  bt  +  B3  sin  (3  bt  +  v'-8)  +  B,  sin  (  5  bt  +  *.'•,)  + 
The  energy  transmitted  is,  then,  per  unit  of  time 

C'CE dt=±    r'cEd (bt) 

If  n  is  the  number  of  complete  periods  in  the  primary  term,  then  b  = 
2;rn  and  the  energy  transmitted  per  second  becomes 

\\.A1B1  cos  <p  +  A3  B,  cos  O3  -  08)  +  A,  B,  cos  (cr5  -  <?'5)  +  etc.] 


284  HENRY  A.  EOWLAND 

An  ordinary  wattmeter  in  the  form  of  an  electrodynamometer  with 
non-inductive  coils  would  give  the  correct  value  of  this  quantity,  but 
any  attempt  to  multiply  the  mean  electromotive  force  by  the  current 
and  the  cosine  of  the  phase  would  lead  to  an  incorrect  result  unless  this 
was  done  for  each  harmonic  separately. 

It  is  to  be  noted  that  the  introduction  of  condensers  to  balance  self- 
induction  will  only  work  for  one  period  at  a  time. 

Indeed  very  many  of  the  results  hitherto  obtained  by  observers  and 
theorists  will  require  modification  in  the  presence  of  these  harmonics. 

It  would  seem  from  the  above  that  the  transmission  of  a  current  for 
electric  lighting  is  quite  a  different  thing  from  the  transmission  of  a 
suitable  current  for  motors.  It  will  be  remembered  that  the  transmis- 
sion in  the  Frankfort-Lauffen  experiment  was  one  of  a  lighting  current 
alone  and  that  some  mystery  seems  to  hang  over  the  motor  tests.  Can 
the  presence  of  these  harmonics  have  anything  to  do  with  this  ? 


53 


[The  Engineering  Magazine,  VIII,  589-596,  January,  1895] 

It  is  not  uncommon  for  electricians  to  be  asked  whether  modern 
science  has  yet  determined  the  nature  of  electricity,  and  we  often  find 
difficulty  in  answering  the  question.  When  the  latter  comes  from  a 
person  of  small  knowledge  which  we  know  to  be  of  a  vague  and  general 
nature,  we  naturally  answer  it  in  an  equally  vague  and  general  manner; 
but  when  it  comes  from  a  student  of  science  anxious  and  able  to  bear 
the  truth,  we  can  now  answer  with  certainty  that  electricity  no  longer 
exists.  Electrical  phenomena,  electrostatic  actions,  electromagnetic 
action,  electrical  waves, — these  still  exist  and  require  explanation;  but 
electricity,  which,  according  to  the  old  theory,  is  a  viscous  fluid  throw- 
ing out  little  amoeba-like  arms  that  stick  to  neighboring  light  sub- 
stances and,  contracting,  draw  them  to  the  electrified  body,  electricity 
as  a  self-repellent  fluid  or  as  two  kinds  of  fluid,  positive  and  negative, 
attracting  each  other  and  repelling  themselves, — this  electricity  no 
longer  exists.  For  the  name  electricity,  as  used  up  to  the  present  time, 
signifies  at  once  that  a  substance  is  meant,  and  there  is  nothing  more 
certain  to-day  than  that  electricity  is  not  a  fluid. 

This  makes  the  task  of  one  who  attempts  to  explain  modern  elec- 
trical theory  a  very  difficult  one,  for  the  idea  of  electricity  as  a  fluid 
pervades  the  whole  language  of  electrical  science,  and  even  the  defini- 
tions of  electrical  units  as  adopted  by  all  scientists  suggest  a  fluid  theory. 
No  wonder,  then,  that  some  practical  men  have  given  up  in  despair 
and  finally  concluded  that  the  easiest  way  to  understand  a  telegraph 
line  is  to  consider  that  the  earth  is  a  vast  reservoir  of  electrical  fluid, 
which  is  pumped  up  to  the  line  wire  by  the  battery  and  finally  descends 
to  its  proper  level  at  the  distant  end.  Is  not  this  the  proper  conclusion 
to  draw  from  that  unfortunate  term  '  electric  current '  ?  Kemember- 
ing  this  fact, — that  we  cannot  yet  free  ourselves  from  these  old  theories, 
and  exactly  suit  our  words  to  our  meaning, — we  shall  now  try  to  under- 
stand the  modern  progress  in  electrical  theory. 

This  whole  progress  is  based  upon  something  in  the  human  mind 
which  warns  us  against  the  possibility  of  attraction  at  a  distance 


286  HENRY  A.  ROWLAND 

through  vacant  space:  Newton  felt  this  impossibility  in  the  case  of 
gravitation,  but  it  is  to  Faraday  that  we  must  look  principally  for  the 
idea  that  electrical  and  magnetic  actions  must  be  carried  on  by  means 
of  a  medium  filling  all  space  and  usually  called  the  ether.  The  develop- 
ment of  this  idea  leads  to  the  modern  theory  of  electrical  phenomena. 

Take  an  ordinary  steel  magnet  and,  like  Faraday,  cover  it  with  a 
sheet  of  paper,  and  upon  this  sprinkle  iron  filings.  Mapped  before  us 
we  see  Faraday's  lines  of  magnetic  force  extending  from  pole  to  pole. 
We  can  calculate  the  form  of  these  lines  on  the  supposition  that  a 
magnetic  fluid  is  either  distributed  over  the  poles  of  the  magnet  or 
on  its  molecules,  assuming  that  attraction  takes  place  through  space 
without  an  intervening  medium.  But  at  this  idea  the  mind  of  Faraday 
revolted,  and  he  conceived  that  these  lines,  drawn  for  us  by  the  iron 
filings,  actually  exist  in  the  ether  surrounding  the  magnet;  he  even 
conceived  of  them  as  having  a  tension  along  their  length  and  a  repul- 
sion for  one  another  perpendicular  to  their  length. 

Two  magnets,  then,  near  each  other,  become  connected  by  these  lines, 
which,  like  little  elastic  bands  always  pulling  along  their  length,  strive 
to  bring  the  magnets  together.  These  so-called  lines  of  force  (now 
called  tubes  of  force)  were,  by  his  theory,  conducted  better  by  iron  and 
worse  by  bismuth  than  by  the  ether  of  space,  and  so  gave  the  explana- 
tion of  magnetic  attraction  and  diamagnetic  repulsion. 

The  same  theory  of  lines  of  force  was  also  applied  by  Faraday  to 
electrified  bodies,  and  thus  all  electrostatic  attractions  were  explained. 
By  this  idea  of  lines  of  force  it  will  be  seen  that  Faraday  did  away 
with  all  action  at  a  distance  and  with  all  magnetic  and  electrical  fluids, 
and  substituted,  instead,  a  system  in  which  the  ether  surrounding  the 
magnet  or  the  electrified  body  became  the  all-important  factor  and  the 
magnet  or  electrified  body  became  simply  the  place  where  the  lines  of 
force  ended:  where  a  line  of  magnetic  force  ended,  there  was  a  portion 
of  imaginary  magnetic  fluid:  where  a  line  of  electric  force  ended,  there 
was  a  portion  of  imaginary  electric  fluid.  As  the  quantities  of  so- 
called  plus  and  minus  electricity  in  any  system  are  equal,  we  can 
thus  imagine  every  charged  electrical  system  to  be  composed  of  a 
group  of  tubes  of  electrical  force  (more  strictly  electric  induction) 
which  unite  the  plus  and  minus  electrified  bodies,  each  unit  tube  having 
one  unit  of  plus  electricity  on  one  end  and  one  unit  of  minus  electricity 
on  the  other.  The  tension  along  the  tube  explains  the  reason  why 
such  an  arrangement  acts  as  if  there  were  real  plus  and  minus  elec- 
trical fluids  on  the  ends  of  the  tube,  attracting  one  another  at  a  dis- 


MODERN  THEORIES  AS  TO  ELECTRICITY  287 

tance.  Consider  a  plus  electrified  sphere  far  away  from  other  bodies. 
The  lines  of  force  radiate  from  it  in  all  directions,  and,  heing  symmetri- 
cal around  the  sphere,  they  pull  it  equally  in  all  directions.  Now 
bring  near  it  a  minus  electrified  body,  and  the  lines  of  force  turn  toward 
it  and  become  concentrated  on  the  side  of  the  sphere  toward  such  a 
body.  Hence  the  lines  pull  more  strongly  in  the  direction  of  the 
negative  body,  and  the  sphere  tends  to  approach  it. 

In  the  case  of  a  conducting  body  the  lines  of  force  always  pass  out- 
wards perpendicularly  to  the  surface,  and  hence,  if  we  know  the  distri- 
bution of  the  lines  over  the  surface,  or  the  so-called  surface  density  of 
the  electricity,  we  can  always  tell  in  which  direction  the  body  tends  to 
move.  It  is  not  necessary  to  know  whether  there  are  any  attracting 
bodies  near  the  conductor,  but  only  the  distribution  of  the  lines.  These 
lines  then  do  away  with  all  necessity  for  considering  action  at  a  dis- 
tance, for  we  only  have  to  imagine  a  kind  of  ether  in  which  lines  of 
force  with  given  properties  can  exist,  and  we  have  the  explanation  of 
electric  attraction. 

But  the  question  now  arises  as  to  how  the  lines  of  electric  force  can 
be  produced  in  the  ether,  or,  in  other  words,  how  bodies  can  be  charged. 

In  the  first  place  we  know  that  equal  quantities  of  plus  and  minus 
electricity  are  always  produced.  As  an  illustration,  suppose  it  is  re- 
quired to  charge  two  balls  with  electricity.  Pass  a  conducting  wire 
between  them  with  a  galvanic  battery  in  its  circuit.  The  galvanic 
battery  generates  the  lines  of  force ;  these  crowd  together  around  it  and 
push  each  other  sideways  until  their  ends  are  pushed  down  the  wire 
and  many  of  them  are  pushed  out  upon  the  balls. 

When  the  tension  backwards  along  the  lines  of  force  just  balances 
the  forward  push  of  the  electromotive  force  of  the  battery,  equilibrium 
is  established.  If  the  wire  is  a  good  conductor,  there  may  be  electrical 
oscillations  before  the  lines  come  to  rest  in  a  given  position,  and  this  I 
shall  consider  below. 

The  motion  of  the  ends  of  the  lines  of  force  over  and  in  the  wire 
constitutes  what  is  called  an  electric  current  in  the  wire  which  is 
accompanied  by  magnetic  action  around  it  and  also  by  waves  of  electro- 
magnetic disturbance  which  pass  outward  into  space. 

If,  after  equilibrium  is  established,  we  remove  the  wire,  we  have 
simply  two  charged  spheres  connected  by  lines  of  electrostatic  force 
and  thereby  attracted  to  each  other.  If  we  replace  the  battery  by  a 
dynamo  or  by  an  electric  machine  the  effect  is  the  same. 

But  there  is  another  way  by  which  bodies  are  often  charged  and 


288  HENEY  A.  EOWLAND 

that  is  by  friction.  In  this  case  we  can  suppose  the  glass  to  take  hold 
of  one  end  of  the  lines  of  force  and  the  rubber  the  other  end  and  it  is 
then  only  necessary  to  pull  the  bodies  asunder  to  fill  the  space  with 
lines.  The  friction  is  merely  needed  to  bring  the  two  bodies  into  inti- 
mate contact  and  remove  them  gently  from  each  other. 

The  following  considerations  may  guide  us  in  understanding  the 
details  of  the  process.  It  is  well  known  from  Faraday's  researches 
that  a  given  quantity  of  electricity  has  a  fixed  relation  to  the  chemical 
equivalents  of  substances.  Thus  it  requires  10,000  absolute  electro- 
magnetic units  of  electricity  to  deposit  114  grams  of  silver,  68  grams  of 
copper,  34  grams  of  zinc,  etc. 

Hence  we  can  consider,  for  instance,  in  chloride  of  silver  that  the 
atoms  of  silver  are  joined  to  the  atoms  of  chlorine  by  lines  of  electro- 
static force  which  hold  them  to  each  other.  If,  by  rubbing  the  chloride 
of  silver,  we  could  remove  the  chlorine  on  the  rubber  while  leaving 
the  silver,  we  could  stretch  them  asunder  and  so  fill  space  with  the  lines 
of  electrostatic  force.  According  to  this  theory,  then,  each  atom  has 
a  number  of  lines  of  force  attached  to  it,  and  it  is  only  by  stretching 
the  atoms  apart  that  we  can  fill  an  appreciable  space  with  them  and  so 
cause  electrostatic  action  at  a  distance. 

We  come  to  the  conclusion,  then,  that  all  electrification  is  originally 
produced  by  separating  the  atoms  of  bodies  from  one  another,  which 
can  be  done  by  breaking  contact,  by  friction,  or  by  direct  chemical 
action  of  one  substance  on  another,  or  in  some  other  manner  not  so 
common.  The  lines  of  electrostatic  force  in  a  case  of  electricity  at 
rest  must  always  begin  and  end  on  matter,  and  they  can  never  have 
their  ends  in  space  free  from  matter.  The  ends  can  be  carried  along 
with  the  matter,  constituting  electric  convection,  or  they  can  slide 
through  a  metallic  conductor  or  an  electrolyte  or  rarefied  gas,  making 
what  we  call  an  electric  current;  but,  as  they  cannot  end  in  a  vacuum, 
they  cannot  pass  through  it.  Thus  we  conclude  that  a  vacuum  is  a 
perfect  non-conductor  of  electricity. 

The  exact  process  by  which  the  ends  of  the  lines  of  force  pass 
through  and  along  a  conductor  can  at  present  be  only  dimly  imagined, 
and  no  existing  theory  can  be  considered  as  entirely  satisfactory.  In 
the  case  of  an  electrolyte,  however,  we  can  form  a  fairly  perfect  picture 
of  what  takes  place  as  the  decomposition  goes  on.  Thus,  in  the  case  of 
zinc  and  copper  in  hydrochloric  acid,  we  can  imagine  the  zinc  plate 
attracting  the  chlorine  of  the  acid,  thus  stretching  out  the  natural  line 
of  electric  force  connecting  the  chlorine  atom  and  the  first  hydrogen 


MODERN  THEORIES  AS  TO  ELECTRICITY  289 

atom;  we  can  imagine  the  atoms  of  chlorine  and  hydrogen  in  the  body 
of  the  liquid  recombining  with  each  other  and  their  lines  of  force  unit- 
ing until  they  form  a  complete  line  long  enough  to  stretch  from  the 
zinc  to  the  copper  plate;  and  all  without  once  making  a  line  of  force 
without  its  end  upon  matter.  We  can  further  imagine  the  ends  of  this 
line  sliding  along  the  copper  and  zinc  plates  to  the  conducting  wires 
and  down  their  length,  thus  making  an  electric  current  and  carrying 
the  energy  of  chemical  action  to  a  great  distance. 

If  the  ends  of  the  lines  should  slide  along  the  wire  without  any 
resistance,  the  wire  would  be  a  perfect  conductor:  but  all  substances 
present  some  resistance,  and  in  this  case  heat  is  generated.  This  we 
always  find  where  an  electric  current  passes  along  a  wire:  as  to  the 
exact  nature  of  this  resistance  or  the  nature  of  metallic  conduction  in 
general  we  know  little,  but  I  believe  we  are  approaching  the  time  when 
we  can  at  least  imagine  what  happens  in  this  most  interesting  case. 

Besides  the  heating  due  to  the  electric  current,  steadily  flowing,  we 
must  now  account  for  the  magnetic  lines  of  force  surrounding  the  cur- 
rent and  the  magnetic  induction  of  one  current  on  the  other. 

If  the  current  is  produced  by  the  ends  of  the  tubes  of  electrostatic 
force  moving  along  the  wire,  then  we  may  imagine  that  the  movement 
of  the  lines  of  electrostatic  force  in  space  produces  the  lines  of  mag- 
netic force  in  a  direction  at  right  angles  to  the  motion  and  to  the 
direction  of  the  lines  of  electrostatic  force.  At  the  same  time  we  must 
be  careful  not  to  assume  too  readily  that  one  is  the  cause  and  the  other 
the  effect :  for  we  well  know  that  a  moving  line  of  magnetic  force  (more 
properly  induction)  produces,  as  Faraday  and  Maxwell  have  shown,  an 
electric  force  perpendicular  to  the  magnetic  line  and  to  the  direction  of 
motion.  Neither  line  can  move  without  being  accompanied  by  the 
other,  and  we  can,  for  the  moment,  imagine  either  one  as  the  cause  of 
the  other.  However,  for  steady  currents,  it  is  simpler  to  take  the  mov- 
ing lines  of  electrostatic  force  as  the  cause  and  the  magnetic  lines  as 
the  effect. 

We  have  now  to  consider  what  happens  when  we  have  to  deal  with 
variable  currents  rather  than  steady  ones. 

In  this  case  we  know  from  the  calculations  of  the  great  Maxwell 
and  the  demonstrations  of  Hertz  that  waves  of  electromagnetic  disturb- 
ance are  given  out.  To  produce  these  waves,  however,  very  violent 
disturbances  are  necessary.  A  fan  waved  gently  in  the  air  scarcely 
produces  the  mildest  sort  of  waves,  while  a  bee,  with  comparatively 
small  wings  moved  quickly  and  vigorously,  emits  a  loud  sound. 
19 


%\ 


290  HENKY  A.  KOWLAND 

So,  with  electricity,  we  must  have  a  very  violent  electrical  vibration 
before  waves  carrying  much  energy  are  given  out. 

Such  a  vibration  we  find  when  a  spark  passes  from  one  conductor 
to  another.  The  electrical  system  may  be  small  in  size,  but  the  im- 
mensely rapid  vibrations  of  millions  of  times  per  second,  like  the  quick 
vibration  of  a  bee's  wing,  sends  out  a  volume  of  waves  that  a  slowly 
moving  current  is  not  capable  of  producing.  The  velocity  of  these 
waves  is  now  known  to  be  very  nearly  300,000  kilometers  per  second. 
This  is  exactly  the  velocity  of  waves  of  light,  or  other  radiation  in 
general,  and  there  is  no  doubt  at  present  in  the  minds  of  physicists 
that  these  waves  of  radiation  are  electromagnetic  waves. 

By  this  great  discovery,  which  almost  equals  in  importance  that  of 
gravitation,  Maxwell  has  connected  the  theories  of  electricity  and  of 
light,  and  no  theory  of  one  can  be  complete  without  the  other.  Indeed 
they  must  both  rest  upon  the  properties  of  the  same  medium  which 
fills  all  space — the  ether. 

Not  only  must  this  ether  account  for  all  ordinary  electrical  and  mag- 
netic actions,  and  for  light  and  other  radiation,  but  it  must  also  account 
for  the  earth's  magnetism  and  for  gravitation. 

To  account  for  the  earth's  magnetism,  we  must  suppose  the  ether 
to  have  such  properties  that  the  rotation  of  ordinary  matter  in  it  pro- 
duces magnetism.  To  account  for  gravitation  it  must  have  such  prop- 
erties that  two  masses  of  matter  in  it  tend  to  move  toward  each  other 
with  the  known  law  of  force,  and  without  any  loss  of  time  in  the  action 
of  the  force.  We  know  that  moving  electrical  or  magnetic  bodies  re- 
quire a  time  represented  by  the  velocity  of  light  before  they  can  attract 
each  other  in  the  line  joining  them.  But,  for  gravitation,  no  time  is 
allowable  for  the  propagation  of  the  attraction. 

But  the  problem  is  not  so  hopeless  as  it  at  fiist  appears.  Have  we 
not  in  two  hundred  and  fifty  years  ascended  from  the  idea  of  a  viscous 
fluid  surrounding  the  electrified  body  and  protruding  arms  outward  to 
draw  in  the  light  surrounding  bodies  to  the  grand  idea  of  a  universal 
medium  which  shall  account  for  electricity,  magnetism,  light,  and 
gravitation  ? 

The  theory  of  electricity  and  magnetism  reduces  itself,  then,  to  the 
theory  of  the  ether  and  its  connection  with  ordinary  matter,  which  we 
imagine  to  be  always  immersed  in  it.  The  ether  is  the  medium  by 
which  alone  one  portion  of  matter  can  act  upon  another  portion  at  a 
distance  through  apparently  vacant  space. 

Let  us  then  attempt  to  see  in  greater  detail  what  the  ether  must 
exDlain  in  order  that  we  may,  if  possible,  imagine  its  nature. 


MODERN  THEORIES  AS  TO  ELECTRICITY  291 

1st.  It  must  be  able  to  explain  electrostatic  attraction.  These 
electrostatic  forces  are  mostly  rather  feeble  as  we  ordinarily  see  them. 
Air  breaks  down  and  a  spark  passes  when  the  tension  on  the  ether 
amounts  to  about  j^-g-  pound  to  the  square  inch.  It  is  the  air,  how- 
ever, that  causes  the  break-down.  Take  the  air  entirely  away,  and  we 
then  know  no  limit  to  this  force.  In  a  suitable  liquid  it  may  amount 
to  500  times  that  in  air  or  5  pounds  to  1  square  inch,  and  become  a 
very  strong  force  indeed.  In*  a  perfect  vacuum  the  limit  is  unknown, 
but  it  cannot  be  less  than  in  a  liquid,  and  may  thus  possibly  amount 
to  hundreds,  if  not  thousands,  of  pounds  to  the  square  inch. 

2d.  It  must  explain  magnetic  action.  These  actions  are  apparently 
stronger  than  electrostatic  actions,  but  in  reality  they  are  not  neces- 
sarily so.  A  tension  on  the  ether  of  only  a  few  hundred  pounds  on 
the  square  inch  will  account  for  all  magnetic  attraction  that  we  know  of, 
although  we  are  able  to  fix  no  limit  to  the  force  the  ether  will  sustain. 
No  signs  have  ever  been  discovered  of  the  ether  breaking  down. 

Again,  we  must  be  able  to  account  for  the  magnetic  rotation  of 
polarized  light  as  it  passes  through  the  magnetic  field;  and  it  can  only 
be  accounted  for  by  assuming  a  rotation  around  the  lines  of  mag- 
netic force.  This  action,  however,  takes  place  only  while  the  lines 
of  magnetic  force  pass  through  matter,  and  it  has  never  been  observed 
in  the  ether  itself.  The  velocity  of  rotation,  however,  is  immense,  the 
plane  of  polarization  rotating  in  some  cases  300,000,000  times  per 
second. 

The  ether  must  also  account  for  the  earth's  magnetism.  If  we 
assume  that  magnetic  lines  of  force  are  simply  vortex  filaments  in  the 
ether,  we  have  only  to  suppose  that  the  ether  is  carried  around  by  the 
rotation  of  the  earth,  and  we  have  the  explanation  needed.  The  mag- 
netism of  the  earth  would  then  be  simply  a  whirlpool  in  the  ether. 

3d.  The  ether  must  be  able  to  transmit  to  a  distance  an  immense 
amount  of  energy  either  by  means  of  electromagnetic  waves  as  in  light 
or  by  the  similar  action  which  takes  place  in  the  ether  surrounding  a 
wire  carrying  an  electric  current. 

The  amount  of  energy  which  can  be  transmitted  by  the  ether  in 
this  manner  is  enormous,  far  exceeding  that  which  can  be  carried  by 
anything  composed  of  ordinary  matter.  Thus  take  the  case  of  sun- 
light: on  the  earth's  surface  illuminated  by  strong  sunlight  a  horse- 
power of  energy  falls  on  every  7  square  feet.  At  the  surface  of  the 
sun  the  etherial  waves  carry  energy  outward  at  the  rate  of  nearly  8000 
horse-power  per  square  foot! 


292  HENRY  A.  EOWLAND 

Again,  an  electric  wire  as  large  as  a  knitting  needle,  surrounded 
with  a  tube  half  an  inch  in  diameter  in  which  a  perfect  vacuum  has 
been  made  to  prevent  the  escape  of  electricity,  may  convey  to  a  dis- 
tance a  thousand  horse-power,  indeed  even  ten  thousand  or  more  horse- 
power, there  being  apparently  no  limit  to  the  amount  the  ether  can 
carry. 

Compare  this  with  the  steam-engine,  where  only  a  few  hundred 
horse-power  require  an  enormous  and  clumsy  steam  pipe.  Or,  again, 
the  amount  carried  by  a  steel  shaft,  which,  at  ordinary  rate  of  speed, 
would  require  to  be  about  a  foot  in  diameter  to  transmit  10,000  horse- 
power. 

When  we  compare  the  energy  transmitted  through  a  square  foot  of 
ether  in  waves,  as  in  the  case  of  the  sun,  with  the  amount  that  can  be 
conveyed  by  means  of  sound  waves  in  air  or  even  sound  waves  in  steel, 
the  comparison  becomes  simply  ridiculous,  the  ether  being  so  im- 
mensely superior.  As  quick  as  light,  the  ether  sends  its  wave  energy 
to  the  distance  of  a  million  miles  while  the  sluggard  air  carries  it  one. 
Thus,  with  equal  strain  on  each,  the  ether  carries  away  a  million  times 
the  energy  that  the  air  could  do. 

4th.  The  ether  must  account  for  gravitation.  For  this  purpose  we 
are  allowed  no  time  whatever  to  transmit  the  attraction.  As  soon  as 
the  position  of  two  bodies  is  altered,  just  so  soon  must  the  line  of  action 
from  one  to  the  other  be  in  the  straight  line  between  them. 

If  this  were  not  so,  the  motion  of  the  planets  around  the  sun  would 
be  greatly  altered.  Toward  the  invention  of  such  an  ether,  capable 
of  carrying  on  all  these  actions  at  once,  the  minds  of  many  scientific 
men  are  bent.  Now  and  then  we  are  able  to  give  the  ether  such  proper- 
ties as  to  explain  one  or  two  of  the  phenomena,  but  we  always  come 
into  conflict  with  other  phenomena  that  equally  demand  explanation. 

There  is  one  trouble  about  the  ether  which  is  rather  difficult  to 
explain,  and  that  is  the  fact  that  it  does  not  seem  to  concentrate  itself 
about  the  heavenly  bodies.  As  far  as  we  are  able  to  test  the  point, 
light  passes  in  a  straight  line  through  space  even  when  near  one  of 
the  larger  planets,  unless  the  latter  possesses  an  atmosphere.  This 
could  hardly  happen  unless  the  ether  was  entirely  incompressible  or 
else  possessed  no  weight. 

If  the  ether  is  the  cause  of  gravitation,  however,  it  is  placed  out- 
side the  category  of  ordinary  matter,  and  it  may  thus  have  no  weight 
although  still  having  inertia, — a  thing  impossible  for  ordinary  matter 
where  the  weight  is  always  exactly  proportional  to  inertia. 


MODEEN  THEOKIES  AS  TO  ELECTBICITY  293 

Ether,  then,  is  not  matter,  but  something  on  which  many  of  the 
properties  of  matter  depend. 

It  is  curious  to  note  that  Newton  conceived  of  a  theory  of  gravita- 
tion based  on  the  ether,  which  he  supposed  to  be  more  rare  around 
ordinary  matter  than  in  free  space.  But  the  above  considerations 
would  cause  the  rejection  of  such  a  theory.  We  have  absolutely  no 
adequate  theory  of  gravitation  as  produced  by  ether. 

To  explain  magnetism,  physicists  usually  look  to  some  rotation  in 
the  ether.  The  magnetic  rotation  of  the  plane  of  polarization  of  light 
together  with  the  fact  of  the  mere  rotation  of  ordinary  matter,  as 
exemplified  by  the  earth's  magnetism,  both  point  to  rotation  in  the 
ether  as  the  cause  of  magnetism.  A  smoke  ring  gives,  to  some  extent, 
the  modern  idea  of  a  magnetic  line  of  force.  It  is  a  vortex  filament 
in  the  ether. 

Electrostatic  action  is  more  difficult  to  explain,  and  we  have  hardly 
got  further  than  the  vague  idea  that  it  is  due  to  some  sort  of  elastic 
yielding  in  the  ether. 

Light  and  radiation  in  general  are  explained  when  we  understand 
clearly  magnetic  and  electrostatic  actions  as  the  two  are  linked  together 
with  certainty  by  MaxwelFs  theory. 

Where  is  the  genius  who  will  give  us  an  ether  that  will  reconcile 
all  these  phenomena  with  one  another  and  show  that  they  all  come 
from  the  properties  of  one  simple  fluid  filling  all  space,  the  life-blood 
of  the  universe — the  ether? 


60 


[American  Journal  of  Science  [4],  IV,  429-448,  1897 ;  Philosophical  Magazine  [5],  XL  V, 

66-85,  1898] 

The  electrical  quantities  pertaining  to  an  electric  current  which  it 
is  usually  necessary  to  measure,  outside  of  current,  electromotive  force, 
watts,  etc.,  are  resistances,  self  and  mutual  inductances  and  capacities. 
I  propose  to  treat  of  the  measurement  of  alternating  currents,  electro- 
motive force  and  watts  in  a  separate  paper.  Eesistances  are  ordinarily 
best  dealt  with  by  continuous  currents,  except  liquid  resistances.  I 
propose  to  treat  in  this  paper,  however,  mainly  of  inductances,  self  and 
mutual,  and  of  capacities  together  with  their  ratios  and  values  in  abso- 
lute measure  as  obtained  by  alternating  currents.  I  also  give  a  few 
methods  of  resistance  measurement  more  accurate  than  usually  given 
by  means  of  telephones  or  electrodynamometers  as  usually  used  and 
specially  suitable  for  resistances  of  electrolytic  liquids. 

I  have  introduced  many  new  and  some  old  methods,  depending  upon 
making  the  whole  current  through  a  given  branch  circuit  equal  to  zero. 
These  always  require  two  adjustments  and  they  must  often  be  made 
simultaneously.  However,  some  of  them  admit  of  the  adjustments 
being  made  independently  of  each  other,  and  these,  of  course,  are  the 
most  convenient.  But  all  these  zero  methods  do  not  admit  of  any 
great  accuracy  unless  very  heavy  currents  are  passed  through  the 
resistances.  The  reason  of  this  is  that  an  electrodynamometer  cannot 
be  made  nearly  as  sensitive  for  small  currents  as  a  magnetic  galvano- 
meter. The  deflection  of  an  electrodynamometer  is  as  the  square  of 
the  current.  To  make  it  doubly  sensitive  requires  double  the  number 
of  turns  in  both  the  coils.  Hence  we  quickly  reach  a  limit  of  sensitive- 
ness. It  is  easy  to  measure  an  alternating  current  of  -0001  ampere  and 
difficult  for  -00001  ampere.  A  telephone  is  more  sensitive  and  an 
instrument  made  by  suspending  a  piece  of  soft  iron  at  an  angle  of  45°, 
as  invented  by  Lord  Eayleigh,  is  also  probably  more  sensitive. 

For  this  reason  I  have  introduced  here  many  new  methods,  depend- 
ing upon  adjusting  two  currents  to  a  phase-difference  of  90°  which  I 
believe  to  be  a  new  principle.  This  I  do  by  passing  one  current  through 


ELECTEICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      295 

the  fixed  and  the  other  through  the  suspended  coil  of  an  electrodynamo- 
meter.  By  this  means  a  heavy  current  can  be  passed  through  the  fixed 
coils  and  a  minute  current  through  the  movable  coil,  thus  multiplying 
the  sensitiveness  possibly  1000  times  over  the  zero  current  method. 

I  have  also  found  that  many  of  the  methods  become  very  simple  if 
we  use  mutual  inductances  made  of  wires  twisted  together  and  wound 
into  coils.  In  this  way  the  self  inductances  of  the  coils  are  all  practi- 
cally equal  and  the  mutual  inductances  of  pairs  of  coils  also  equal. 
Hence  we  have  only  to  measure  the  minute  difference  of  these  two  to 
reduce  the  constants  of  the  coil  to  one  constant,  and  yet  by  proper 
connections  we  can  vary  the  inductances  in  many  ratios.  Three  wires 
is  a  good  number  to  use.  However,  the  electrostatic  induction  between 
the  wires  must  be  carefully  allowed  for  or  corrected  if  much  greater 
accuracy  than  y^  is  desired. 

By  these  various  methods  the  measurement  of  capacities  and  induc- 
tances has  been  made  as  easy  as  the  measurement  of  resistances,  while 
the  accuracy  has  been  vastly  improved  and  many  sources  of  error 
suggested. 

Relative  results  are  more  accurate  than  absolute  as  the  period  of  an 
alternating  current  is  difficult  to  determine,  and  its  wave  form  may 
depart  from  a  true  sine  curve. 

Let  self  inductances,  mutual  inductances,  capacities  and  resistances 
be  designated  by  L  or  I,  M  or  ra,  C  or  c,  E  or  r  with  the  same  suffixes 
when  they  apply  to  the  same  circuit,  the  mutual  inductance  having  two 
suffixes.  Let  &  be  2  TT  times  the  number  of  complete  periods  per  second, 

or  &  =  2-n.     The  quantities  &L,  bM  or  ^  are  of  the  dimensions  of 

resistance  and  thus  -^.,  &*LC  or  b*MC  have  no  dimensions.     I'LM,  -^ 

M 

or  -fy  have  dimensions  of  the  square  of  resistances. 

Where  we  have  a  mutual  inductance  M12,  we  have  also  the  two  self 
inductances  of  the  coils  Lt  and  L2.  When  these  coils  are  joined  in  the 
two  possible  manners,  the  self  inductance  of  the  whole  is 

L,  +  Z2  +  ZMU  or  L!  +  L,  -  2Mn. 

In  case  of  a  twisted  wire  coil  the  last  is  very  small.  Likewise 
L1L2  —  3/212  will  be  very  small  for  a  twisted  wire  coil,  as  is  found  by 
multiplying  the  first  two  equations  together. 

If  there  are  more  coils  we  can  write  similar  equations.  For  three 
coils  we  have 


296  HENRY  A.  KOWLAND 

12  +  2M1 


2. 
3. 

Connecting  them  in  pairs,  we  have  the  self  inductances 


L1  +  L2—2M12  L1  +  L3—2M13 

There  are  many  advantages  in  twisting  the  wires  of  the  standard 
inductance  together,  but  it  certainly  increases  the  electrostatic  action 
between  the  coils.  This  latter  source  of  error  must  be  constantly  in 
mind,  however,  and,  for  great  accuracy,  calculated  and  corrected  for. 
But  by  proper  choice  of  method  we  may  sometimes  eliminate  it. 

For  the  most  accurate  standards,  I  do  not  recommend  the  use  of 
twisted  wire  coils,  at  least  without  great  caution.  But  for  many  pur- 
poses it  certainly  is  a  great  convenience,  especially  where  only  an 
accuracy  of  one  per  cent  is  desired.  In  some  calculations  I  have  made, 
I  have  obtained  corrections  of  from  one  to  one-tenth  per  cent  from 
this  cause. 

For  twisted  wires  the  above  results  reduce  to  3L  -f-  61f,  3L  —  2M  . 
Similar  equations  can  be  obtained  for  a  larger  number  of  wires.  For 
twisted  wire  coils,  n  wires  joined  abreast,  the  self  induction  is 

-=1  —  ,  which  is  practically  equal  to  L  or  M.     The  resistance 

is  E/n. 

When  we  have  n  =  p  -\-  m  wires  twisted  and  wound  in  a  coil  and  we 
connect  them  p  direct  and  m  reverse,  the  resistance  and  self  induction 
will  be 

nR*+FR[AC+£C—nAB]       ,  If  [n  (A  +  B)  —  0~\  +  VABC 
(nR)*+(bC?  2 

where  R  is  the  resistance  of  one  coil  and 

A  =  L  +  (n 
B=L  -  M 


This  gives  self  inductances  and  resistances  equal  or  less  than  L  and  R. 
The  correction  for  electrostatic  induction  remains  to  be  put  in.  For 
the  general  case,  the  equation  is  very  complicated  for  coils  abreast, 
with  mutual  inductances. 

The  number  of  mutual  inductances  to  be  obtained  is  M  for  two 
wires,  0,  M,  2M  for  three  wires,  0,  M,  2M,  3M  for  four  wires,  etc.     From 


297 

these  results  we  see  that  we  are  always  able  to  reduce  mutual  to  self 
inductance.  Measuring  the  self  inductance  of  a  coil  connected  in 
different  ways,  we  can  always  determine  the  mutual  inductances  in 
terms  of  the  self  inductances. 

Thus  we  need  not  search  for  methods  of  directly  comparing  mutual 
inductances  with  each  other,  although  I  have  given  two  of  these,  but 
we  can  content  ourselves  with  measuring  self  inductances  and  capaci- 
ties. Fortunately  most  of  the  methods  are  specially  adapted  to  the 
latter,  the  ratio  of  self  inductance  to  capacity  being  capable  of  great 
exactness  by  many  methods. 

In  the  use  of  condensers  I  have  met  with  great  difficulty  from  the 
presence  of  electric  absorption.  I  have  found  that  this  can  be  repre- 
sented by  a  resistance  placed  in  the  circuit  of  the  condenser,  which 
resistance  is  a  function  of  current  period. 

I  have  developed  MaxwelPs  theory  of  electric  absorption  in  this 
manner.  Correcting  his  equations  for  a  small  error,  I  have  developed 
the  resistance  and  capacity  of  a  condenser  as  follows: 

Let  a  condenser  be  made  of  strata  of  thicknesses  ax  a2,  etc.,  and 
specific  induction  capacities  fcx  Jc2)  etc.,  and  resistances  p^  p2,  etc.  Then 
we  have 


where 


etc. 


etc. 

Mr.  Penniman  has  experimented  in  the  Johns  Hopkins  University 
laboratory  with  condensers  by  method  25  and  found  some  interesting 
results.  With  a  mica  standard  condenser  of  £  microfarad  he  was  not 


298  HENEY  A.  KOWLAND 

able  to  detect  any  electric  absorption,  although  I  have  no  doubt  one 
of  the  more  accurate  methods  will  show  it. 

With  a  condenser,  probably  of  waxed  paper,  he  found 

Number  of  complete  Capacity  in  Apparent  resistance 

periods  per  second.  microfarads.  in  ohms. 

14-0  4-64  139-6 

32-0  4-96  34-1 

53-3  4-96  20-5 

131-1  4-94  5-2 

The  first  value  of  the  capacity  seems  to  be  in  error,  possibly  one  of 
calculation.  However,  the  result  seems  to  show  a  nearly  constant 
capacity  but  a  resistance  increasing  rapidly  with  decrease  of  period,  as 
Maxwell's  formula  show.  The  constant  value  of  the  capacity  remains 
to  be  explained. 

Mr.  Penniman  will  continue  the  investigation  with  other  condensers, 
liquid  and  solid,  as  well  as  plates  in  electrolytic  liquids. 

The  results  in  the  other  measurements  have  been  fairly  satisfactory, 
but  many  of  the  better  methods  have  only  been  recently  discovered  and 
are  thus  untried.  But  we  must  acknowledge  at  once  that  work  of  the 
nature  here  described  is  most  liable  to  error.  Every  alternating  cur- 
rent has,  not  only  its  fundamental  period,  but  also  its  harmonics,  so 
that  very  accurate  absolute  values  are  almost  impossible  to  be  obtained 
without  great  care.  To  eliminate  them,  I  propose  to  use  an  arrange- 
ment of  two  parallel  circuits,  one  containing  a  condenser  and  the  other 
a  self-inductance,  each  with  very  little  resistance.  The  long  period 
waves  will  pass  through  the  second  side  and  the  short  ones  through  the 
condenser  side.  By  shunting  off  some  of  the  current  from  the  second 
side,  it  will  be  more  free  from  harmonics  than  the  first  one. 

However,  in  a  multipolar  dynamo,  especially  one  containing  iron, 
there  is  danger  of  long  period  waves  also,  which  this  method  might 
intensify.  A  second  arrangement,  using  the  condenser  side,  might 
eliminate  them.  However,  many  dynamos  without  iron  and  without 
too  many  poles  and  properly  wound  produce  a  very  good  curve  without 
harmonics,  especially  if  the  resistance  in  the  circuit  is  replaced  by  a 
self  inductance  having  no  iron.  These  remarks  apply  only  to  absolute 
determinations.  Eatios  of  inductance,  self  and  mutual,  and  capacity 
are  independent  of  the  period,  and  thus  it  can  always  be  eliminated. 
Measurements  of  resistances  also  are  independent. 

But  there  are  other  errors  which  one  who  has  worked  with  continuous 


ELECTRICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      299 

currents  may  fall  into.  Nearly  all  alternating  currents  generate  elec- 
tromagnetic waves  which  are  so  strong  that  currents  exist  in  every 
closed  circuit  with  any  opening  between  conductors  in  the  vicinity. 

We  eliminate  this  source  of  error  by  twisting  wires  together  and  other 
expedients.  But  in  avoiding  one  error,  we  plunge  into  another.  For, 
by  twisting  wires  we  introduce  electrostatic  capacity  between  them, 
which  may  vitiate  our  results.  Thus,  in  methods  23  or  24  for  com- 
paring mutual  inductances,  if  there  is  electrostatic  capacity  between 
the  wires,  a  current  will  flow  through  the  electrodynamometer  in  the 
testing  circuit  and  destroy  the  balance. 

Various  expedients  suggest  themselves  to  eliminate  this  trouble,  as, 
for  instance,  the  variation  of  the  resistance  A  in  the  above,  but  I  shall 
reserve  them  for  a  future  paper.  I  may  say,  however,  that  it  is  some- 
times possible,  as  in  method  12  for  instance,  to  choose  a  method  in 
which  the  error  does  not  exist. 

However,  with  the  best  of  methods,  much  rests  with  the  experimenter, 
as  errors  from  electromagnetic  and  electrostatic  induction  are  added 
to  errors  from  defective  insulation  when  we  use  alternating  currents. 

These  errors  are  generally  less  than  one  per  cent,  however,  and  intel- 
ligent and  careful  work  reduces  them  to  less  than  this. 

The  following  methods  generally  refer  by  number  to  the  plate  on 
which  the  resistances,  etc.,  are  generally  marked.  One  large  circle 
with  a  small  one  inside  represent  an  electrodynamometer.  Of  course 
the  circuit  of  the  small  coil  can  be  interchanged  with  the  large  one. 
Generally  we  make  the  smaller  current  go  through  the  hanging  coil. 

By  the  methods  1  to  14,  we  adjust  the  electrodynamometer  to  zero 
by  making  the  phase  difference  in  the  two  coils  90°.  For  greatest 
sensitiveness,  the  currents  through  the  two  coils  must  be  the  greatest 
possible,  heating  being  the  limit.  This  current  should  be  first  calcu- 
lated from  the  impedance  of  the  circuit,  as  there  is  danger  of  making 
it  too  great. 

In  the  second  series  of  methods,  15-26,  the  branch  circuit  in  which 
the  current  is  to  be  0  is  indicated  by  0. 

Resistances  in  the  separate  circuits  are  represented  by  R,  R',  Rt,  etc., 
and  r,  r',  rt,  etc.  Corresponding  self  inductances  and  capacities  in  the 
same  circuits  are  L,  L',  Lt,  etc.,  and  I,  I',  I,,  etc.,  or  C,  C',  C ',,  etc.,  and 
c,  c',  ct,  etc.  b  =  27tn  where  n  is  the  number  of  complete  current  waves 
per  second. 

The  currents  must  be  as  heavy  as  possible,  ^  ampere  or  more,  and  it 
is  well  to  make  those  that  require  a  current  of  more  than  j-^  ampere  of 


300  HENKY  A.  EOWLANB 

larger  wire  freely  suspended  in  oil.  A  larger  current  can,  however,  be 
passed  through  an  ordinary  resistance  box  for  a  second  or  two  without 
danger.  A  few  fixed  coarse  resistances  of  large  wire  in  air  or  oil  with 
ordinary  resistance  boxes  for  fine  adjustment,  are  generally  all  that 
are  required.  Special  boxes  avoiding  electrostatic  induction  are,  how- 
ever, the  best,  but  are  not  now  generally  obtainable. 

In  some  methods,  such  as  8,  9,  10,  etc.,  we  can  eliminate  undesirable 
terms  containing  the  current  period  by  using  a  key  which  suddenly 
changes  the  connections  before  the  period  has  time  to  change  much. 

In  using  twisted  wire  mutual  inductances,  methods  7  and  12  are 
about  or  entirely  free  from  error  due  to  electrostatic  action  between 
the  wires.  In  all  the  methods  this  error  is  less  when  the  resistance  of 
the  coils  is  least  and  in  23  and  24  when  A  is  least.  In  method  8  the 
error  is  very  small  when  the  coil  resistances  and  R  are  small  and  r  great. 
In  this  method  with  1  henry  and  1  microfarad  the  error  need  not 
exceed  1  in  1000.  Probably  the  same  remarks  apply  to  9,  10,  11,  also. 
By  suitable  adjustment  of  resistances  in  the  other  method,  the  error 
may  be  reduced  to  a  minimum.  It  can,  of  course,  be  calculated  and 
corrected  for. 

An  electrodynamometer  can  be  made  to  detect  -OOC1  ampere  without 
making  the  self  inductance  of  the  suspended  coil  more  than  -0007 
henrys  or  that  of  the  stationary  coils  more  than  -0006  henrys,  the 
latter  coil  readily  sustaining  a  current  of  -^  amperes  without  much 
heating. 

An  error  may  creep  in  by  methods  1-14  if  the  current  through  the 
suspension  is  too  great,  thus  heating  it  and  possibly  twisting  it.  This 
should  be  tested  by  short  circuiting  the  suspended  coil  or  varying  the 
current.  For  the  zero  method  it  is  eliminated  by  always  adjusting 
until  there  is  no  motion  on  reversing  the  current  through  one  coil. 

Inductances  containing  iron  introduce  harmonics  and  vary  with  cur- 
rent strength.  Thus  they  have  no  fixed  value. 

Closed  circuits  or  masses  of  metal  near  a  self  inductance,  dimmish 
it,  and  increase  the  apparent  resistance  which  effects  vary  with  the 
period.  Short  circuits  in  coils  are  thus  detected. 

Electrolytic  cells  act  as  capacities  which,  as  well  as  the  apparent 
resistance,  vary  with  the  current  period.  They  also  introduce  har- 
monics. The  same  may  be  said  of  an  electric  arc. 

An  incandescent  lamp  or  hot  wire  introduces  harmonics  into  the 
circuit. 

Hysteresis  in  an  iron  inductance  acts  as  an  apparent  resistance  in 


ELECTKICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      301 

the  wire  almost  independent  of  the  current  period,  and  does  not,  of 
itself,  introduce  harmonics.  The  harmonics  are  due  to  the  variation 
of  the  magnetic  permeability  with  the  amount  of  magnetization. 

Electric  absorption  in  a  condenser  acts  as  a  resistance  varying  with 
the  square  of  the  period,  the  capacity  also  varying,  as  I  have  shown 
above. 

In  general  any  circuit  containing  resistances,  inductances  and  capaci- 
ties combined  acts  as  a  resistance  and  inductance  or  capacity,  both  of 
which  vary  with  the  current  period,  the  square  of  the  current  period 
alone  entering.  For  symmetry  the  square  of  the  current  period  can 
alone  enter  in  all  these  cases  and  those  above. 

Hence  only  inductances  containing  no  iron  or  not  near  any  closed 
metallic  circuits  have  a  fixed  value.  The  same  may  be  said  of  con- 
densers, as  they  must  be  free  from  electric  absorption  or  electrolytic 
action  to  have  constants  independent  of  the  period.  There  is  no  ap- 
parent hysteresis  in  condensers  and  the  constants  do  not  apparently 
vary  with  the  electrostatic  force. 

The  following  numbers  indicate  both  the  number  of  the  method  and 
the  figures  in  the  plate,  p.  302. 

Method  1. 


L'  _  [r  (R.  +  R' 
~c 


Method  2. 


-R.R"}  \_R,  (r+R"}  +  Ru  (r  +  fl,)] 


Method  3. 
In  (1)  make  R'  =  R"  =  R,t  =  Q  or  in  (2)  make  R"  =  Rt  =  0,  R,,  =  <x>  , 

^  =  rR 

c 

In  case  the  circuit  r  contains  some  self  inductance,  I,  we  can  correct 
for  it  by  the  equation 


302 


HENRY  A.  EOWLAND 


17. 


In  methods  1  to  14  inclusive  the  concentric  circles  are  the  coils  of  the  electro- 
dynamometer.  Either  one  is  the  fixed  coil  and  the  other  the  hanging  coil.  Oblong 
figures  are  inductances  and  when  near  each  other,  are  mutual  inductances.  A  pair 
of  cross  lines  is  a  condenser. 


ELECTRICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      303 

Method  4- 

+  fl,,)]  [#  ( 
R'  R" 

Method  5. 


L,  =  [jy  (r  +  Rit)  +  R"(R' 


A  _  [fl,  (^" 

c  '  (Rr  +  R")  (R"  +  R 

Method  6. 


c        O 

We  can  correct  for  self  inductions,  U,  L"  in  the  circuits  R',  R"  by 
using  the  exact  equation 


R'R"(r+R")(R+R')=--0 
or  approximately 

±  =  (R+B)  (R'^--^- 


-. 
+  etc. 

Method  7. 
R,R3M13Ml2  +  b*\_L3Ml2-MrM  [^J/M-  Jf.JfJ  =  0 

For  a  coil  containing  three  twisted  wires,  M12  =  M1S  =  M23  and  the 
self  inductions  of  the  coils  are  also  equal  to  each  other  and  nearly  equal 
to  the  mutual  inductions.  Put  an  extra  self  induction  L3  in  R3  and  a 

capacity  C2  in  R2.     Replace  L3  by  L  -f-  L3  and  L2  by  L  —         and  we 

0  62 

can  write 


As  L  —  M  is  very  small  and  can  be  readily  known,  the  formula  will 
give  ^r  •    When  L  —  M  =  0  we  have 

Method  8. 

V  M(M+  1)  =  rR  2b*  M*   =~rR+(rR)' 

or  V  M(M—  L)  =  (rR)'        2b2  LM  —  rR—  (rR)' 


304  HENRY  A.  EOWLAKD 

Placing  a  capacity  in  the  circuit  R,  we  have  also 
b'M  (M+  L)  -  %=  rR 


In  case  the  coil  is  wound  with  two  or  more  twisted  wires,  M  —  L  is 
small  and  known.  For  two  wires,  M  —  L  is  negative.  For  three 
wires,  two  in  series  against  the  third,  M  can  be  made  nearly  equal  to 
2L.  Hence  M,  L  and  C  can  be  determined  absolutely,  or  C  in  terms 
of  M  or  vice  versa. 

To  correct  for  the  self  induction,  I,  or  r  we  have  the  exact  equations 


If  the  condenser  is  put  in  r,  we  have 


T       M 

or  —  -  =  rR  +  VM(L-M} 

Method  9. 
MM-*,  =  R, 

or  -  VL'M  +  *=RI 

Making  R"  =  co  and  r  +  R'  =  r  we  have 
-  VL'M+  M  or  VUM-  ^t 

C  Lr 

Taking  two  observations  we  can  eliminate  WL'M  and  we  have 


Knowing  L'M  we  can  find  C'.  Throwing  out  C'  (i.  e.,  making  it 
oo  )  we  can  find  WL'M  in  absolute  measure  :  then  put  in  C'  and  find  its 
value  as  above. 

To  correct  for  self  induction  in  R/f  we  have  for  case  R"  =  oo  ,  the 
exact  equation 


ELECTRICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      305 


The  correction,  therefore,  nearly  vanishes  for  two  twisted  wires  in  a 
coil  where  U  —  M  =  0  and  C  is  taken  out. 

Method  10. 


c  c 

\_R,R"  -  RltR'-\  \rlR'  +  R"  +  R,+  fl,,]  +  («  +  R)  (R"  +  £„)  \ 


This  can  be  used  in  the  same  manner  as  9  to  which  it  readily  reduces. 
But  it  is  more  general  and  always  gives  zero  deflection  when  adjusted, 
however  M  is  connected.  To  throw  out  (7  make  it  oo  . 


Method  11. 
L  —  M_ 

c 
L  +  M 


-  M}  (L-  M} 


c 

For  the  upper  equation  the  last  term  may  be  made  small  and  the 
method  may  be  useful  for  determining  L  —  M  when  c  is  known. 
Me'thod  8,  however,  is  better  for  this. 

Method  12. 

L'  =  R+R' 
I  ~        r 

Should  the  circuits  R  and  r  also  have  small  self  inductances,  L  and  I, 
we  can  use  the  exact  equation 


rR 


When  L'  and  Z  are  approximately  known,  we  can  write  the  following, 
using  the  approximate  value  on  the  right  side  of  the  equation 
L'_  R+R'T,       Lr      L      r       ,  VLl  , 


I  '        r 
Taking  out  L'  and  putting  a  condenser,  (7,  in  R  we  have 


For  a  condenser,  R  can  be  small  or  zero. 
20 


306  HENRY  A,.  BOWLAND 

Method  13. 

(A}  \bL"-    1  ,,T  -  [RtlR'-R,R"'\  I 
[_  bC"_\ 

This  determines  capacities  or  self  inductions  in  absolute  value.  As 
described  above,  mutual  induction  can  also  be  determined  by  convert- 
ing it  into  self  induction. 


Method 


Of  course,  in  any  of  these  equations,  methods  13  or  14,  L"  is  elimi- 
nated by  making  L"  =  0  or  the  condenser,  C,  is  omitted  by  making 
C  =  oo. 

Method  15. 


/ 

R'R- 


R'"R 


or  ^-  or  -  52Z  6V/—  R'"R'"R~R'R"  (^ 
"  '      ~     '"       '"-" 


— 

C,       L 

When  ^//;  =  oo  we  have 

A  —  -fl'^y,  (R"  +  R"')  —  R"RlR"t      _    ft,  r>  ^"    r  7->"/  r>          E>'  E>    T 

^r/  -  ^>///  —  ~  Ka>u       ~f>rrt  I2i    &—&  **u\ 

b2L  c"  —  R^Rt—R'R,! 

'  R"R'" 

If  we  adjust  by  continuous  current,  we  shall  have  R'"RI  —  R'Rtt  =  Q. 
For  a  condenser  we  can  made  R"  =  0  provided  there  is  no  electric 
absorption.  In  this  case  l}2LtC"  is  indeterminate  and  we  can  adjust 

to  findw,.     However,  two  simultaneous  adjustments  are  required. 

But  I  have  shown  that  the  presence  of  electric  absorption  in  a  con- 
denser causes  the  same  effect  as  a  resistance  in  its  circuit,  the  resist- 
ance, however,  varying*  with  the  period  of  the  current.  Hence  R"  must 


ELECTRICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      307 

include  this  resistance.     However,  the  value  of  R"  will  not  affect  the 
first  adjustment  much  and  so  the  method  is  easy  to  work.     If  it  is 
sensitive  enough  it  will  be  useful  in  measuring  the  electric  absorption 
of  condensers  in  terms  of  resistance. 
It  has  the  advantage  of  being  practically  independent  of  the  current 

period  for  ^  as  it  should  be. 
0 

For  comparison  of  capacities  the  same  simplification  does  not  occur. 
Indeed  the  method  is  of  very  little  value  in  this  case,  being  sur- 
passed by  16. 

Method  16. 
(A)  [R,R"-Rl,R'-\[W+r'  +  r"]  +  W[Rlr"-rfRJ  =  0 


t_ 

L,  °r  C"  ~  R,,  +  Rtl  (  W+  r'r  +  ") 

The  first  equation  is  satisfied  by  adjusting  the  Wheatstone  bridge  so 
as  to  make 

(RIR'—RIIR)=Q    R/'-Rl/=Q     Rl(Rll  +  r")-Rll(K  +  r')=Q 
That  is 

R,  -R'  -^ 

Rtl  ~  ~R"  ~  r" 

We  can  then  adjust  W  with  alternating  currents.  This  is  a  very 
good  method  and  easy  of  application  but  requires  many  resistances  of 
known  ratio.  Many  of  these,  however,  may  be  equal  without  disad- 
vantage. A  well  known  case  is  given  by  making  r'  and  r"  =  0. 

(B)  By  placing  self  inductions  or  condensers  in  R,  and  r"  instead 
of  the  above  we  have  the  following 

or      VL  ,-"  or  L>  -  << 

L''      r'-" 


Wr 


+      1      or  —  -•  or  +  VL  1"= 
FUP  c" 


")  (Rfi'-RuR)*  W(R/'-Rllrf) 
W+R" 


Making  R"  =  0  we  have 

c"         «r  "     L, 

or  -  VLp"  or  -'  = 


In  case  we  adjust  the  bridge  to  R,W  —  R'R/I  =  0  and  a  condenser 


308  HENRY  A.  EOWLAJSTD 

is  in  r"  so  that  we  can  make  r"  =  0,  the  value  of  —  l2Ltc"  will  be  inde- 
terminate and  we  can  find  —Jf  by  the  adjustment  of  W  alone. 

i  C  • 

This  is  an  excellent  method,  apparently,  as  only  one  adjustment  is 
required. 
However,  see  the  remarks  on  method   15.     This  present  method 

r"  =  0  for  —  is  Anderson's  with,  however,  alternating  currents  instead 

C 

of  direct  as  in  his. 

The  other  two  values  are  imaginary  in  this  case.     Indeed  the  whole 

method,  B,  is  only  of  special  value  for  —  ,  as  two  adjustments  are  needed 

c 

for  the  others. 

Method  17. 
(A)   TF=oo.  72=00 

VML'=  RtR"  -  RtlR 
L' 


By  this  method  the  self  induction  of  the  mutual  induction  coil  is 
eliminated.  But  it  is  difficult  to  apply,  as  two  resistances  must  be 
adjusted  and  the  adjustment  will  only  hold  while  the  current  period 
remains  constant.  The  same  remarks  apply  to  B  and  C  following. 

(B)  R=«>. 


,+  R"  +  #„]  +  (R  +  JB,)  (R" 


M~  RW 

x> 


L'  _  R  (R  +  R,  +  R"  +  #„)  +  (K  +  #,)  (R" 
M~  RRtl 

Method  18. 
RtR"  -  R'Rtl  =  0 

L'  -  i    L  R"  a.  R'  +  R" 
W'~      *"%,       ~W^~ 

L'  and  M'  belong  to  the  same  coil.     By  adjusting  the  Wheatstone 
bridge  first,  W  can  then  be  afterwards  adjusted. 


ELECTRICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      309 
To  find  the  ratio  for  any  other  coil  independent  of  the  induction  coil, 

TJ 

we  can  first  find  ^  as  above.     Then  add  L  to  the  same  circuit  and  we 
M 

L  4-  L' 
can  find  —  ^,  —     Whence  we  can  get  L.      This  seems  a  convenient 

jj 

method  if  it  is  sensitive  enough,  as  the  value  of  -jj,  should  be  accurately 

jd 

known  for  the  inductance  standard. 

Method  19. 
'l-M*}  =  S-  [RRt-R"Rl 


L'  _R'  +  RL'l-M*l     ,,\_K  +  R.      R'R^-R'R.jl    ,  , 

~        ~    ~~~  ~~  * 


M~       r  r*       \M 

This  is  useful  in  obtaining  the  constants  of  an  induction  standard. 
For  twisted  wires  L'l  —  M2  should  be  nearly  0,  depending,  as  it  does, 

on  the  magnetic  leakage  between  the  coils,     -^.is  often  known  suffi- 

ciently nearly  for  substitution  in  the  right  hand  member.     It  can, 
however,  be  found  by  reversing  the  inductance  standard. 

Method  20. 
R'Rtl  -  R'R,  =  0 
W       R  L 


L'  any  value. 

In  case  of  a  standard  inductance,  M  and  L  are  known,  especially 
when  the  wires  are  twisted. 

The  method  can  then  be  used  for  determining  any  other  inductance, 
L',  and  is  very  convenient  for  the  purpose. 

Rn  and  Rt  +  Rtl  are  first  calculated  from  the  inductance  standard. 
The  Wheatstone  bridge  is  then  adjusted  and  W  varied  until  a  balance 
is  obtained.  This  balance  is  independent  of  the  current  period,  as  also 
in  the  next  two  methods. 

Method  21. 
R'Rtl  -  R"R,  =  0 

I  _R'  +  R,    L'  _(K  +  Rp.  L'  _R  +  Rll^M 
M  --  ^^;  Tt~       rR,        T  =     ~^T~ 

This  is  Niven's  method  adapted  to  alternating  currents.  See  re- 
marks to  method  20. 


310  HEXEY  A.  EOWLAXD 

Methods  20  and  21  are  specially  useful  when  one  wishes  to  set  up  an 
apparatus  for  measuring  self  induction,  as  the  resistances  R',  R", 
Rt,  Rlt  can  be  adjusted  once  for  all  in  case  of  a  given  induction  standard 
and  only  W  or  r  need  be  varied  afterwards. 

Method  22. 
L'1  =  K±A.  M=R  R"-  ^  =  R"  (i 

This  is  Carey  Foster's  method  adapted  to  alternating  currents  and 
changed  by  making  R"  finite  instead  of  zero. 

The  ratio  of  R'  -f-  R,  to  Rt  is  computed  from  the  known  value  of 
the  induction  standard.  R"  is  then  adjusted  and  C"  obtained.  In 
general  the  adjustment  can  be  obtained  by  changing  Rt  and  R".  The 
adjustment  is  independent  of  the  current  period. 

Method  23. 

"rJvA^r+s+n, 

m 
If  we  make  R  =  0  we  have 

tfmL'  =  rRt 

M^r+R'  +  R, 

m  ~          r 

This  method  requires  two  simultaneous  adjustments.  M  must  also 
be  greater  than  m.  As  M  and  L'  belong  to  the  same  coil,  we  can  con- 
sider this  method  as  one  for  determining  m  in  terms  of  the  M  and  L'  of 
some  standard  coil. 

The  resistance,  A,  can  be  varied  to  test  for,  or  even  correct,  the  error 
due  to  electrostatic  action  between  the  wires  of  the  induction  standard. 

Method  2.L 


Mt      M'r"    M'~r,( 
This  is  a  good  method  for  comparing  standards.     We  first  determine 

-^  for  each  coil  by  one  of  the  previous  methods.     Then  we  can  calcu- 
late ^  and  adjust  the  other  resistances  to  balance. 

It  is  independent  of  the  period  of  the  current  and  suitable  for  stand- 


ELECTRICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      311 

ards  of  equal  as  well  as  of  different  values,  as  the  mutual  inductances 
can  have  any  ratio  to  each  other. 

For  twisted  wire  coils  rt  =  r'  very  nearly.  See  method  23  for  the 
use  of  the  resistance,  A. 

Method  25. 

In  Fig.  6  remove  the  shunt  R'  and  self  induction  L. 

This  method  then  depends  upon  the  measurement  of  the  angular 
deflection  when  a  self  induction  or  a  capacity  is  put  in  the  circuit  of 
the  small  coil  of  the  electrodynamometer  and  comparing  this  with  the 
deflection,  when  the  circuit  only  contains  resistance. 

The  resistance  of  the  circuit,  r,  is  supposed  to  be  so  great  compared 
with  R  that  the  current  in  the  main  circuit  remains  practically  un- 
altered during  the  change. 

There  is  also  an  error  due  to  the  mutual  induction  of  the  electro- 
dynamometer  coils  which  vanishes  when  r  is  great. 


'Z  0i       r+R" 
L-j--   -grr-J 


These  formulas  assume  that  the  deflection  is  proportional  to  6.     This 
assumption  can  be  obviated  by  adjusting  6  =  6'  when  we  have 

1 


W  R" 

These  can  be  further  simplified  by  making  R  "  —  R". 
The  method  thus  becomes  very  easy  to  apply  and  capable  of  con- 
siderable accuracy.  As  the  absolute  determination  depends  on  the 
current  period,  however,  no  great  accuracy  can  be  expected  for  absolute 
values  except  where  this  period  is  known  and  constant,  a  condition 
almost  impossible  to  be  obtained.  The  comparison  of  condensers  or  of 
inductances  is,  however,  independent  of  the  period  and  can  be  carried 
out,  however  variable  the  period,  by  means  of  a  key  to  make  the  change 
instantaneously. 

Method  26. 

Similar  results  can  be  obtained  by  putting  the  condenser  or  induc- 
tance in  R"  instead  of  r,  but  the  current  through  the  electrodynamo- 
meter suspension  is  usually  too  great  in  this  case  unless  r  is  enormous. 
We  have  in  this  case  for  equal  deflections, 

1  //r  7?"  _  v    7?"\ 

^  or  PL'"  =  R"  (R"+r)  pr>'' 
where  r,  and  R"  are  the  resistances  without  condenser  or  self  induction. 


312  HENKY  A.  EOWLAND 

This  is  a  very  good  method  in  many  respects. 

For  using  25  and  26,  a  key  to  make  instantaneous  change  of  connec- 
tions is  almost  necessary. 

To  measure  resistance  by  alternating  currents,  a  Wheatstone  bridge 
is  often  used  with  a  telephone. 

I  propose  to  increase  the  sensitiveness  of  the  method  by  using  my 
method  of  passing  a  strong  current  through  the  fixed  coils  of  an 
electrodynamometer  while  the  weaker  testing  current  goes  through  the 
suspended  system. 

Using  non-inductive  resistances,  methods  10,  13  A,  B,  C,  and  14  all 
reduce  to  proper  ones.  10  or  14  is  specially  good  and  I  have  no  doubt 
will  be  of  great  value  for  liquid  resistances.  The  liquid  resistances 
must,  however,  be  properly  designed  to  avoid  polarization  errors.  The 
increase  of  accuracy  over  using  the  electrodynamometer  in  the  usual 
manner  is  of  the  order  of  magnitude  of  1000  times. 


Since  writing  the  above  I  have  tried  some  of  the  methods,  especially 
6  and  12,  with  much  satisfaction.  By  the  method  12,  results  to  1  in 
1000  can  be  obtained.  Eeplacing  U  by  an  equal  coil,  the  ratio  of  the 
two,  all  other  errors  being  eliminated,  can  be  obtained  to  1  in  10,000, 
or  even  more  accurately. 

The  main  error  to  be  guarded  against  in  method  12,  or  any  other 
where  large  inductances  or  resistances  are  included,  arises  from  twist- 
ing the  wires  leading  to  these.  The  electrostatic  action  of  the  leads, 
or  the  twisted  wire  coils  of  an  ordinary  resistance  box,  may  cause  errors 
of  several  per  cent.  Using  short  small  wire  leads  far  apart,  the  error 
becomes  very  small. 

Method  6  is  also  very  accurate,  but  the  electric  absorption  of  the 
condensers  makes  much  accuracy  impossible  unless  a  series  of  experi- 
ments is  made  to  determine  the  apparent  resistance  due  to  this  cause. 

In  method  12  I  have  not  yet  detected  any  error  due  to  twisting  the 
wires  of  coils  I.  However,  the  electrostatic  action  of  twisted  wire  coils 
is  immense  and  the  warning  against  their  use  which  I  have  given  above 
has  been  well  substantiated  by  experiment.  Only  in  case  of  low  resist- 
ances and  low  inductances  or  in  cases  like  that  just  mentioned  is  it  to 
be  tolerated  for  a  moment.  Connecting  two  twisted  wires  in  a  coil  in 
series  with  a  resistance  between  them,  I  have  almost  neutralized  the 
self  induction,  which  was  one  henry  for  each  coil  or  four  henrys  for 
them  in  series;! 

Altogether  the  results  of  experiment  justify  me  in  claiming  that 


ELECTRICAL  MEASUREMENT  BY  ALTERNATING  CURRENTS      313 

these  methods  will  take  a  prominent  place  in  electrical  measurement, 
especially  where  fluid  resistances,  inductances  and  capacities  are  to  be 
measured.  They  also  seem  to  me  to  settle  the  question  as  to  standard 
inductances  or  capacities,  as  inductances  have  a  real  constant  which  can 
now  be  compared  to  1  in  10,000,  at  least. 

The  new  method  of  measuring  liquid  resistances  with  alternating 
currents  allows  a  tube  of  quite  pure  water  a  meter  long  and  6  Tnm. 
diameter  having  a  resistance  of  10,000,000  ohms  to  be  determined  to  1 
in  1000  or  even  1  in  10,000.  The  current  passing  through  the  water 
is  very  small,  being  at  least  500  times  less  than  that  required  when  the 
bridge  is  used  in  the  ordinary  way.  Hence  polarization  scarcely  enters 
at  all. 

It  is  to  be  noted  that  all  the  methods  15  to  24  can  be  modified  by 
passing  the  main  current  through  one  coil  of  the  electrodynamometer 
and  the  branch  current  through  the  other.  The  deflection  will  then  be 
zero  for  a  more  complicated  relation  than  the  ones  given.  If,  however, 
one  adjustment  is  known  and  made,  the  method  gives  the  other  equa- 
tion. 

Thus  method  18  requires  RtE" — R'RII  =  Q.  Hence,  when  this  is 
satisfied  we  must  have  the  other  condition  alone  to  be  satisfied.  Also  in 
method  22,  when  we  know  the  ratio  of  the  self  and  mutual  inductances 
in  the  coil,  the  resistances  can  be  adjusted  to  satisfy  one  equation  while 
the  experiment  will  give  the  other  and  hence  the  capacity  in  terms  of 
the  inductances. 

Again,  pass  a  current  whose  phase  can  be  varied  through  one  coil  of 
the  electrodynamometer,  and  the  circuit  to  be  tested  through  the  other. 
Vary  the  adjustments  of  resistances  until  the  deflection  is  zero,  how- 
ever the  phase  of  current  through  the  first  coil  may  be  varied. 

The  best  methods  to  apply  the  first  modification  to  are  15  A,  16  A 
and  B,  18,  20,  21,  22  and  24.  In  these,  either  a  Wheatstone  bridge  can 
be  adjusted  or  the  ratio  of  the  self  and  mutual  inductances  in  a  given 
coil  can  be  assumed  as  known  and  the  resistances  adjusted  thereby. 

The  value  of  this  addition  is  in  the  increased  accuracy  and  sensitive- 
ness of  the  method,  an  increase  of  more  than  one  hundred  fold  being 
assured. 

As  a  standard  I  recommend  two  or  three  coils  laid  together  with  their 
inductances  determined  and  not  a  condenser,  even  an  air  condenser. 


62 
ELECTEICAL  MEASUREMENTS 

BT  HENRY  A.  ROWLAND  AND  THOMAS  DOBBIN  PENNIMAN 
[American  Journal  of  Science  [4],  VIII,  35-57,  1899] 

In  a  previous  article  *  mention  was  made  of  some  work  then  being 
carried  on  at  the  Johns  Hopkins  University  to  test  the  methods  for 
the  measurement  and  comparison  of  self -inductance,  mutual  inductance, 
and  capacity  there  described. 

In  the  present  paper,  there  will  be  given  an  account  of  the  experi- 
ments performed  with  some  of  the  methods  described  in  the  previous 
article,  together  with  a  method  for  the  direct  measurement  of  the 
effect  of  electric  absorption  in  terms  of  resistance. 

The  methods  that  were  tried  were  25,  26,  9,  3,  12  and  6. 


Description    of    the   Electrodynamometer,    Dynamos,    Coils,    Condensers, 
Resistances  and  Connections  used  in  the  Experiments 

Electrodynamometer. — The  electrodynamometer  was  one  constructed 
at  the  University,  having  a  sensitiveness,  with  the  coils  in  series,  of  1 
scale  division  deflected  for  -0007  ampere. 

The  hanging  coil  was  made  up  of  240  turns  of  No.  34  copper  wire  B 
and  S  gauge.  The  coil  was  suspended  by  a  bronze  wire  connected  with 
one  terminal  of  the  coil.  The  other  terminal  of  the  coil  was  a  loop  of 
wire  hanging  from  the  bottom  of  the  coil  and  attached  to  the  side  of 
the  case;  both  the  suspension  and  the  loop  were  brought  out  to  binding 
posts.  The  resistance  of  the  coil  with  suspension  was  21-7  ohms. 

The  fixed  coils  were  made  up  of  300  turns  each  of  No.  30  B  and  S 
gauge  copper  wire.  The  coils  were  wound  on  cup-shaped  metal  forms 
and  soaked  in  a  preparation  of  wax.  The  form  was  then  removed  and 
the  coils  placed  a  radius  apart  as  in  the  arrangement  of  Helmholtz. 

Dynamos. — There  were  two  dynamos  used,  a  Westinghouse  alter- 
nator, and  a  small  alternating  dynamo  constructed  at  the  University. 

Journal,  iv,  p.  429,  December,  1897;   Philosophical  Magazine,  January,  1898. 


ELECTRICAL  MEASUREMENTS  315 

The  Westinghouse  dynamo  was  one  having  10  poles  so  that  each  revo- 
lution of  the  armature  produced  5  complete  periods.  The  period  of 
this  dynamo  was  determined  by  taking  the  time  of  1000  revolutions  of 
the  armature.  This  was  accomplished  by  having  the  armature  make 
an  electric  connection  with  a  bell  every  200  revolutions  and  taking  the 
time  of  5  of  these.  The  taking  of  the  speed  during  every  experiment 
gave  more  regular  results,  as  the  speed  was  constantly  changing,  the 
dynamo  being  run  by  the  engine  in  the  University  power-house  when  it 
was  subject  to  great  change  of  load.  This  dynamo  had  a  period  of 
about  132  complete  periods  per  second. 

For  the  production  of  a  current  of  less  period  than  that  of  the  West- 
inghouse, the  small  alternator  constructed  at  the  University  was  used. 
This  dynamo  was  run  by  a  small  continuous  Sprague  motor.  The  arma- 
ture of  the  small  alternator  consisted  of  8  coils,  which  coils  were  fas- 
tened flat  on  a  German  silver  plate,  the  plate  revolving  between  8  field 
pieces  producing  4  poles.  The  object  of  having  the  coils  of  the  arma- 
ture on  a  metal  plate  was  to  secure  a  nearly  constant  speed.  The  metal 
plate  produced  a  load  that  varied  as  the  velocity  and  due  to  induced 
currents  in  the  plate.  The  varying  load,  depending  on  the  velocity  of 
the  moving  plate,  produced  a  nearly  constant  speed,  which  rendered 
unnecessary  the  constant  taking  of  the  speed.  When  this  dynamo  was 
used,  the  speed  was  only  determined  two  or  three  times  during  a  series 
of  readings  or  experiments.  The  average  of  these  determinations  was 
taken  as  the  speed  during  the  whole  series  of  experiments  under  con- 
sideration. 

Coils. — The  coils  whose  inductances  were  determined  were  all  made 
in  the  same  way,  being  wound  on  a  metal  form  and  soaked  in  a  prepa- 
ration of  wax.  When  the  wax  was  hard  the  metal  form  was  removed. 
This  enabled  the  coils  to  be  placed  close  together,  as  their  sides  were 
flat  and  smooth.  The  coils  all  had  the  same  internal  and  external 
diameter,  but  their  width  varied,  that  being  determined  by  the  number 
of  turns  that  were  desired. 

Coils.  Pv  External  diameter  35-46  cm.,  internal  diameter  23-8 
cm.,  was  made  up  of  about  1200  turns  of  No.  16  B  and  8  gauge  single 
covered  cotton  copper  wire,  roughly  wound;  the  turns  were  not  smooth; 
self-inductance  as  finally  determined  -566  henry. 

P2.,  Same  dimensions.  Turns  were  put  on  evenly.  The  number 
of  turns  was  1300  of  No.  16  B  and  8  single  covered  cotton  copper  wire. 
Self-inductance  -724  henry. 

A.  Same  internal  and  external  diameters  as  P,  but  the  width  was 


316  HENKY  A.  EOWLAND 

4-3  cm.  Number  of  turns  3700  No.  20  B  and  8  gauge  single  covered 
cotton  copper  wire.  Self -inductance  as  determined  5-30  henrys. 

BI  B2.  This  coil  was  made  by  winding  two  wires  in  parallel  and  all 
four  of  the  terminals  brought  out  to  binding  posts.  Thus  the  coils 
could  be  used  as  two  single  coils,  when  the  coils  will  be  denoted  by  the 
symbols  B^  and  B2  as  the  case  may  be,  or  as  a  single  coil,  the  coils  51 
and  B2  being  joined  up  in  series  or  in  parallel.  The  dimensions  of  the 
coils  BI  B2  were  the  same  as  A.  Each  of  the  coils  B^  and  B2  were 
made  up  of  1600  turns  of  No.  22  B  and  8  single  covered  cotton  copper 
wire.  The  self-inductance  of  these  coils  taken  separately  when  com- 
pared with  P,  which  was  determined  absolutely,  was  nearly  1  henry. 
On  this  account  B  was  taken  as  being  1  henry,  and  the  other  coils  were 
compared  with  it  as  a  standard. 

C.  Same  dimensions  as  P2.  Number  of  turns  1747  of  No.  22  B  and 
8  single  covered  cotton  copper  wire.  Self-inductance  as  determined 
1-30  henrys. 

Condensers. — 2  and  3.  Two  paraffined  paper  condensers  that  had  a 
capacity  of  2  and  3  microfarads  respectively. 

•Jd  Troy.  A  -Jd  microfarad  standard  mica  condenser  built  by  the 
Troy  Electric  Co. 

•Jd  Elliott.  A  -Jd  microfarad  standard  mica  condenser  built  by  Elliott 
Bros. 

Resistances. — The  resistances  used  in  the  experiments  were  of  two 
kinds,  those  wound  with  double  wire  so  as  to  have  no  self-inductance, 
as  the  ordinary  resistance  box,  and  those  wound  on  frames  or  cards 
which  had  some  small  self-inductance,  but  almost  no  electrostatic 
capacity.  The  resistances  which  had  self-inductance  are  called  open 
resistances  to  distinguish  them  from  resistance  boxes,  and  were  of 
different  kinds  and  dimensions. 

Sources  of  Error  and  Experimental  Difficulties 

In  all  work  with  alternating  currents  there  are  two  great  sources  of 
error  that  have  to  be  guarded  against.  These  are  the  errors  that  may 
arise  from  the  inductance  of  one  part  of  the  apparatus  on  another,  as, 
for  example,  the  direct  induction  of  a  coil  in  the  circuit  on  the  coils 
of  -the  electrodynamometer,  and  the  effect  of  the  electrostatic  capacity 
of  the  leads  and  connections.  In  connecting  the  coils  great  care  had 
to  be  taken  to  avoid  the  effect  of  electrostatic  action  of  the  leads  and 
connections.  For  if  there  was  a  current  of  very  considerable  magni- 


ELECTEICAL  MEASUREMENTS  317 

tude,  the  difference  of  potential  between  the  terminals  of  the  coil 
might  be  great.  If  the  connections  under  these  circumstances  were 
made  with  double  wire,  as  is  customary,  a  great  error  was  introduced 
due  to  the  electrostatic  capacity  of  the  leads.  The  error  was  sometimes 
as  much  as  7  per  cent  (see  method  24).  This  error  could  be  shown  to 
be  due  to  the  electrostatic  action  of  the  leads  by  shifting  a  resistance  in 
circuit  with  the  coil  in  question  from  one  end  of  the  double  wire  to 
the  other  .  The  effect  of  this  was  to  still  further  increase  the  difference 
of  potential  between  the  leads,  and  this  increased  the  error.  Experi- 
ments of  this  character  showed  the  necessity  of  using  open  leads  and 
open  resistances  having  little  or  no  capacity  in  all  cases  in  which  the 
coils  experimented  on  and  the  resistance  boxes  used  in  their  determina- 
tion have  a  current  of  any  considerable  magnitude  passing  through 
them.  In  several  of  the  following  methods  constancy  of  current  was 
necessary.  This  was  accomplished  by  various  means  that  will  be  de- 
scribed in  their  actual  application. 

METHODS 

The  methods  that  were  tried  were  25,  26,  9,  3,  12  and  6  described  in 
this  Journal,  December,  1897.2 

Method  25. — Method  of  equal  deflections.  Absolute  method  for  the 
determination  of  self-inductance  or  capacity  in  terms  of  electromagnetic 
units. 

In  this  method  the  hanging  coil  is  shunted  off  the  fixed  coils  circuit, 
and  this  with  a  non-inductive  resistance  in  circuit  with  the  hanging 
coils  is  made  the  same  as  that  of  a  certain  inductive  resistance  in  cir- 
cuit with  the  hanging  coil.  The  connections  are  made  as  in  the  Figs. 
1,  2,  where  C0eibt,  Cr1e*'M+*i),  C^^+W  are  currents.  R,  R',  r,  resist- 
ances. They  represent  the  entire  resistance  of  their  respective  branches. 
L  represents  self-inductance  of  the  coil  by  which  it  is  placed.  The 
outer  circle  in  Fig.  1  represents  the  fixed  coils  and  the  small  circle  the 
hanging  coil  of  the  electrodynamometer.  In  Fig.  2  the  terminals  of 
the  fixed  and  hanging  coils  are  represented  by  F  and  H.  D  is  a  revers- 
ing commutator.  K  is  a  key  to  send  the  current  first  through  the 
inductive  and  then  through  the  non-inductive  resistance.  &  =  Z-xn, 
n  =  complete  alternations  per  sec.  This  is  the  general  notation  adopted 
throughout  the  article. 

2  Phil.  Mag.,  January,  1898. 


318 


HENEY  A.  ROWLAND 


The  quantity  to  be  found  is  C0C^  cos^,  which  is  proportional  to 
the  deflection  of  the  hanging  coil  in  the  two  positions  of  K. 
In  one  position 


FIG.  2. 


Therefore 

In  the  other  position  of  K 
Therefore 


ELECTRICAL  MEASUREMENTS  319 

0=0,  as  0  is  an  angle  whose  tangent  is    „,  and  (7  =  0  nearly.     In  the 
case  of  equal  deflection  D  =  D'  and  therefore 
VD=(R'-R)  (R+r} 

If  capacity  had  been  used  in  the  place  of  self-inductance  the  formula 
would  be 


If  self-inductance  and  capacity  were  used  in  series 


The  application  of  this  formula  to  the  measurement  of  self-induc- 
tance gave  results  that  agreed  to  within  the  accuracy  with  which  the 
period  of  the  alternations  could  be  determined.  That  is,  the  results 
agreed  to  within  about  1  per  cent.  In  the  determination  of  L  the 
resistance  in  circuit  R  was  varied  from  the  least  possible  resistance  as 
determined  by  the  coils  up  to  1000  ohms  and  more,  and  the  self- 
inductance  was  determined  under  these  various  conditions.  These 
results  agreed  among  themselves,  and  were  apparently  independent  of 
the  resistance  in  circuit  with  it.  In  the  application  of  this  method  to 
the  determination  of  capacity,  however,  great  trouble  was  encountered, 
as  the  capacity  apparently  varied  both  with  the  resistance  in  circuit 
with  it  and  with  the  period.  This  variation  was  regular  for  each  period, 
the  value  derived  depending  on  the  resistance  in  circuit.  This  irregu- 
larity of  derived  value  of  the  capacity  led  to  the  investigation  and 
development  of  Maxwell's  formula  on  the  effect  of  absorption,  a  neces- 
sary characteristic  of  heterogeneous  substances. 

When  the  formula  was  deduced,  as  may  be  seen  in  the  article  already 
referred  to,  the  absorption  comes  in  as  an  added  resistance,  the  resist- 
ance being  constant  for  a  given  period.  By  an  inspection  of  the  results 
this  was  found  to  be  the  case.  The  finding  of  the  resistance  due  to 
absorption  in  this  method  is  one  of  approximation,  but  the  values 
deduced  compare  very  favorably  with  those  determined  by  direct  meas- 
urement, as  will  be  seen  later  when  various  results  are  collected.  In 
the  actual  experiments  the  condensers  used  were  two  paraffined  paper 
condensers  of  about  2  and  3  microfarads.  The  currents  used  had 
different  periods,  as  seen  in  the  table  following,  where  n  =  133,  53-3, 
31 -9  and  14. 

The  process  was  to  place  in  the  condenser  circuit  a  resistance  R,  and 


320  HENEY  A.  EOWLAND 

then  to  move  the  key  K  back  and  forth  until  R'  was  found  that  gave 
the  same  deflection.  D,  Fig.  2,  was  now  reversed  and  the  process 
repeated.  This  was  repeated  with  different  values  of  R  and  n  and  the 
apparent  capacity.  This  gave  great  variation  of  apparent  capacity  with 
different  values  of  R,  which  should  not  be  the  case,  and,  therefore, 
gave  a  means  of  finding  the  resistance  due  to  absorption  or  absorption 
resistance,  as  we  will  designate,  by  approximation.  As  the  effect  of 
absorption  is  a  resistance  it  is  possible  to  find  what  resistance,  if  added 
to  R,  will  make  all  the  values  of  the  capacity  as  determined  for  the 
different  values  of  R  the  same.  Therefore  it  should  be  the  same  for 
any  two  values  of  R.  Calling  the  two  values  of  R  in  the  two  cases 
R%  and  J?2  respectively  and  the  two  corresponding  values  of  R',  R^',  and 
R%,  and  let  A  be  the  added  resistance  due  to  absorption,  the  capacity 
should  be  the  same  in  the  two  cases,  or 


+  r)  -  (#- 


A  _        - 

From  this  A  is  found  for  the  period  used.  By  doing  this  for  a 
number  of  different  values  of  R,  the  true  value  of  A  is  approximated. 
A  was  thus  found  for  the  condensers  2  and  3  microfarads  with  different 
values  of  n.  The  calculations  were  again  performed  adding  to  the 
different  values  of  R  a  constant  resistance  A.  The  capacity  that  was 
found  when  A  is  added  to  R  is  called  the  corrected  capacity.  In  the 
table  below  are  collected  the  corrected  values  of  the  capacities  together 
with  n  and  the  resistance  A. 

Capacity        4-94          4-96         4-96  4-64         microfarads. 

n        131-1          53-3         31-98          14-  complete  alternations. 

A  '5-19        20-5         34-09         139-62         absorption  resistance  in  ohms. 

The  last  value  of  the  capacity  seems  'to  be  an  error,  possibly  one  of 
calculation.  However,  the  results  seem  to  show  a  nearly  constant 
capacity,  but  a  resistance  increasing  rapidly  with  decrease  of  period,  as 
Maxwell's  formula  shows.  The  constant  value  of  the  capacity  remains 
to  be  explained. 

But  in  the  above,  determinations  of  absorption  resistance  are  by 
approximation.  Professor  Eowland  has,  therefore,  devised  a  method 
by  which  it  can  be  measured  directly.  This  method,  with  the  results 
that  have  been  derived  by  it,  will  now  be  given. 


ELECTEICAL  MEASUBEMENTS 


321 


Method  for  the  Direct  Measurement  of  Absorption  Resistance 
In  a  Wheatstone  bridge  (Fig.  3)  let  the  resistance  of  the  different 

arms  be  denoted  by  R,,  R',  Rtl,  R"  and  r.     Let  J^have  in  circuit  a 

self-inductance  Lt  and  let  r  have  in  circuit  with  it  a  self-inductance. 
Let  C,£ibt  be  the  current  through  R,  and  C  «*«*  +  *)  be  the  current 

through  r  when  a  periodic  electromotive  force  is  applied  to  a  and  d  in 

the  figure. 

Let  C'  be  the  current  through  Rt,  and  C"  be  the  current  through  r 

when  there  is  a  constant  difference  of  potential  between  a  and  d.     The 

ratio  of  the  current  in  this  case  is 


c' 


R"R-R'R 


R  (R" 


_ 
r(R'  +  R"} 


i 

i 

FIG.  3. 

R,          \ 
R'  b        /n 

SA 

,_  Kn  a 

a 

v£ 

J    r  c 

/ 
R" 

FIG.  4. 


When  a  periodic  electromotive  force  is  applied  to  a  and  d,  the  ratio 
of  the  currents  in  this  case  is 


__ 

C1        ~  R  (R>r+RJ  +  r  (R~+~R')  +  ibl  (R  +  R") 

Separating  the  real  and  imaginary  parts 
o         ,_  (R"R 


If  now  the  fixed  coils  of  the  electrodynamometer  are  placed  in  the 
R,  arm  of  the  bridge,  and  the  hanging  coil  is  placed  in  cross  connection 
of  the  bridge,  as  in  Fig.  4,  the  different  resistances  may  be  adjusted 
21 


322 


HENRY  A.  KOWLAXD 


until  there  is  no  deflection,  in  which  case  <f>  =  90°  or  cos<£=  0,  therefore 

(R"Rt  -  RRJ  [#'  (R"  +  RJ  +  r  (R'  +  R"}-]  +  VILfl'  (R'  +  R"}  =  0 , 

R"  (R  +  R") 


.'.     R'R.  =  R'R..  -  VIL. 


I    J?f  (  J?"     i      J?    \     i     /».  /  V     i      ZP"\  ' 
K    \±t      T  -tv.)  -\-  T  (^JV    +  JK    ) 

If  in  connection  with  L'  a  capacity  C  is  added,  the  formula  becomes, 
substituting  for  L/t  Lt  —  j~-  . 

(R'R'  +  .R") 


c  J  R'  (R"  +  £„)  -  r  (R  +  R"} ' 
In  most  cases  since  I  and  L,  are  generally  the  self-inductances  of  the 


instruments  the  term  &2 1  Lt  can  be  neglected  in  comparison  with  - 

C 

and  the  equation  becomes 

Tftt  T> T>t  -p    ,    I  R"  (R1  +  R  ) 

*  -       *    +  ~ 


FIG.  5. 


In  this  equation  R,  includes  both  the  ohmic  and  the  absorption  resist- 
ance. The  value  of  R,  is  determined  in  terms  of  known  quantities, 
that  is  the  resistance  and  2  and  C.  It  was  not  necessary  that  I  and  C 
should  be  exactly  known  as  the  last  term  in  the  equation  above  plays 
the  part  of  a  correction  term,  and  is  in  all  cases  below  small  and  in 
some  cases  negligible.  The  capacities  that  were  used  in  the  experi- 
ments were  the  2  and  3  microfarads,  the  ^  microfarad  Elliott  condenser, 
and  the  £  microfarad  Troy  condenser. 

Experiments. — The  process  of  experimenting  was  to  apply  a  periodic 
electromotive  force  to  a  and  d,  and  to  adjust  the  different  resistances 
until  there  was  no  deflection  of  the  coil  in  the  same  way  as  in  the 
ordinary  measurement  of  resistance  on  a  Wheatstone  bridge.  The 
different  resistances  R',  R",  Rn  and  r  being  known,  the  apparent  value 
of  the  resistance  R,  was  found,  and  knowing  the  ohmic  resistance  of 
the  R,  circuit,  the  absorption  resistance  appears  as  the  difference. 


ELECTBICAL  MEASUBEMENTS 


323 


Some  interest  lies  not  alone  in  that  the  method  is  applicable,  but  that 
it  confirmed  the  supposition  that  absorption  resistance  acts  as  an  ordi- 
nary ohmic  resistance  in  series  in  the  circuit.  This  was  confirmed  by 
the  fact  that  when  condensers  were  in  series  and  in  parallel,  their 
absorption  resistances  acted  under  these  conditions  like  ohmic  resist- 
ances, being  increased  in  the  one  case  and  decreased  in  the  other,  and 
in  the  right  ratio.  This  agreement  was  not  exact,  as  the  absorption 
resistance  was  extremely  sensitive  both  to  change  of  period  and  change 
of  temperature.  The  great  sensitiveness  to  change  of  temperature  was 
shown  either  by  letting  the  current  go  through  the  condensers  for  a 
little  time,  or  placing  the  condensers  before  a  hot  air  flue;  in  either 
case  after  cooling,  the  absorption  resistance  returned  to  its  original 
value.  The  cooling  was  very  slow,  as  there  was  very  little  radiation 
from  the  condensers  inclosed  in  wooden  boxes. 

The  results  are  now  given  for  the  condensers  2  and  3  microfarads. 
In  the  calculation  of  the  results  the  last  term  of  the  equation,  that  is 

7    ry>  f  nr     , 

—  „,  ,  „„  —  ^-  -  - 


—  ™ 
condensers  2  and  3  microfarads  were  used. 


has  been  left  out,  as  it  was  very  small  when 


CONDENSERS  2  AND  3  MICROFARADS  IN 

PARALLEL. 

«=134,  Z=-0007  .-. 

last 

term  negligible. 

R" 

Ry/                    r                      R' 

R/ 

Resis.  of 
R'  circuit 
in  ohms. 

Resistance 
due  to 
absorption. 

422- 

6             488-6             5457-3             347 

•9 

39-29 

33 

•77 

5-30 

1488- 

6             488-2 

123 

•4 

40-50 

« 

6-73 

984- 

1 

82 

•1 

40-72 

33 

81 

6-91 

2671- 

6 

22 

5 

41-116 

| 

7-30 

423- 

0 

357 

•3 

41-237 

« 

7-42 

5474- 

3 

464 

5 

41-42 

i 

7-61 

6734- 

374 

•9 

41-67 

« 

7-86 

1  ohm  in  R"=f 

scale  divisi 

n. 

i 

7486- 

638 

•6 

41-64 

i 

7-83 

9466- 

81 

•15 

41-85 

i 

8-04 

Condensers  2  and  3  placed  before  the  register  and  heated  for  1  hour : 

7489-7     488-27      «        713-8     46-534     34-33      12-20 

After  standing  1£  hours  in  air  at  temperature  of  12° -2  C.  condenser 
has  been  open  so  that  resistances  have  been  cooled: 

1240-5  487-8  «  109-  42-86  34-  8-86 

After  standing  some  little  time: 

7482-5  487-8  "  651-6  42-47  34-  8-49 

The  above  table  shows  conclusively  the  heating  of  the  condenser  by 
the  current,  and  the  dependence  of  the  absorption  upon  the  temper- 
ature. 


K" 

R// 

R, 

r 

R, 

348-5 

488-6 

396-3 

11020-7 

55-61 

7488- 

it 

849-2 

u 

55-41 

(i 

(i 

844-1 

4026- 

55-07 

3485- 

u 

396-1 

u 

55-58 

324  HENRY  A.  ROWLAND 

CONDENSERS  2  AND  3  IN  PARALLEL.     N=57-6. 

R,  in 
ohms.  A. 

33-77  21-84 

"  21-64 

«  21-30 

«  21-81 

Average,  21-63 
N=56-6  per  second. 
3485-  200-24  976-7  4026-  56-00  22-23 

Comparing  these  values  with  those  found  in  the  use  of  method  25 
the  agreement  is  at  once  apparent. 

N=  _  134-  131-  _  57-6  _  56-6  _  53- 

Method  25  _  5-19  20-5 

Direct  measure-  5-30  cold  21-63  22-23 

ment.  7-00  warm 

It  should  be  remembered,  in  comparing  the  results,  that  the  values 
obtained  by  method  25  would  naturally  be  smaller  than  those  found  by 
direct  measurement,  as  in  method  25  the  current  going  through  the 
condensers  was  extremely  small;  there  was  therefore  practically  no 
heating. 

The  experiments  that  confirm  the  mathematical  theory  that  the 
absorption  resistance  could  be  treated  as  ordinary  ohmic  resistance  were 
performed  with  the  two  condensers,  ^  Troy  and  ^  Elliott  microfarad 
condensers.  These  are  next  given. 

In  these  results  it  was  necessary  to  take  into  account,  in  the  calcula- 
tion of  the  apparent  value  of  R,,  the  last  term  of  the  equation,  that  is 

L  R"  (R'  +  R"} 

c    R' 


$  Troy  and  ^  Elliott  in  series,  1  o'clock. 

Apparent          Ohmic  resist-      Absorption 
value  ance  resistance 

R"  R/,  R'  r  ofR,  of  R,  A. 

4751-8  499-9  404-8  4754-  43-141  34-143  8-998 

^  Troy,  2  o'clock. 

4750-      497  75    352-4      «        37-288       34-144       3-144 

i  Elliott,  2.45  o'clock. 

4749-3     497-67    390-3      "        41-260         "         7-116 

£  Troy  and  ^  Elliott  in  parallel,  4  o'clock. 

4749-3     497-6     350-23     "        36-94        34-15        2-79 

£  Troy  and  £  Elliott  in  series. 

4748-5     497-55    418-15     "        44-612       34-12       10-492 


ELECTRICAL  MEASUREMENTS  325 

Calculating  what  the  absorption  resistance  should  be  for  £  Troy  and 
^  Elliott  in  series,  from  the  absorption  resistances  of  the  two  con- 
densers when  determined  separately,  it  is  equal  to  10-26  ohms,  which  is 
greater  than  the  first  and  less  than  the  last  value  above,  showing  that 
the  condensers  were  heating  during  the  experiments.  Calculating  the 
absorption  resistance  of  £  Troy  and  -J  Elliott  in  parallel  in  the  same 
way,  it  is  equal  to  2-209  ohms,  which  is  less  than  the  value  afterwards 
obtained  by  experiment  for  the  same  reason. 

The  method  was  shown  not  to  be  based  on  any  false  supposition,  by 
substituting  in  place  of  the  condenser  a  coil  of  known  self-inductance. 
When  this  was  done  the  value  of  R^  as  calculated  from  the  other  resist- 
ances and  the  self-inductances  should  be  the  same  as  the  actual  ohmic 
resistance  of  the  circuit. 

This  was  tried  with  two  coils  P2  and  A  and  the  agreement  was  re- 
markably close,  as  seen  in  the  next  table. 

Coil  P  used  in  place  of  condenser  in  the  Et  circuit: 

Deduced  value    Actual  value 

R"  R,,  R'  r  ofR,  of  R, 

474-9  487-8  758-2  5457-  77-86  77-8 

Coil  A  in  place  of  condenser  in  the  R,  circuit: 

474-9  487-8  218-3  "  224-12  223-9 

In  these  experiments  great  care  was  taken  that  the  measurements 
of  the  resistances  were  performed  immediately  after  the  adjustment. 
In  this  way  the  actual  resistances  at  the  time  of  the  experiment  were 
obtained,  and  so  the  effect  of  the  heating  by  the  current  was  some- 
what eliminated. 

Methods  26,  9  and  3  give  good  results,  but  the  methods  that  gave 
the  most  satisfaction  were  methods  12  and  6,  method  12  being  for  the 
comparison  of  two  self-inductances  and  method  6  for  the  comparison 
of  a  self-inductance  with  a  capacity.  These  give  some  remarkable 
results,  the  theory  and  deductions  of  the  methods  being  as  follows : 

Method  12. — Zero  Method  for  the  Comparison  of  two  8  elf -Inductances 

Let  the  connections  be  made  as  in  the  figure  where  the  hanging  coil 
and  the  fixed  coils  are  in  two  distinct  circuits. 

Let  C<fiu  etc.  be  the  currents,  A'  and  A"  reversing  commutators, 
R",  R  and  r  the  resistance  of  the  different  circuits,  L"  and  L  the  self- 
inductances,  If  the  mutual  inductance  of  the  coils  B\  and  B2  by  which 
it  is  placed.  When  a  periodic  electromotive  force  a£m  is  applied  to 
A,  B  the  quantity  to  be  found  is  C^  C8  cos  ($3  —  0J  where  <p,  —  fa 
is  the  difference  of  phase. 


326  HENRY  A.  KOWLAND 

The  current  in  the  R"  circuit  is  then 

C  ci  (bt  +  <»  —  J^/ 
^  r  -  T>H 


+  ibL" 


The  current  in  the  E  circuit  is 


=  (7  e»t. 


Substituting  the  value  of  C"0efbt  in  equation  (1)  and  simplifying,  it 
becomes 


"r  —  ibL"r 


FIG.  6. 

Therefore  the  deflection  is  proportional  to 
cos  ($,— 0,)  =  (7|~ 


and  the  condition  for  zero  deflection  is 


-  VLMR'r  +  VL"Mr(R+r)  =  0, 
L    _R+r 


The  condition  therefore  of  zero  deflection  is  independent  of  M  .  But 
M  is  one  of  the  factors  of  the  electromotive  force  in  the  R"  circuit,  and 
on  it  therefore  depends  the  sensitiveness,  as  it  determines  the  current 
through  the  R"  circuit.  In  the  first  figures  of  this  method  the  fixed 
coils  are  in  the  R"  circuit,  and  the  hanging  coil  in  the  R  circuit,  but 
this  is  not  necessary,  as  the  fixed  and  hanging  coils  can  be  reversed. 
The  choice  of  which  of  the  above  arrangements  should  be  used  depends 


ELECTEICAL  MEASUREMENTS 


327 


on  the  impedances  of  the  two  circuits,  as  other  things  being  equal  the 
smaller  current  should  go  through  the  hanging  coil. 

Experiments. — The  coils  used  in  the  experiments  were  coils  Plf  P2, 
C,  B1}  B2,  and  A,  which  coils  are  described  on  page  315.  From  the 
dimensions  of  P2  and  its  self-inductance  as  found  by  method  25,  Bt  was 
designed  to  have  a  self-inductance  of  one  henry.  This  will  be  shown 
to  be  nearly  the  case.  For  ease  of  comparison  B1  has  been  taken  in 
the  calculations  of  the  results  as  being  equal  to  one  henry,  and  the 
other  coils  were  compared  with  this  coil  as  a  standard. 


In  these  experiments  the  connections  were  made  as  in  the  figure  7, 
the  coil  BI  that  was  taken  as  the  standard  being  placed  in  circuit  with 
the  fixed  coils  of  the  electrodynamometer  as  L"  and  the  resistance  of 
this  circuit  was  unaltered  during  the  experiments  in  any  particular 
series.  The  coils  whose  self-inductances  were  to  be  determined  were 
placed  in  the  hanging  coil  circuit  and  the  resistance  R  was  changed 
until  there  was  no  deflection.  The  resistance  of  the  two  circuits,  R" 
and  R  -{-  r  were  then  measured  by  a  Wheatstone  bridge. 

The  resistance  r  was  in  all  cases  small  in  order  that  (70£ibt  should  be 
large,  and  therefore  by  induction  <71£*<M+*>  the  current  through  the 
fixed  coils  was  made  large  and  the  instrument  sensitive.  The  method 


328  HENRY  A.  KOWLAND 

being  very  accurate,  as  will  be  seen  later,  great  care  had  to  be  used  to 
eliminate  all  sources  of  error,  as  for  example,  electrostatic  action.  In 
the  first  trial  of  the  method  small  differences  were  noticed  in  the  ratio 
of  two  self-inductances,  depending  both  on  the  resistances  used,  and 
also  on  the  connections  of  the  coils,  whether  the  leads  were  double, 
single,  long  or  short.  The  same  variation  was  noticed  when  several 
coils  were  joined  in  series  and  compared  with  another  coil,  and  when 
these  coils  were  compared  separately  and  their  sum  taken. 

This  irregularity  led  to  an  investigation  of  the  effects  of  various 
resistances  and  connections  in  one  of  the  circuits,  the  other  circuit 
being  unaltered.  A  little  farther  on,  the  variation  in  the  deduced  value 
of  the  self -inductance  of  one  of  the  coils,  when  different  resistances  and 
leads  were  used,  will  be  given,  which  variation  was  caused  by  the 
electrostatic  action  of  the  connections,  etc.  (Page  316.) 

The  necessity  of  eliminating  electrostatic  action  made  obligatory  the 
use  of  open  resistances  which  had  small  self-inductances.  These  re- 
sistances were  of  three  kinds — resistances  in  the  form  of  spirals,  resist- 
ances wound  on  thin  strips  of  micanite  or  paper,  and  those  wound  on 
open  frames;  see  page  316. 

The  self-inductance  of  the  first  and  second  classes  of  resistances  was 
very  small,  as  in  one  case  there  were  only  a  few  turns,  and  in  the  other 
the  cross-section  was  very  small. 

The  third  class  were  those  wound  on  frames  whose  self-inductances 
were  calculated.  There  were  several  resistances  of  2000  ohms  each, 
whose  self -inductances  were  -0000436  henry,  which  would  hardly  affect 
the  phase  of  the  current  or  the  impedance  of  the  circuit. 

These  coils  were  subdivided  into  resistances  of  various  amounts. 
Another  frame  resistance  used  was  of  7463  ohms  divided  into  parts  of 
about  250  ohms  each.  The  self-inductance  of  the  entire  7463  ohms 
was  -000105  henry. 

As  the  open  resistances  were  not  divided  into  small  amounts  it  was 
necessary  to  use  resistance  boxes  for  adjustment;  as  few  ohms  as  possi- 
ble were  used  in  each  case. 

From  the  fact  that  the  coils  of  the  electrodynamometer  had  self- 
inductance  a  correction  was  introduced  in  order  that  the  ratio  of  the 
resistances  should  give  the  ratio  of  the  self-inductances  of  the  coils 
direct. 

The  value  of  this  correction  in  ohms  was  calculated  as  follows: 


ELECTRICAL  MEASUREMENTS  329 

Calculation  of  Correction  Due  to  Fixed  and  Hanging  Coils 

Self-inductance  of    fixed    coils  =f=  *0164  henry 
"  "  "  hanging  coil  —  h  =  -0007       " 

Correction  due  to  fixed  coils.     From  an  inspection  of  the  tables  it 
is  seen  that 

L         R+r  L          R  +  r 

01 


B,+f~     R"  1.0164  ~~~90T' 

rhere  L  is  the  self  -inductance  of  some  coil  and  R  -\-  r  is  the  corre- 
sponding resistance.     B,  is  taken  as  equal  to  1  henry 

L 


R  +  r~     902    ' 
But  the  comparison  of  L  with  B^  =  1  is  wanted,  therefore  both  numer- 

ator and  denominator  of  ~  ~  are  divided  by  1-0164  or 

yo« 

.         L         \=B 


R+r      887-45  ' 
.       L_  R  +  r 

B       ~  887-45  ' 

That  is,  the  self-inductance  of  -0164  henry  of  the  fixed  coils  produced  a 
correction  of  887-45  —  902  =  —  14-55  ohms,  which  must  be  applied  to 
the  R"  circuit  if  the  self-inductance  of  that  circuit  is  to  be  considered 
as  1  henry. 

Correction  due  to  hanging  coil.  The  self-inductance  =  -0164  henry 
of  the  fixed  coils  gives  a  correction  of  —  *  14-55  ohms,  therefore  the  self- 
inductance  -0007  henry  of  the  hanging  coil  gives  a  correction  of  —  -62 
ohms  to  the  R  -\-  r  circuit.  Applying  these  corrections,  the  results 
obtained  for  the  several  coils  under  various  conditions  are  given  below. 
The  results  are  given  in  the  following  order. 

First.  The  values  are  calculated  using  double  leads  in  the  circuits 
but  open  resistances  as  far  as  possible. 

Second.  The  variation  of  the  apparent  value  of  the  self-inductance 
of  one  of  the  coils  with  different  positions  of  the  coil,  resistances,  and 
different  kinds  of  leads. 

Third.  Short  leads  separated  about  6  inches  and  crossed,  used  with 
all  the  coils  except  B^. 

Fourth.  Open  leads  aad  open  resistances  in  the  determinations.  In 
the  table  R"  was  open  resistance  plus  the  resistance  of  coil  B^  and 
fixed  coils  of  instrument.  R  +  r  was  made  up  of  the  small  coil  and 
open  resistance  plus  the  amount  in  the  Queen  ordinary  resistance  box. 


330 


HENRY  A.  KOWLAXD 


After  all  the  inductive  effect  of  the  leads  was  removed  and  the  ordi- 
nary resistance  box  used  as  little  as  possible,  there  was  a  different  value 
obtained  for  the  ratio  of  the  self -inductances  dependent  on  the  position 
of  the  reversing  commutator  A'.  With  all  the  coils  used  the  greater 
value  occurred  with  the  same  position  of  A'.  This  was  due  to  the 
electrostatic  action  between  the  coils  B^  and  B2,  for  if  the  terminals  of 
the  coil  B2  and  the  commutator  A'  were  reversed  at  the  same  time, 
there  was  no  change  in  the  value  of  the  ratio  of  the  inductances.  This 
showed  that  it  was  dependent  on  the  coil  itself  and  not  on  the  leads 
and  it  could  therefore  not  be  eliminated. 

It  is  to  be  noticed  that  the  values  obtained  for  the  lower  number 
of  alternations  are  always  greater  than  those  found  with  the  higher 
number  of  alternations.  This  was  caused  by  the  electrostatic  action  of 
the  turns  of  the  coil  on  each  other.  In  the  case  of  the  coil  P2  this  effect 
would  be  caused  by  supposing  a  capacity  of  -0007  microfarads  shunted 
across  the  terminals. 

The  results  are  now  given  comparing  the  different  coils  with  B^  as 
a  standard  and  equal  to  1  henry. 


DOUBLE  LEADS  OF  BELL  WIRE  AND  OPEN  RESISTANCE 
r  =  106  ohms,  n  =  45  complete  periods  per  second. 

".  Correc. 


Coils. 


+  C 


901-6 


-14-55 


901-7 


Cor-         Aver- 

Com. 

Queen. 

R+r.          rec.           age. 

A'. 

Ratio. 

887-05     292 

2300 

2       —-62       2304-9 

1 

2-5983 

310 

2311 

•0 

2 

19 

1158 

3 

1159-0 

1 

1-3099 

22 

1161 

2 

2 

103 

1659 

1661-2 

1 

1-8727 

109 

1664 

8 

2 

92 

1800 

2 

1802-6 

1 

2-0288 

99 

1806 

5 

2 

887-15     149 

4776 

5 

4786-5 

1 

5-3956 

«          196 

4818 

0 

2 

Current  increased  about  2    times. 


A  +  C       901 


902 


P, 


141 

4787 

0 

4781 

3 

1 

5-3898 

184 

4807 

2 

887 

05  211 

5936 

5958 

3 

1 

6-7170 

264 

5982 

2 

51 

6575 

5 

6602 

5 

1 

7-4430 

104 

6631 

0 

2 

887 

45  158 

4778 

9 

4795 

25 

1 

5-4036 

192 

4813 

2 

183 

1146 

5 

1146 

7 

1 

1-9922 

186 

1148 

5 

2 

7 

643 

15 

642 

67 

1 

•7242 

8 

643 

6 

2 

91 

502 

5 

502 

16 

1 

•5658 

503 

1 

2 

ELECTRICAL  MEASUREMENTS 


331 


DOUBLE  LEADS.     n=about  133  complete  alternations  per  sec. 


Coils.           R"  Correc.  Queen.    R+r. 

P,  901-9  —14-55       887-85  90  +  s     500-4 

««               u  «  «<        500-23 

P.,              «  "  3     639-35 

u               «  "  4     639-6 

A  901-87  887-32  ?  4742-2 

«               «  "  133  4760-0 

C  901-9  887-35  44  1151-4 

«               «  «  44  1151-4 


Cor-           Aver- 

Coi 

rec.             age. 

A' 

f-62         499-69 

1 

2 

638-85 

1 

2 

4750-48 

1 

2 

1150-94 

1 

8 

Ratio. 
•5631 


•7198 


5-3537 


1-2970 


In  the  above  determinations  the  coils  were  arranged  in  the  way  as 
indicated  in  the  figure  having  leads  of  double  bell  wire. 

A  SERIES  OF  DETERMINATIONS  OF  A  UNDER  VARIOUS  CONDITIONS. 
Open  resistance  R  on  table  (original  position). 

Cor- 

Coils.  R"          Correc.  Queen.     R+r.         rec. 

A          902-0       —14-55       887-45     149  +  s  4776-5     —-62 
"  "  "  "          196  +  s  4818-  " 

"  901-95  "  887-4  ?         4783-5          " 

"  "  "  "          190  +  s  4808-5  " 

Open  resistance  E  moved  up  to  coil  A  (b^). 


Aver-    Com. 
age.       A'.       Ratio. 

4786-58     1       5-3936 

2 
4795-38     1       5-403 

2 


u  «  «  "  ?         4518-  "          4517-38     2       5-0905 

Open  resistance  E  moved  to  the  other  side  of  A  (&2). 

«      «        «        «    144  +  s  4518-     "    4518-88  1   5-0922 
<(      u       u        u       ci   4521-      "  2 

Coil  A  placed  in  Px  position  and  open  resistance  E  restored  to  its 
position,  and  159'  of  double  wire  added  to  the  circuit. 

Cor-  Aver-     Com. 

Coils.         R".          Correc.  Queen.       R+r.  rec.  age.        A'.       Ratio. 

A  901-95     —14-55      887-4         547-  +  4129  —-62 

547  "  1 


4676 

583  +  4129 
583 

4712 


4693-38     2      5-2888 


Coil  A  at  end  of  double  wire  69'  +  159'  =  228'  long. 


607  +  4129 
607 

4736 

634  +  4129 
634 

4763 


New  leads  placed  in  B±  circuit,  the  wires  were  about  6"  from  each 
other. 


332 


HENRY  A.  EOWLAND 


Coils.        R".  Correc.  Queen.       R+7-, 

A  902-6       —14-55       888-05       569+4129 

"  «  «  "  569 


4698 

594  +  4129 
594 


Open  resistance  placed  next  Coil  A. 


4723 


663  +  4129 
663 


4292 


Cor-          Com. 

rec.       Average.      A'.      Ratio. 


4709-88     1       5-3088 
2 


4791-3       1       5-3956 
4292-         2 

•7 
0-6 


In  the  following  all  connections  were  made  with  open  leads,  and  open 
resistances  were  used. 


Pe- 

Cor-        Aver-  Com. 

riod. 

Coils. 

R" 

Correc. 

Queen. 

R+r. 

rec.           age. 

A'. 

Ratio. 

40 

P, 

902- 

-14-55  887- 

46 

90  +  s 

503 

•07 

-•62        502 

71 

1 

•5664 

'i 

it 

it 

u             u 

90+s 

503 

•6 

M 

2 

133 

it 

it 

u             it 

88  +  s 

522 

•53 

ti 

1 

n 

11 

ti 

it             u 

88  +  8 

502 

•15 

501 

72 

2 

•5653 

40 

PQ 

902  55 

888 

17  +  s 

644 

•3 

u 

1 

M 

u 

it 

u             u 

18  +  s 

644 

•76 

"           643 

91 

0 

•7251 

133 

it 

it 

11             u 

17+s 

643 

•05 

M 

1 

u 

it 

ii 

u             11 

17  +  s 

643 

•1 

"          642 

45 

2 

•7234 

40 

C 

902-4 

"        887- 

So 

28  +  s 

1159 

•6 

ti 

1 

it 

u 

" 

it             ti 

28  +  s 

1159 

•1 

1158- 

73 

2 

1-3050 

133 

ti 

it 

it             u 

24  +  8 

1157 

•0 

ii 

1 

ii 

tt 

M 

it             it 

26  +  s 

1158 

•8 

"         1157 

28 

2 

1-3034 

40 

C  +  PI 

902- 

'        887 

45 

105  +  s 

1658 

•8 

it 

1 

ii 

it 

it 

I                          11 

110  +  s 

1664 

•1 

1660 

77 

2 

1-8713 

133 

it 

u 

1                  If 

101+8 

1656 

•7 

ti 

1 

M 

it 

f- 

t                  II 

106  +  s 

1660 

•3 

"        1657 

96 

2 

1  •  8683 

40 

C  +  Pa 

902-5 

'        887- 

95 

10  +  8 

1803 

•0 

u 

1 

'i 

tf 

it 

u              u 

12+8 

1805 

•0 

"        1803 

3 

2 

2-0261 

133 

II 

it 

ti              i< 

8+8 

1800 

•5 

n 

1 

ii 

II 

11 

It                           11 

8  +  8 

1800 

•2 

"         1799 

65 

2 

2-0221 

40 

PI  +  PS 

902-4 

"        887- 

85 

60  +  s 

2306 

•3 

«        2307 

98 

1 

2-5995 

+  c 

u 

11 

u 

u              u 

I 

2310 

•9 

u 

2 

133 

11 

ii 

11             11 

56  +  s 

2304 

•1 

2304 

13 

1 

2-5951 

ii 

II 

it 

tt              u 

57  +  s 

2305 

•4 

tt 

2 

40 

A 

902-43 

"         887- 

88 

85  +  s 

4703 

ti 

1 

n 

it 

u 

II                          11 

106  +  s 

4724 

•2 

"         4712 

98 

2 

5-3080 

133 

it 

902-4 

"         887- 

85 

82  +  8 

4704 

•2 

it 

1 

u 

ti 

it 

11                           It 

85  +  s 

4707 

•0 

ii        4704 

98 

2 

5-2991 

40 

A  +  C 

902-35 

887- 

8 

1146+s 

9149 

•5 

" 

1 

—  2M 

it 

11 

u 

u              u 

1227  +  8 

9233 

•5 

"         9190 

88 

2 

10-3515 

133 

u 

902-4 

887- 

85 

1170  +  s 

9171 

•7 

it 

1 

11 

ti 

11 

u             u 

1194  +  s 

9191 

•7 

9181 

08 

2 

10-3395 

40 

A  +  C 

902  •  35 

"        887- 

8 

111+s 

2550 

•9 

ii 

1 

+  2M 

n 

u 

u 

it             it 

146  +  8 

2556 

•4 

«        2553 

03 

2 

2-8716 

133 

u 

u 

u              u 

38+s 

2548 

•7 

u 

1 

11 

u 

u 

u              it 

38  +  s 

2548 

•7 

"        2548 

08 

2 

2-8701 

40 

A  +  C 

902  •  6 

888-05 

123 

5852 

ii 

1 

u 

11 

u 

ii              if 

169 

5898 

"        5880 

13 

2 

6-6225 

133 

it 

u 

u              u 

134 

5863 

•5 

u 

1 

u 

it 

ii 

u             u 

140 

5869 

• 

"         5865 

63 

2 

6-6054 

ELECTRICAL  MEASUREMENTS  333 

The  above  results  show  to  what  accuracy  self-inductances  of  different 
values  can  be  compared  to  each  other,  or  to  one  of  the  self-inductances 
taken  as  a  standard.  The  reason  that  the  agreement  between  the 
different  determinations  is  not  greater  than  it  is,  even  though  the  elec- 
trodynamometer  was  sensitive  to  a  change  of  1  part  in  10000  in  R  -\-  r, 
is  that  there  was  always  some  little  heating  of  the  resistances,  and 
although  they  were  measured  in  each  determination  on  a  Wheatstone 
bridge,  still  it  was  impossible  to  determine  the  exact  resistance  at  the 
time  that  the  experiment  was  made.  This  slight  effect  of  the  heating 
of  the  resistance  would  not  enter  in  the  comparison  of  two  nearly  equal 
self-inductances,  that  is  the  comparison  of  a  coil  with  a  standard.  The 
accuracy  of  this  comparison  can  be  made  to  depend  on  the  accuracy 
with  which  R  -j-  r  can  be  determined  for  zero  deflection,  and  this  can 
be  done  to  about  1  part  in  10000.  To  do  this,  first  the  standard  coil 
and  the  coil  to  be  compared  are  substituted  in  turn  in  place  of  L  in 
figure;  they  are  thus  compared  separately  to  a  third  coil.  But  as  the 
standard  and  the  coil  to  be  compared  are  nearly  equal  in  self-inductance, 
the  difference  or  self-inductance  can  be  determined  by  the  amount 
necessary  to  change  R  -\-  r,  and  this  change  will  be  nearly  independent 
of  the  slight  heating  of  the  resistances.  To  make  a  coil  of  the  same 
self -inductance  as  the  standard,  the  standard  is  placed  in  the  R  -\-  r 
circuit  and  the  value  of  R  -\-  r  is  found  that  produces  no  deflection. 
The  coil  to  be  compared  is  then  substituted  in  place  of  the  standard 
keeping  R  -)-  r  fixed,  and  the  self-inductance  of  this  coil  is  changed 
until  there  is  no  deflection,  as  in  the  case  of  the  standard.  The 
accuracy  with  which  this  can  be  done  depends  on  the  accuracy  with 
which  R  -f-  r  can  be  set  or  1  part  in  10000.  The  method  therefore 
gives  a  means  of  comparing  and  constructing  coils  to  agree  in  self- 
inductance  to  within  1  part  in  10000  with  a  standard. 

Method  6. — Zero  Method  for  the  Comparison  of  8  elf -Inductance  with 

Capacity 

This  method  resembles  method  12  and  the  connections  are  made  as 
in  the  figures  when  both  the  hanging  coil  and  fixed  coils  of  the  electro- 
dynamometer  are  shunted  off  the  main  circuit. 

Let  the  currents  be  denoted  by  C>«>*,  C^+M,  (72e*(W+W,  O.eW+fc), 
and  (74£itbt+<M.  The  resistance  by  R",  /,  R  and  r.  The  capacity  by  C. 
The  self -inductance  by  L.  A'  and  A"  are  reversing  commutators  and 
F  the  terminals  of  the  fixed  coils  and  H  the  terminals  of  the  hanging 
coil  of  the  electrodynamometer. 


334 


HENEY  A.  EOWLAND 


If  now  a  periodic  electromotive  force  is  applied  to  the  terminals  A 
and  B  the  equations  connecting  the  different  currents  are  as  below, 
from  which  equations  the  quantity  C^CZ  cos  (fa  —  <£3)  is  to  be  found, 
which  is  proportional  to  the  deflection.  From  the  figure 

"+  -i-V 
ibc  / 


FIG.  8. 

In  the  same  way  it  is  found  that 
0*™  =  i 


FIG.  9. 


Therefore  the  real  part  is 


&  cos  (t,  -  0.)  =  01 


ibc 


/ rr' 

c 


D, 


ELECTRICAL  MEASUREMENTS 


335 


where  D  is  the  deflection.     When  D  is  equal  to  zero 

\-r'}  —  A  =  o 


or 


In  the  experiments  by  this  method  the  £  microfarad  Elliott  condenser 
was  used,  and  it  was  compared  with  the  different  coils  P1}  Pz,  A,  and  C. 
The  connections  were  made  with  open  leads  and  open  resistances  were 
used  as  far  as  possible,  but  it  was  necessary  to  use  resistance  boxes  for 
the  last  adjustments.  The  connections  having  been  made  as  in  figure, 
the  process  of  experimenting  was  to  keep  r  and  /  constant  and  to 
adjust  R"  and  R  until  there  was  no  deflection  of  the  hanging  coil.  The 
resistance  of  the  circuits  R"  -\-  r'  and  R  -\-  r  were  then  measured  on  a 
Wheatstone  bridge.  The  commutator  A'  was  reversed  and  the  process 
was  repeated.  The  condenser  had  absorption  (see  p.  323)  which  caused 
the  resistance  R"  -f-  r'  to  be  increased  by  7-11  ohms.  When  the  capac- 
ity is  calculated,  taking  into  account  the  absorption,  it  is  called  the 
corrected  capacity,  as  in  the  other  tables  of  the  paper. 

COLLECTED  RESULTS. 

n=133. 

Results  found  by  taking  sum 

and  diff .  of  separate 

measurements. 

5648  (C  +  Yl)—C=Pl 

5730  (C  +  PI  +  Pa)— (C  +  Pa)=P, 

7187  (C  +  Pa)— C=P2 

7269  (C  +  P.  +  P,)— (C  +  P,)  =  P, 

3029  (C  +  P,)— P,  =  C 

2990  (C  +  PS)— P4=C 

3065  (C  +  P,  +  Pa)— P,— P2=C 

3022  (A  +  C)— C=A 

2917  (C  +  P,  +  P2)— C=P,  +  Pa 

2888  P,  +  Pa 

8677  C  +  P, 

8718  (C  +  Pj  +  P.,)— Pa=C  +  P1 

0298  (C  +  P,  +  Pa)—  P,=C  +  Pa 

5920  P!  +  Pa  +  C 

6025  A  +  C=A  +  C 

In  method  12  corrections  due  to  the  hanging  coil  and  fixed  coils  were 
calculated  so  that  the  ratio  of  the  resistances  would  give  the  ratio  of  the 
self-inductances  direct.  In  this  method  (6)  since  the  capacity  was  in 
circuit  with  the  hanging  coil,  the  self-inductance  was  so  small  that  it 
was  neglected.  The  self-inductance  of  the  coils  P,  etc.,  which  were 
joined  in  circuit  with  the  fixed  coils,  were  increased  by  the  self-induc- 
tance of  the  fixed  coils,  that  is  by  -0164  henry. 


Coils. 

n=40. 
Results  found 
by  direct 
measurement, 

Results  found  Results  found 
by  taking          by  direct 
sum  diff.,  etc.,   meas.  of  coils 
of  separate    and  combination 
meas.              of  coils. 

PI 

11 

•5664 

•5663 
•5734 

•5653 

P2 

•7251 

•7211 

•7282 

•7233 

9  1 

C 

1-3050 

1-3049 

1-3034 

ii 

1-3010 

ii 

1-3070 

A 

5-3080 

5-3175 

5-2991 

5-: 

P  +P 

1-2945 

1- 

ii 

1-2915 

1- 

C  +  P, 
ii 

1-8713 

1-8714 
1-8744 

1-8683 

1- 
1- 

C  +  Pa 

+  PI  +  PJ 

2-0261 
2-5995 

2-0331 
2-5965 

2-0221 
2-5951 

2- 
2- 

A  +  C 

6-6225 

6-6130 

6-6054 

6- 

336 


HENEY  A.  ROWLAND 


The  table  below  gives  the  various  results. 


N.     Coil. 

Queen  in                                              Position 
current  with                                                of 
R"+r.         H"+r.         R+r.            Product.         A'.            L. 

C. 

40       P 

(1                  U 

2008- 
2005- 

205- 
200- 

1095-7         2198522-          1 

2 

•7251 
•0164 

•3373 

•7415 

33        " 

<i                  U 

2024-5 
2025-5 

221- 
222- 

"               2218792-          1 
"                                       2 

•7223 
•0164 

•3330 

Cor. 
C. 


•3323 


40   A   12741-5 


133 


40 


133 


40 


«   12720- 
"   12716- 


3430-8 
3425-8 


3448-8 
3447-0 


1578-5 
1578-4 


30- 
30- 


236- 
220- 


98- 
93- 


1241-85  15922394- 


15775610- 


1140-8 


106  +  s   1140-8 
105  +  s    « 


57  +s   1088-9 

58 +  s    '< 


3911004- 


3933354- 


1718719-7 


•7397 

5-3080 
•0164 

5-3244 

5-2991 
•0164 

5-3155 

1 • 3050 
•0164 

1-3214 

1-3034 
•0164 

1-3198 

•5653 
•0164 

•5817 


•3344 


•3368 


•3379 


•3355 


•3384 


•3363 


•3346 


This  method  can  be  used  with  great  accuracy  for  the  comparison  of 
the  capacity  of  a  condenser  with  a  standard  condenser.  In  the  com- 
parison, first  one  condenser  and  then  the  other  would  be  placed  in  the 
R  -f-  r  circuit.  If  the  two  condensers  are  of  nearly  the  same  capacity, 
the  degree  of  accuracy  of  the  comparison  depends  upon  the  accuracy 
with  which  R"  -f-  r'  can  be  set.  The  degree  of  accuracy  of  setting 
R"  -f-  r'  varies  with  the  value  of  the  self -inductance  with  which  the 
condensers  are  compared.  In  the  experiments  just  given,  using  the 
different  coils,  the  degree  of  accuracy  with  which  two  ^  microfarad  con- 
densers could  have  been  compared  would  vary  from  1  part  in  2000  to 
one  part  in  14000.  The  two  condensers  are  supposed  to  be  without 
absorption,  as  its  presence  would  cause  trouble  unless  the  absorption 
resistances  were  known. 


ELECTFJCAL  MEASUREMENTS  337 

Resume. — Summing  up  the  results  deduced  in  this  paper,  it  is  seen 
that  the  methods  for  the  absolute  determination  of  self-inductance 
and  capacity  do  not  give  as  concordant  results  as  could  be  wished.  The 
irregularity  of  results  was  caused,  in  the  most  part,  both  in  the  deter- 
mination of  self -inductance  and  capacity  by  the  variation  of  the  periods 
of  the  currents  used  in  the  experiments.  As  the  period  enters  directly 
into  the  determination  of  self-inductance  and  capacity,  all  variations 
of  the  period  will  appear  in  the  results.  The  determination  of  capacity 
is  complicated  by  the  presence  of  electric  absorption  (p.  323  et  seq.). 
The  effect  of  electric  absorption  is  shown  to  be  that  of  an  added  resist- 
ance in  series  with  the  condenser,  called  absorption  resistance.  A 
direct  method  is  given  by  which  absorption  resistance  can  be  measured 
(p.  319),  and  experiments  are  given  which  show  that  when  condensers 
possessing  absorption  are  in  series  or  in  parallel,  their  absorption  re- 
sistances act  under  these  conditions  as  ohmic  resistances  in  series  with 
the  separate  condensers  (p.  323).  Absorption  resistance  is  also  found 
to  be  extremely  sensitive  to  temperature. 

The  methods  for  the  comparison  of  two  self-inductances  or  a  self- 
inductance  and  a  capacity  are  independent  of  the  period,  and  when  the 
self-inductances  are  of  different  magnitudes  the  comparison  can  be 
made  with  an  accuracy  of  1  part  in  10000.  These  methods,  therefore, 
give  a  means  of  comparison  of  a  self-inductance  with  a  standard  self- 
inductance,  or  a  capacity  with  a  standard  capacity  to  an  accuracy  of  1 
part  in  10000,  or  they  allow  the  establishment  of  standards. 


22 


63 

EESISTANCB  TO  ETHEEEAL  MOTION 

Br  H.  A.  ROWLAND,  N.  E.  GILBERT  AND  P.  C.  MCJUNCKIN 
[Johns  Hopkins  University  Circiilars,  No.  146,  p.  60,  1900] 

An  attempt  has  been  made  to  determine  within  what  limits  it  is 
possible  to  say  that  there  is  no  frictional  or  viscous  resistance  in  the 
ether  of  space.  Modern  theories  of  magnetism  are  based  on  some  kind 
of  rotary  or  vortical  motion  in  the  ether  and  if  a  piece  of  iron  is  mag- 
netized we  imagine  that  the  molecules,  or  something  about  them,  rotate 
also.  The  existence  of  permanent  magnets  shows  that  any  retardation 
due  to  any  kind  of  resistance  must  be  very  slight. 

In  the  case  of  an  electro-magnet,  any  energy  used  in  overcoming  such 
resistance,  if  it  exists,  must  be  derived  from  the  exciting  current  and 
the  disappearance  of  such  energy  will  produce  an  apparent  resistance 
added  to  that  of  the  wire.  An  attempt  was  therefore  made  to  deter- 
mine whether  a  wire  carrying  a  current  had  the  same  electrical  resist- 
ance when  producing  a  magnetic  field  that  it  had  when  not  producing  it. 

The  experiment  consisted  in  winding  two  coils  of  wire  together  on 
an  iron  core  and  determining  whether  the  resistance  was  the  same  in 
two  cases : — 

(1).  When  the  current  was  so  passed  through  the  coils  that  both 
produced  a  field  in  the  same  direction. 

(2).  When  the  current  was  so  passed  that  the  fields  produced  counter- 
balanced each  other. 

The  great  difficulty  in  the  experiment  lay  in  the  necessity  of  measur- 
ing the  resistance  of  a  coil  in  which  a  comparatively  large  current  was 
flowing.  In  order  to  overcome  the  effect  of  changes  in  resistance  due 
to  changes  in  temperature,  two  coils  were  wound,  as  nearly  as  possible 
identical,  and  these  double  coils  were  used  for  the  four  arms  of  a 
Wheatstone's  bridge  so  that  the  temperature  would  rise  in  all  four  arms 
equally.  Each  coil  consisted  of  about  2500  turns  of  doubled  No.  30 
copper  wire,  the  whole  enclosed  in  an  iron  case,  boiled  in  wax  for  five 
hours  and  cooled  in  a  vacuum.  The  insulation  resistance  was  then 
about  eleven  megohms.  Iron  cores  were  used  and  it  was  found  that 
the  cases  effectually  protected  the  coils  against  sudden  changes  in  tern- 


339 

perature  due  to  air  currents  as  well  as  serving  for  yokes  to  the  magnets. 
A  current  of  one-tenth  ampere  was  used  which  insured  a  high  state 
of  magnetization  in  the  iron  when  two  coils  were  in  series,  giving  5000 
turns. 

The  coils  were  connected  in  the  bridge  in  such  a  way  that  the  two 
coils  in  one  case  formed  the  opposite  arms  of  the  bridge.  By  means 
of  a  reversing  switch  the  current  in  one  of  these  coils  could  be  reversed. 
This  changed  the  field  which  might  affect  two  opposite  arms  of  the 
bridge  and  thus  doubled  the  deflection.  Another  switch  might  have 
been  inserted  in  the  other  pair  of  arms  and  thus  doubled  the  deflection 
again  but  errors  due  to  the  switches  would  also  have  been  doubled  and 
no  advantage  gained.  The  switch  was  carefully  constructed  with  large 
copper  rods  dipping  into  copper  mercury  cups  but,  at  best,  the  inac- 
curacies of  the  switch  limited  the  accuracy  of  the  experiment. 

The  fine  adjustments  were  made  by  resistance  boxes  shunted  round 
one  of  the  coils.  About  15,000  ohms  in  this  shunt  balanced  the  bridge. 
A  change  of  one  ohm  in  the  shunt  gave  a  deflection  of  two  millimeters 
and  indicated  a  change  in  the  resistance  of  the  arm  of  yinnnnr  ohm.  The 
whole  resistance  being  over  100  ohms  this  would  give  a  determination 
of  one  part  in  2,000,000  or,  since  the  deflection  is  doubled,  one  part  in 
4,000,000  for  each  arm.  The  result  of  30  readings  each  way  was  that 
the  shunt  resistance  was  about  3-4  ohms  less  with  magnetic  field  than 
without.  The  shunt  was  so  placed  that  this  gives  a  less  resistance  by 
one  part  in  1,200,000  when  producing  a  magnetic  field. 

The  above  result  is  in  the  wrong  direction.  The  difficulty  may  lie  in 
the  fact  that  the  galvanometer,  though  used  at  night,  was  unsteady  at 
best,  or  it  may  be  due  to  leakage.  The  resistance  of  the  coils  was  100 
ohms  while  the  insulation  resistance  was  11,000,000  ohms.  If  the  leak- 
age is  symmetrical  along  the  doubled  wire  it  will  not  affect  the  galvano- 
meter upon  reversing  the  current  in  one  coil.  This  assumption  may 
not  be  justified. 


PART  III 

HEAT 


16 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT,  WITH  SUB- 
SIDIAEY  RESEAKCHES  ON  THE  VARIATION  OF  THE 
MERCURIAL  FROM  THE  AIR  THERMOMETER,  AND  ON 
THE  VARIATION  OF  THE  SPECIFIC  HEAT  OF  WATER l 

[Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  XV,  75-200,  1880] 

INVESTIGATIONS  ON  LIGHT  AND  HEAT,  made  and  published  wholly  or  in  part  with 
appropriation  from  the  RUMFOBD  FUND 

Presented  June  llth,  1879 


CONTENTS 


I.  Introductory  remarks  ....  343 

II.  Thermometry 345 

(a.)  General  view  of  Thermom- 
etry     345 

(&.)  The  Mercurial  Thermometer  346 
(c.)  Relation  of   the  Mercurial 

and  Air  Thermometers  352 

1.  General  and  Historical 

Remarks     ....     352 

2.  Description   of    Appa- 

ratus       358 

3.  Results  of  Comparison  366 
(d.)  Reduction  to  the  Absolute 

Scale 381 

Appendix  to  Thermometry    .     384 

III.  Calorimetry 387 

(a.)  Specific  Heat  of  Water     .     387 
(6.)  Heat  Capacity  of  the  Calo- 
rimeter   399 

IV.  Determination  of  Equivalent  .     404 


V. 


(a.)  Historical  Remarks  .     .     .  404 

1.  General      Review      of 

Methods 405 

2.  Results  of  Best  Deter- 

minations    ....  409 
(&.)  Description  of  Apparatus     422 

1.  Preliminary  Remarks  .  422 

2.  General  Description  .     424 

3.  Details 426 

(c)  Theory  of  the  Experiment    430 

1.  Estimation    of     Work 

Done 430 

2.  Radiation 435 

3.  Corrections     to    Ther- 

mometers, etc.       .     .  439 
(d.)  Results 441 

1.  Constant  Data     .     .     .  441 

2.  Experimental  Data  and 

Tables  of  Results     .     441 
Concluding  Remarks  and  Criti- 
cism of  Results  and  Methods  465 


I.— INTRODUCTOKY  REMARKS 


Among  the  more  important  constants  of  nature,  the  ratio  of  the 
heat  unit  to  the  unit  of  mechanical  work  stands  forth  prominent,  and 


1  This  research  was  originally  to  have  been  performed  in  connection  with  Professor 
Pickering,  but  the  plan  was  frustrated  by  the  great  distance  between  our  residences. 
An  appropriation  for  this  experiment  was  made  by  the  American  Academy  of  Arts 
and  Sciences  at  Boston,  from  the  fund  which  was  instituted  by  Count  Rumford,  and 
liberal  aid  was  also  given  by  the  Trustees  of  the  Johns  Hopkins  University,  who  are 
desirous,  as  far  as  they  can,  to  promote  original  scientific  investigations. 


344  HENEY  A.  KOWLAND 

is  used  almost  daily  by  the  physicist.  Yet,  when  we  come  to  consider 
the  history  of  the  subject  carefully,  we  find  that  the  only  experimenter 
who  has  made  the  determination  with  anything  like  the  accuracy 
demanded  by  modern  science,  and  by  a  method  capable  of  giving  good 
results,  is  Joule,  whose  determination  of  thirty  years  ago,  confirmed 
by  some  recent  results,  to-day  stands  almost,  if  not  quite,  alone  among 
accurate  results  on  the  subject. 

But  Joule  experimented  on  water  of  one  temperature  only,  and  did 
not  reduce  his  results  to  the  air  thermometer;  so  that  we  are  still  left 
in  doubt,  even  to  the  extent  of  one  per  cent,  as  to  the  value  of  the 
equivalent  on  the  air  thermometer. 

The  reduction  of  the  mercurial  to  the  air  thermometer,  and  thence 
to  the  absolute  scale,  has  generally  been  neglected  between  0°  and  100° 
by  most  physicists,  though  it  is  known  that  they  differ  several  tenths 
of  a  degree  at  the  45°  point.  In  calorimetric  researches  this  may  pro- 
duce an  error  of  over  one,  and  even  approaching  two  per  cent,  especially 
when  a  Geissler  thermometer  is  used,  which  is  the  worst  in  this  respect 
of  any  that  I  have  experimented  on;  and  small  intervals  on  the  mer- 
curial thermometers  differ  among  themselves  more  than  one  per  cent 
from  the  difference  of  the  glass  used  in  them. 

Again,  as  water  is  necessarily  the  liquid  used  in  calorimeters,  its 
variation  of  specific  heat  with  the  temperature  is  a  very  important 
factor  in  the  determination  of  the  equivalent.  Strange  as  it  may 
appear,  we  may  be  said  to  know  almost  nothing  about  the  variation 
of  the  specific  heat  of  water  with  the  temperature  between  0°  and 
100°  C. 

Regnault  experimented  only  above  100°  C.  The  experiments  of 
Hirn,  and  of  Jamin  and  Amaury,  are  absurd,  from  the  amount  of  varia- 
tion which  they  give.  Pfaundler  and  Platter  confined  themselves  to 
points  between  0°  and  13°.  Miinchausen  seems  to  have  made  the  best 
experiments,  but  they  must  be  rejected  because  he  did  not  reduce  to 
the  air  thermometer. 

In  the  present  series  of  researches,  I  have  sought,  first,  a  method 
of  measuring  temperatures  on  the  perfect  gas  thermometer  with  an 
accuracy  scarcely  hitherto  attempted,  and  to  this  end  have  made  an 
extended  study  of  the  deviation  of  ordinary  thermometers  from  the 
air  thermometer;  and,  secondly,  I  have  sought  a  method  of  determin- 
ing the  mechanical  equivalent  of  heat  so  accurate,  and  of  so  extended 
a  range,  that  the  variation  of  the  specific  heat  of  water  should  follow 
from  the  experiments  alone. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  345 

As  to  whether  or  not  these  have  been  accomplished,  the  following 
pages  will  show.  The  curious  result  that  the  specific  heat  of  water 
on  the  air  thermometer  decreases  from  0°  to  about  30°  or  35°,  after 
which  it  increases,  seems  to  be  an  entirely  unique  fact  in  nature,  seeing 
that  there  is  apparently  no  other  substance  hitherto  experimented  upon 
whose  specific  heat  decreases  on  rise  of  temperature  without  change  of 
state.  From  a  thermodynamic  point  of  view,  however,  it  is  of  the 
same  nature  as  the  decrease  of  specific  heat  which  takes  place  after 
the  vaporization  of  a  liquid. 

The  close  agreement  of  my  result  at  15° -7  C.  with  the  old  result  of 
Joule,  after  approximately  reducing  his  to  the  air  thermometer  and 
latitude  of  Baltimore,  and  correcting  the  specific  heat  of  copper,  is 
very  satisfactory  to  us  both,  as  the  difference  is  not  greater  than  1  in 
400,  and  is  probably  less. 

I  hope  at  some  future  time  to  make  a  comparison  with  Joule's  ther- 
mometers, when  the  difference  can  be  accurately  stated. 

II.— THERMOMETKY 
(a.)  General  View 

The  science  of  thermometry,  as  ordinarily  studied,  is  based  upon 
the  changes  produced  in  bodies  by  heat.  Among  these  we  may  mention 
change  in  volume,  pressure,  state  of  aggregation,  dissociation,  amount 
and  color  of  light  reflected,  transmitted,  or  emitted,  hardness,  pyro-elec- 
tric  and  thermo-electric  properties,  electric  conductivity  or  specific  in- 
duction capacity,  magnetic  properties,  thermo-dynamic  properties,  &c.; 
and  on  each  of  these  may  be  based  a  system  of  thermometry,  each  one 
of  which  is  perfect  in  itself,  but  which  differs  from  all  the  others  widely. 
Indeed,  each  method  may  be  applied  to  nearly  all  the  bodies  in  nature, 
and  hundreds  or  thousands  of  thermometric  scales  may  be  produced, 
which  may  be  made  to  agree  at  two  fixed  points,  such  as  the  freezing 
and  boiling  points  of  water,  but  which  will  in  general  differ  at  nearly, 
if  not  all,  other  points. 

But  from  the  way  in  which  the  science  has  advanced,  it  has  come 
to  pass  that  all  methods  of  thermometry  in  general  use  to  the  present 
time  have  been  reduced  to  two  or  three,  based  respectively  on  the 
apparent  expansion  of  mercury  in  glass  and  on  the  absolute  expansion  of 
some  gas,  and  more  lately  on  the  second  law  of  thermodynamics. 

Each  of  these  systems  is  perfectly  correct  in  itself,  and  we  have  no 
right  to  designate  either  of  them  as  incorrect.  We  must  decide  a  priori 


346  HEJOIY  A.  EOWLAND 

on  some  system,  and  then  express  all  our  results  in  that  system:  the 
accuracy  of  science  demands  that  there  should  be  no  ambiguity  on  that 
subject.  In  deciding  among  the  three  systems,  we  should  be  guided 
by  the  following  rules : — 

1st.  The  system  should  be  perfectly  definite,  so  that  the  same  tem- 
perature should  be  indicated,  whatever  the  thermometer. 

2d.  The  system  should  lead  to  the  most  simple  laws  in  nature. 

Sir  William  Thomson's  absolute  system  of  thermometry,  coinciding 
with  that  based  on  the  expansion  of  a  perfect  gas,  satisfies  these  most 
nearly.  The  mercurial  thermometer  is  not  definite  unless  the  kind  of 
glass  is  given,  and  even  then  it  may  vary  according  to  the  way  the  bulb 
is  blown.  The  gas  thermometer,  unless  the  kind  of  gas  is  given,  is  not 
definite.  And,  further,  if  the  temperature  as  given  by  either  of  these 
thermometers  was  introduced  into  the  equations  of  thermo-dynamics, 
the  simplest  of  them  would  immediately  become  complicated. 

Throughout  a  small  range  of  temperature,  these  systems  agree  more 
or  less  completely,  and  it  is  the  habit  even  with  many  eminent  physi- 
cists to  regard  them  as  coincident  between  the  freezing  and  boiling 
points  of  water.  We  shall  see,  however,  that  the  difference  between 
them  is  of  the  highest  importance  in  thermometry,  especially  where 
differences  of  temperature  are  to  be  used. 

For  these  reasons  I  have  reduced  all  my  measures  to  the  absolute 
system. 

The  relation  between  the  absolute  system  and  the  system  based  on 
the  expansion  of  gases  has  been  determined  by  Joule  and  Thomson 
in  their  experiments  on  the  flow  of  gases  through  porous  plugs  (Philo- 
sophical Transactions  for  1862,  p.  579).  Air  was  one  of  the  most 
important  substances  they  experimented  upon. 

To  measure  temperature  on  the  absolute  scale,  we  have  thus  only  to 
determine  the  temperature  on  the  air  thermometer,  and  then  reduce 
to  the  absolute  scale.  But  as  the  air  thermometer  is  very  inconvenient 
to  use,  it  is  generally  more  convenient  to  use  a  mercurial  thermometer 
which  has  been  compared  with  the  air  thermometer.  Also,  for  small 
changes  of  temperature  the  air  thermometer  is  not  sufficiently  sensi- 
tive, and  a  mercurial  thermometer  is  necessary  for  interpolation.  I  shall 
occupy  myself  first  with  a  careful  study  of  the  mercurial  thermometer. 

(6.)   The  Mercurial  Thermometer 

Of  the  two  kinds  of  mercurial  thermometers,  the  weight  thermometer 
is  of  little  importance  to  our  subject.  I  shall  therefore  confine  myself 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  347 

principally  to  that  form  having  a  graduated  stem.  For  convenience 
in  use  and  in  calibration,  the  principal  bulb  should  be  elongated,  and 
another  small  bulb  should  be  blown  at  the  top.  This  latter  is  also  of 
the  utmost  importance  to  the  accuracy  of  the  instrument,  and  is  placed 
there  by  nearly  all  makers  of  standards.2  It  is  used  to  place  some  of 
the  mercury  in  while  calibrating,  as  well  as  when  a  high  temperature 
is  to  be  measured;  also,  the  mercury  in  the  larger  bulb  can  be  made 
free  from  air-bubbles  by  its  means. 

Most  standard  thermometers  are  graduated  to  degrees;  but  Regnault 
preferred  to  have  his  thermometers  graduated  to  parts  of  equal  capacity 
whose  value  was  arbitrary,  and  others  have  used  a  single  millimeter 
division.  As  thermometers  change  with  age,  the  last  two  methods  are 
the  best;  and  of  the  two  I  prefer  the  latter  where  the  highest  accuracy 
is  desired,  seeing  that  it  leaves  less  to  the  maker  and  more  to  the 
scientist.  The  cross-section  of  the  tube  changes  continuously  from 
point  to  point,  and  therefore  the  distribution  of  marks  on  the  tube 
should  be  continuous,  which  would  involve  a  change  of  the  dividing 
engine  for  each  division.  But  as  the  maker  divides  his  tube,  he  only 
changes  the  length  of  his  divisions  every  now  and  then,  so  as  to  average 
his  errors.  This  gives  a  sufficiently  exact  graduation  for  large  ranges 
of  temperature;  but  for  small,  great  errors  may  be  introduced.  Where 
there  is  an  arbitrary  scale  of  millimeters,  I  believe  it  is  possible  to 
calibrate  the  tube  so  that  the  errors  shall  be  less  than  can  be  seen  with 
the  naked  eye,  and  that  the  table  found  shall  represent  very  exactly 
the  gradual  variation  of  the  tube. 

In  the  calibration  of  my  thermometers  with  the  millimetric  scale,  I 
have  used  several  methods,  all  of  which  are  based  upon  some  graphical 
method.  The  first,  which  gives  all  the  irregularities  of  the  tube  with 
great  exactness,  is  as  follows: 

A  portion  of  the  mercury  having  been  put  in  the  upper  bulb,  so  as 
to  leave  the  tube  free,  a  column  about  15  mm.  long  is  separated  off. 
This  is  moved  from  point  to  point  of  the  tube,  and  its  length  carefully 
measured  on  the  dividing  engine.  It  is  not  generally  necessary  to 
move  the  column  its  own  length  every  time,  but  it  may  be  moved 
20  mm.  or  25  mm.,  a  record  of  the  position  of  its  centre  being  kept. 
To  eliminate  any  errors  of  division  or  of  the  dividing  engine,  readings 
were  then  taken  on  the  scale,  and  the  lengths  reduced  to  their  value 
in  scale  divisions.  The  area  of  the  tube  at  every  point  is  inversely  as 

*Geissler  and  Casella  omit  it,  which  should  condemn  their  thermometers. 


348  HENEY  A.  EOWLAND 

the  length  of  the  column.  We  shall  thus  have  a  series  of  figures  nearly 
equal  to  each  other,  if  the  tube  is  good.  By  subtracting  the  smallest 
from  each  of  the  others,  and  plotting  the  results  as  ordinates,  with  the 
thermometer  scale  as  abscissas,  and  drawing  a  curve  through  the  points 
so  found,  we  have  means  of  finding  the  area  at  any  point.  The  curve 
should  not  be  drawn  exactly  through  the  points,  but  rather  around 
them,  seeing  they  are  the  average  areas  for  some  distance  each  side  of 
the  point.  With  good  judgment,  the  curve  can  be  drawn  with  great 
accuracy.  I  then  draw  ordinates  every  10  mm.,  and  estimate  the  aver- 
age area  of  the  tube  for  that  distance,  which  I  set  down  in  a  table. 
As  the  lengths  are  uniform,  the  volume  of  the  tube  to  any  point  is 
found  by  adding  up  the  areas  to  that  point. 

But  it  would  be  unwise  to  trust  such  a  method  for  very  long  tubes, 
seeing  the  mercury  column  is  so  short,  and  the  columns  are  not  end  to 
end.  Hence  I  use  it  only  as  supplementary  to  one  where  the  column 
is  about  50  mm.  long,  and  is  always  moved  its  own  length.  This  estab- 
lishes the  volumes  to  a  series  of  points  about  50  mm.  apart,  and  the 
other  table  is  only  used  to  interpolate  in  this  one.  There  seems  to  be 
no  practical  object  in  using  columns  longer  than  this. 

Having  finally  constructed  the  arbitrary  table  of  volumes,  I  then 
test  it  by  reading  with  the  eye  the  length  of  a  long  mercury  column. 
No  certain  error  was  thus  found  at  any  point  of  any  of  the  thermom- 
eters which  I  have  used  in  these  experiments. 

While  measuring  the  column,  great  care  must  be  taken  to  preserve 
all  parts  of  the  tube  at  a  uniform  temperature,  and  only  the  extreme 
ends  must  be  touched  with  the  hands',  which  should  be  covered  with 
cloth. 

If  V  is  the  volume  on  this  arbitrary  scale,  the  temperature  on  the 
mercurial  thermometer  is  found  from  the  formula  T  =  C  V  —  t0,  where 
C  and  t0  are  constants  to  be  determined.  If  the  thermometer  contains 
the  0°  and  100°  points,  we  have  simply 

r_       100 
T~^T"  * 

'100  '0 

Otherwise  C  is  found  by  comparison  with  some  other  thermometer, 
which  must  be  of  the  same  kind  of  glass. 

It  is  to  be  carefully  noted  that  the  temperature  on  the  mercurial 
thermometer,  as  I  have  defined  it,  is  proportional  to  the  apparent  ex- 
pansion of  mercury  as  measured  on  the  stem.  By  defining  it  as  pro- 
portional to  the  true  volume  of  mercury  in  the  stem,  we  have  to  intro- 
duce a  correction  to  ordinary  thermometers,  as  Poggendorff  has  shown. 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  349 

As  I  only  use  the  mercurial  thermometer  to  compare  with  the  air 
thermometer,  and  as  either  definition  is  equally  correct,  I  will  not 
further  discuss  the  matter,  but  will  use  the  first  definition,  as  being 
the  simplest. 

In  the  above  formula  I  have  implicitly  assumed  that  the  apparent 
expansion  is  only  a  function  of  the  temperature;  but  in  solid  bodies 
like  glass  there  seems  to  be  a  progressive  change  in  the  volume  as  time 
advances,  and  especially  after  it  has  been  heated.  And  hence  in  mer- 
curial and  alcohol  thermometers,  and  probably  in  general  in  all  ther- 
mometers which  depend  more  or  less  on  the  expansion  of  solid  bodies, 
we  find  that  the  reading  of  the  thermometer  depends,  not  only  on  its 
present  temperature,  but  also  on  that  to  which  it  has  been  subjected 
within  a  short  time;  so  that,  on  heating  a  thermometer  up  to  a  certain 
temperature,  it  does  not  stand  at  the  same  point  as  if  it  had  been  cooled 
from  a  higher  temperature  to  the  given  temperature.  As  these  effects 
are  without  doubt  due  to  the  glass  envelope,  we  might  greatly  diminish 
them  by  using  thermometers  filled  with  liquids  which  expand  more 
than  mercury :  there  are  many  of  these  which  expand  six  or  eight  times 
as  much,  and  so  the  irregularity  might  be  diminished  in  this  ratio.  But 
in  this  case  we  should  find  that  the  correction  for  that  part  of  the 
stem  which  was  outside  the  vessel  whose  temperature  we  were  deter- 
mining would  be  increased  in  the  same  proportion;  and  besides,  as  all 
the  liquids  are  quite  volatile,  or  at  least  wet  the  glass,  there  would  be 
an  irregularity  introduced  on  that  account.  A  thermometer  with  liquid 
in  the  bulb  and  mercury  in  the  stem  would  obviate  these  inconven- 
iences ;  but  even  in  this  case  the  stem  would  have  to  be  calibrated  before 
the  thermometer  was  made.  By  a  comparison  with  the  air-thermom- 
eter, a  proper  formula  could  be  obtained  for  finding  the  temperature. 

But  I  hardly  believe  that  any  thermometer  superior  to  the  mercurial 
can  at  present  be  made, — that  is,  any  thermometer  within  the  same 
compass  as  a  mercurial  thermometer, — and  I  think  that  the  best  result 
for  small  ranges  of  temperature  can  be  obtained  with  it  by  studying 
and  avoiding  all  its  sources  of  error. 

To  judge  somewhat  of  the  laws  of  the  change  of  zero  within  the 
limits  of  temperature  which  I  wished  to  use,  I  took  thermometer  No. 
6163,  which  had  lain  in  its  case  during  four  months  at  an  average 
temperature  of  about  20°  or  25°  C.,  and  observed  the  zero  point,  after 
heating  to  various  temperatures,  with  the  following  result.  The  time 
of  heating  was  only  a  few  minutes,  and  the  zero  point  was  taken  imme- 


350 


HENRY  A.  KOWLAKD 


diately  after;  some  fifteen  minutes,  however,  being  necessary  for  the 
thermometer  to  entirely  cool. 

TABLE  I. — SHOWING  CHANGE  OF  ZERO  POINT.  - 


Temperature 
of  Bulb 
before  finding 
the  0  Point. 

Change  of 
0  Point. 

Temperature 
of  Bulb 
before  finding 
the  0  Point. 

Change  of 
0  Point. 

22°-  5 

0 

70-0 

115 

30-0 

—  •016 

81-0 

—  •170 

40-5 

—  •033 

90-0 

—  •231 

51-0 

—  •039 

100-0 

—  •313 

60-0 

—  •105 

100-0 

—  •347 

The  second  100°  reading  was  taken  after  boiling  for  some  time. 

It  is  seen  that  the  zero  point  is  always  lower  after  heating,  and  that 
in  the  limits  of  the  table  the  lowering  of  the  zero  is  about  proportional 
to  the  square  of  the  increase  of  temperature  above  25°  C.  This  law 
is  not  true  much  above  100°,  and  above  a  certain  temperature  the 
phenomenon  is  reversed,  and  the  zero  point  is  higher  after  heating; 
but  for  the  given  range  it  seems  quite  exact. 

It  is  not  my  purpose  to  make  a  complete  study  of  this  phenomenon 
with  a  view  to  correcting  the  thermometer,  although  this  has  been 
undertaken  by  others.  But  we  see  from  the  table  that  the  error  can- 
not exceed  certain  limits.  The  range  of  temperature  which  I  have 
used  in  each  experiment  is  from  20°  to  30°  C.,  and  the  temperature 
rarely  rose  above  40°  C.  The  change  of  zero  in  this  range  only  amounts 
to  0°-03C. 

The  exact  distribution  of  the  error  from  this  cause  throughout  the 
scale  has  never  been  determined,  and  it  affects  my  results  so  little  that 
I  have  not  considered  it  worth  investigating.  It  seems  probable,  how- 
ever, that  the  error  is  distributed  throughout  the  scale.  If  it  were 
uniformly  distributed,  the  value  of  each  division  would  be  less  than 
before  by  the  ratio  of  the  lowering  at  zero  to  the  temperature  to  which 
the  thermometer  was  heated. 

The  maximum  errors  produced  in  my  thermometers  by  this  cause 
would  thus  amount  to  1  in  1300  nearly  for  the  40°  thermometer,  and 
to  about  1  in  2000  for  the  others.  Eather  than  allow  for  this,  it  is 
better  to  allow  time  for  the  thermometer  to  resume  its  original  state. 

Only  a  few  observations  were  made  upon  the  rapidity  with  which 
the  zero  returned  to  its  original  position.  After  heating  to  81°,  the 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  351 

zero  returned  from  — 0°-170  to  — 0°-148  in  two  hours  and  a  half. 
After  heating  to  100°,  the  zero  returned  from  — 0°-347  to  — 0°-110 
in  nine  days,  and  to  — 0°-022  in  one  month.  Eeasoning  from  this,  I 
should  say  that  in  one  week  thermometers  which  had  not  been  heated 
ahove  40°  should  be  ready  for  use  again,  the  error  being  then  supposed 
to  be  less  than  1  in  4000,  and  this  would  be  partially  eliminated  by 
comparing  with  the  air  thermometer  at  the  same  intervals  as  the  ther- 
mometer is  used,  or  at  least  heating  to  40°  one  week  before  comparing 
with  the  air  thermometer. 

As  stated  before,  when  a  thermometer  is  heated  to  a  very  high 
point,  its  zero  point  is  raised  instead  of  lowered,  and  it  seems  probable 
that  at  some  higher  point  the  direction  of  change  is  reversed  again; 
for,  after  the  instrument  comes  from  the  maker,  the  zero  point  con- 
stantly rises  until  it  may  be  0°-6  above  the  mark  on  the  tube.  This 
gradual  change  is  of  no  importance  in  my  experiments,  as  I  only  use 
differences  of  temperature,  and  also  as  it  was  almost  inappreciable  in 
my  thermometers. 

Another  source  of  error  in  thermometers  is  that  due  to  the  pressure 
on  the  bulb.  In  determining  the  freezing  point,  large  errors  may  be 
made,  amounting  to  several  hundredths  of  a  degree,  by  the  pressure  of 
pieces  of  ice.  In  my  experiments,  the  zero  point  was  determined  in 
ice,  and  then  the  thermometer  was  immersed  in  the  water  of  the  com- 
parator at  a  depth  of  about  60  cm.  The  pressure  of  this  water  affected 
the  thermometer  to  the  extent  of  about  0°-01,  and  a  correction  was 
accordingly  made.  As  differences  of  temperature  were  only  needed, 
no  correction  was  made  for  variation  in  pressure  of  the  air. 

It  does  not  seem  to  me  well  to  use  thermometers  with  too  small  a 
stem,  as  I  have  no  doubt  that  they  are  subject  to  much  greater  irregu- 
larities than  those  with  a  coarse  bore.  For  the  capillary  action  always 
exerts  a  pressure  on  the  bulb.  Hence,  when  the  mercury  rises,  the 
pressure  is  due  to  a  rising  meniscus  which  causes  greater  pressure  than 
the  falling  meniscus.  Hence,  an  apparent  friction  of  the  mercurial 
column.  Also,  the  capillary  constant  of  mercury  seems  to  depend  on 
the  electric  potential  of  its  surface,  which  may  not  be  constant,  and 
would  thus  cause  an  irregularity. 

My  own  thermometers  did  not  show  any  apparent  action  of  this  kind, 
but  Pfaimdler  and  Platter  mention  such  an  action,  though  they  give 
another  reason  for  it. 


352  HENRY  A.  EOWLAND 

t         * 
(c.)  Relation  of  the  Mercurial  and  Air  Thermometers  ,J* 

'  ••  •'      & 
1.  GENERAL  AND  HISTORICAL  REMARKS 

*    .-* 
Since  the  time  of  Dulong  and  Petit,  many  experiments  Have  been 

made  on  the  difference  between  the  mercurial  and  the  air  thermometer, 
but  unfortunately  most  of  them  have  been  at  high  temperatures.  As 
weight  thermometers  have  been  used  by  some  of  the  best  experimenters, 
I  shall  commence  by  proving  that  the  weight  thermometer  and  stem 
thermometer  give  the  same  temperature;  at  the  same  time,  however, 
obtaining  a  convenient  formula  for  the  comparison  of  the  air  ther- 
mometer with  the  mercurial. 

For  the  expansion  of  mercury  and  of  glass  the  following  formulae 
must  hold : — 

For  mercury,     V  —  V0  (I  +  at  +~W  +  &c.} ; 
"    glass.  V  =  V\  (1  +  at  +  /3f  +  tic.} ; 

In  both  the  weight  and  stem  thermometers  we  must  have  V  =  V. 

•    •  '0    0  "i ! 7      ! /vTo      ! ~p         '  0  V -^      •      •L*~V      I       X>£      ~P    O£6,  ). 

1  +  at  +  pt    +  <XC. 

where  V0  and  V0  are  the  volumes  of  the  glass  and  of  the  mercury 
reduced  to  zero,  and  t  is  the  temperature  on  the  air  thermometer. 
The  temperature  by  the  weight  thermometer  is 

P°     -1 

P7 


where  P0,  P ,  &c.,  are  the  weights  of  mercury  in  the  bulb  at  0°  C., 
t°  C.,  &c. 

Now  these  weights  are  directly  as  the  volumes  of  the  mercury  at  0°. 

/.     -p°  =  1  +  At  +  Bt*  +  &c., 
seeing  that  V  is  constant. 

...      7'=100ra^+B/'  +  *<;- 


+  &c.' 

In  the  stem  thermometers  we  have  V0,  the  volume  of  mercury  at  0°, 
constant,  and  the  volume  of  the  glass  that  the  mercury  fills,  reduced 
to  0°,  variable.  As  the  volume  of  the  glass  T'0  is  the  volume  reduced 
to  0°,  it  will  be  proportional  to  the  volume  of  bulb  plus  the  volume  of 
the  tube  as  read  off  on  the  scale  which  should  be  on  the  tube. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  353 


T  =  100  -Af,  °;t  _  (V',)  •  =  10°  (  F 
^  +  5f  +  &c. 


7*=  100 


100  ^4  +  (100)'  B  +  &c. 
which  is  the  same  as  for  the  weight  thermometer. 
If  the  fixed  points  are  0°  and  t'°  instead  of  0°  and  100°,  we  can  write 

&C' 


At'  +  Et"  +  Ct's  +  &c. 


T-f 


T=  t     1  +  (t  -  t) 


As  T  and  £  are  nearly  equal,  and  as  we  shall  determine  the  constants 
experimentally,  we  may  write 

t  =  T  -  at  (f  -  t)  (b  -  t}  +  &c., 

where  t  is  the  temperature  on  the  air  thermometer,  and  T  that  on  the 
mercurial  thermometer,  and  a  and  &  are  constants  to  be  determined  for 
each  thermometer. 

The  formula  might  be  expanded  still  further,  but  I  think  there  are 
few  cases  which  it  will  not  represent  as  it  is.  Considering  &  as  equal 
to  0,  a  formula  is  obtained  which  has  been  used  by  others,  and  from 
which  some  very  wrong  conclusions  have  been  drawn.  In  some  kinds 
of  glass  there  are  three  points  which  coincide  with  the  air  thermometer, 
and  it  requires  at  least  an  equation  of  the  third  degree  to  represent 
this. 

The  three  points  in  which  the  two  thermometers  coincide  are  given 
by  the  roots  of  the  equation 

t(t' 
and  are,  therefore, 


In  the  following  discussion  of  the  historical  results,  I  shall  take  0° 
and  100°  as  the  fixed  points.  Hence,  i'  =  100°.  To  obtain  a  and  &, 
two  observations  are  needed  at  some  points  at  a  distance  from  0°  and 
100°.  That  we  may  get  some  idea  of  the  values  of  the  constants  in 
the  formula  for  different  kinds  of  glass,  I  will  discuss  some  of  the 
experimental  results  of  Eegnault  and  others  with  this  in  view. 
23 


354 


HENRY  A.  ROWLAND 


Regnault's  results  are  embodied,  for  the  most  part,  in  tables  given  on 
p.  239  of  the  first  volume  of  his  Relation  des  Experiences.  The  figures 
given  there  are  obtained  from  curves  drawn  to  represent  the  mean  of 
his  experiments,  and  do  not  contain  any  theoretical  results.  The  direct 
application  of  my  formula  to  his  experiments  could  hardly  be  made  with- 
out immense  labor  in  finding  the  most  probable  value  of  the  constants. 

But  the  following  seem  to  satisfy  the  experiments  quite  well: — 


Cristal  de  Choisy-le-Roi  b  =  0, 

Verre  Ordinaire  b  =  245°, 

Verre  Vert  b  =  270°, 

Verre  de  Suede  b  =  +10° 


a  =  .000  000  32. 
\  =  .000  000  34. 
a  =  .000  000  095 
a  —  .000  000  14. 


From  these  values  I  have  calculated  the  following: — 

TABLE  II. — REGNAULT'S  RESULTS  COMPARED  WITH  THE  FORMULA. 


Choisy-le-Roi. 

Verre  Ordinaire. 

Verre  Vert. 

Verre  de  Suede. 

ti 

1 

j 

® 

•3 

® 

j 

a 

« 

9 

| 

-2 

§ 

•d 

* 

g 

•SJ 

1 

c 

•a 
o 

S 

H 

E 

3 

2 

C 

"3 

0) 

C 

3 

2 

3 

£ 

« 

2 
o 

i 

fi 
5 

s 
i 

o 

•iH 

5 

i 

0 

p 
I 

o 

S 

| 

O 

1 

S 

100 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

120120-12 

120-09 

+  •03 

119-95119-90 

+  •05 

120-07 

120-09 

—  01 

120-04120-04 

0 

140140-29 

140-25 

+  -04 

139-85'139-80 

+  •05 

140-21140-22 

—  01 

140-11140-10 

+  •01 

160160-52 

160  •  49  +  •  03!  159  •  74  159  •  72 

+  •02 

160-40160-39 

+  •01 

160-20160-21 

—  •01 

180180-80 

180-83  —  03 

179-63179-68 

—  •05 

180-60180-62 

—  •02 

180-33180-34 

—  01 

200201-25201-28 

—  •03 

199-70199-69 

+  •01 

200-80,200-89 

—  •09 

200-50200-53 

—  •03 

220221-82221-86 

—  •04 

219-80219-78 

+  •02 

221-20221-23 

—  •03 

320-75220-78 

—  •03 

240242-55!242-56 

—  01 

239-90239-96 

—  •06 

241-60 

241-63 

—  03 

241-16241-08 

+  •08 

260263-44263-46 

—  •02 

260-20260-21 

—  01 

262-15262-09 

+  -07 

280284-48284-52 

•04 

3280-58280-00 

-02 

282-85 

282  •  63 

+  -22 

300305-72305-76 

•04 

301-08301-12 

—  04 

320  S97  •  95  327  •  20 

—  •05 

321-80321  -80 

•00 

340 

349  •  30 

348-88 

+  •42 

434-00 

342-64 

+  •36 

The  formula,  as  we  see  from  the  table,  represents  all  Eegnault's 
curves  with  great  accuracy,  and  if  we  turn  to  his  experimental  results 
we  shall  find  that  the  deviation  is  far  within  the  limits  of  the  experi- 
mental errors.  The  greatest  deviation  happens  at  340°,  and  may  be 
accounted  for  by  an  error  in  drawing  the  curve,  as  there  are  few  experi- 
mental results  so  high  as  this,  and  the  formula  seems  to  agree  with 
them  almost  as  well  as  Regnault's  own  curve. 


3  Corrected  from  280-52  in  Regnault's  table. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


355 


The  object  of  comparing  the  formula  with  Regnault's  results  at 
temperatures  so  much  higher  than  I  need,  is  simply  to  test  the  formula 
through  as  great  a  range  of  temperatures,  and  for  as  many  kinds  of 
glass,  as  possible.  If  it  agrees  reasonably  well  throughout  a  great 
range,  it  will  probably  be  very  accurate  for  a  small  range,  provided 
we  obtain  the  constants  to  represent  that  small  range  the  best. 

Having  obtained  a  formula  to  represent  any  series  of  experiments, 
we  can  hardly  expect  it  to  hold  for  points  outside  our  series,  or  even 
for  interpolating  between  experiments  too  far  apart,  as,  very  often,  a 
small  change  in  one  of  the  constants  may  affect  the  part  we  have  not 
experimented  on  in  a  very  marked  manner.  Thus  in  applying  the 
formula  to  points  between  0°  and  100°  the  value  of  &  will  affect  the 
result  very  much.  In  the  case  of  the  glass  Choisy-le-Eoi  many  values 
of  6  will  satisfy  the  observations  besides  6  =  0.  For  the  ordinary 
glass,  however,  &  is  well  determined,  and  the  formula  is  of  more  value 
between  0°  and  100°. 

The  following  table  gives  the  results  of  the  calculation. 

TABLE  III. — REGNAULT'S  RESULTS  COMPARED  WITH  THE  FORMULA. 


Air 
Thermom- 

Calculated 
a  =  -000  000  32 
b  =  0. 

Calculated 
o  =  -000  000  34 
b  =  245. 

Observed. 

J 

Calculated 
a  =  -000  000  44 

J 

Choisy-le-Koi. 

Verre 
Ordinaire. 

Verre 
Ordinaire. 

Verre 
Ordinaire. 

0 
10 

0 

10-00 

0 
10-07 

0 



0 
10-10 



20 

19-99 

20-12 

20-17 

30 

29-98 

30-15 

30-12 

+  •03 

30-21 

+  •09 

40 

39-97 

40-17 

40-23 

—  •06 

40-23 

0 

50 

49-96 

50-17 

50-23 

—  •06 

50-23 

0 

60 

59  •  95 

60-15 

60-24 

—  •09 

60-21 

—  03 

70 

69-95 

70-12 

70-22 

—  •10 

70-18 

—  04 

80 
90 

79-96 
89-97 

80-09 
90-05 

80-10 

01 

80-11 
90-07 

+  •01 

100 

100 

100 

100 



100 



Kegnault  does  not  seem  to  have  published  any  experiments  on  Choisy- 
le-Roi  glass  between  0°  and  100°,  but  in  the  table  between  pp.  226,  227, 
there  are  some  results  for  ordinary  glass.  The  separate  observations 
do  not  seem  to  have  been  very  good,  but  by  combining  the  total  number 
of  observations  I  have  found  the  results  given  above.  The  numbers  in 
the  fourth  column  are  found  by  taking  the  mean  of  Eegnault's  results 
for  points  as  near  the  given  temperature  as  possible.  The  agreement 


t 

356  HENRY  A.  EOWLAJSTD 

is  only  fair,  but  we  must  remember  that  the  same  specimens  of  glass 
were  not  used  in  this  experiment  as  in  the  others,  and  that  for  these 
specimens  the  agreement  is  also  poor  above  100°.  The  values  a  = 
.000,000,44  and  &  =  260°  are  much  better  for  these  specimens,  and 
the  seventh  column  contains  the  values  calculated  from  these  values. 
These  values  also  satisfy  the  observations  above  100°  for  the  given 
specimens. 

The  table  seems  to  show  that  between  0°  and  100°  a  thermometer  of 
Choisy-le-Eoi  almost  exactly  agrees  with  the  air  thermometer.  But 
this  is  not  at  all  conclusive.  Regnault,  however,  remarks,4  that  be- 
tween 0°  and  100°  thermometers  of  this  glass  agree  more  nearly  with 
the  air  thermometer  than  those  of  ordinary  glass,  though  he  states 
the  difference  to  amount  to  -1  to  -2  of  a  degree,  the  mercurial  ther- 
mometer standing  below  the  air  thermometer.  With  the  exception  of 
this  remark  of  Eegnault's,  no  experiments  have  ever  been  published 
in  which  the  direction  of  the  deviation  was  similar  to  this.  All  ex- 
periments have  found  the  mercurial  thermometer  to  stand  above  the 
air  thermometer  between  0°  and  100°,  and  my  own  experiments  agree 
with  this.  However,  no  general  rule  for  all  kinds  of  glass  can  be 
laid  down. 

Boscha  has  given  an  excellent  study  of  Eegnault's  results  on  this 
subject,  though  I  cannot  agree  with  all  his  conclusions  on  this  subject. 
In  discussing  the  difference  between  0°  and  100°  he  uses  a  formula  of 
the  form 

T— 1=  —  t(lOQ  —  t), 
ct 

and  deduces  from  it  the  erroneous  conclusion  that  the  difference  is 
greatest  at  50°  C.,  instead  of  between  40°  and  50°.  His  results  for 
T  —  t  at  50°  are 

Choisy-le-Eoi    —.22 

Verre  Ordinaire +.25 

Verre  Vert +.14 

Yerre  de-  Suede  +.56 

and  these  are  probably  somewhat  nearly  correct,  except  the  negative 
value  for  Choisy-le-Eoi. 

With  the  exception  of  Eegnault,  very  few  observers  have  taken  up 
this  subject.  Among  these,  however,  we  may  mention  Eecknagel,  who 

4Comptes  Rendus,  Ixix. 


Osr  THE  MECHANICAL  EQUIVALENT  or  HEAT 


357 


has  made  the  determination  for  common  glass  between  0°  and  100°. 
I  have  found  approximately  the  constants  for  my  formula  in  this  case, 
and  have  calculated  the  values  in  the  fourth  column  of  the  following 
table. 

TABLE  IV. — RECKNAGEL'S  RESULTS  COMPARED  WITH  THE  FORMULA. 


Mercurial  Thermometer. 

Air 
Thermometer. 

Difference. 

Observed. 

Calculated. 

0 

0 

0 

0 

10 

10-08 

10-08 

0 

20 

20-14 

20-14 

0 

30 

30-18 

30-18 

0 

40 

40-20 

40-20 

0 

50 

50-20 

50-20 

0 

60 

60-18 

60-18 

0 

70 

70-14 

70-15 

+  •01 

80 

80-10 

80-11 

+  •01 

90 

90-05 

90-06 

+  •01 

100 

100-00 

0 

0 

J=290°,        a  =  .000  000  33, 


It  will  be  seen  that  the  values  of  the  constants  are  not  very  different 
from  those  which  satisfy  Eegnault's  experiments. 

There  seems  to  be  no  doubt,  from  all  the  experiments  we  have  now 
discussed,  that  the  point  of  maximum  difference  is  not  at  50°,  but  at 
some  less  temperature,  as  40°  to  45°,  and  this  agrees  with  my  own 
experiments,  and  a  recent  statement  by  Ellis  in  the  Philosophical 
Magazine.  And  I  think  the  discussion  has  proved  beyond  doubt  that 
the  formula  is  sufficiently  accurate  to  express  the  difference  of  the 
mercurial  and  air  thermometers  throughout  at  least  a  range  of  200°, 
and  hence  is  probably  very  accurate  for  the  range  of  only  100°  between 
0°  and  100°. 

Hence  it  is  only  necessary  to  find  the  constants  for  my  thermometers. 
But  before  doing  this  it  will  be  well  to  see  how  exact  the  comparison 
must  be.  As  the  thermometers  are  to  be  used  in  a  calorimetric  research 
in  which  differences  of  temperature  enter,  the  error  of  the  mercurial 
compared  with  the  air  thermometer  will  be 


=  a  \U'  —  2  (J  + 


358  HENRY  A.  ROWLAND 

which  for  the  constants  used  in  Eecknagel's  table  becomes 

Error  =  d-£-  —  I  =  .000  000  33  1 29000  —  780^  +  3f  \. 
clt 

This  amounts  to  nearly  one  per  cent  at  0°,  and  thence  decreases  to 
45°,  after  which  it  increases  again.  As  only  0°-2  at  the  40°  point 
produces  this  large  error  at  0°,  it  follows  that  an  error  of  only  0°-02 
at  40°  will  produce  an  error  of  y^nro  at  0°.  At  other  points  the  errors 
will  be  less. 

Hence  extreme  care  must  be  taken  in  the  comparison  and  the  most 
accurate  apparatus  must  be  constructed  for  the  purpose. 

2.  DESCRIPTION  OF  APPARATUS 
The  Air  Thermometer 

In  designing  the  apparatus,  I  have  had  in  view  the  production  of 
a  uniform  temperature  combined  with  ease  of  reading  the  thermom- 
eters, which  must  be  totally  immersed  in  the  water.  The  uniformity, 
however,  needed  only  to  apply  to  the  air  thermometer  and  to  the  bulbs 
of  the  mercurial  thermometer,  as  a  slight  variation  in  the  temperature 
of  the  stems  is  of  no  consequence.  A  uniform  temperature  for  the  air 
thermometer  is  important,  because  it  must  take  time  for  a  mass  of  air 
to  heat  up  to  a  given  temperature  within  0°-01  or  less. 

Fig.  1  gives  a  section  of  the  apparatus.  This  consists  of  a  large 
copper  vessel,  nickel-plated  on  the  outside,  with  double  walls  an  inch 
apart,  and  made  in  two  parts,  so  that  it  could  be  put  together  water- 
tight along  the  line  a  &.  As  seen  from  the  dimensions,  it  required 
about  28  kilogrammes  of  water  to  fill  it.  Inside  of  this  was  the  vessel 
mdefghkln,  which  could  be  separated  along  the  line  d Ic.  In  the 
upper  part  of  this  vessel,  a  piston,  q,  worked,  and  could  draw  the  water 
from  the  vessel.  The  top  was  closed  by  a  loose  piece  of  metal,  o  p, 
which  fell  down  and  acted  as  a  valve.  The  bottom  of  this  inner 
vessel  had  a  false  bottom,  c  I,  above  which  was  a  row  of  large  holes ; 
above  these  was  a  perforated  diaphragm,  s.  The  bulb  of  the  air  ther- 
mometer was  at  /,  with  the  bulbs  of  the  mercurial  thermometers  almost 
touching  it.  The  air  thermometer  bulb  was  very  much  elongated,  being 
about  18  cm.  long  and  3  to  5  cm.  in  diameter.  Although  the  bulbs  of 
the  thermometers  were  in  the  inner  vessel,  the  stems  were  in  the 
outer  one,  and  the  reading  was  accomplished  through  the  thick  glass 
window  u  v. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


359 


The  change  of  the  temperature  was  effected  by  means  of  a  Bunsen 
burner  under  the  vessel  w. 

The  working  of  the  apparatus  was  as  follows:  The  temperature 
having  been  raised  to  the  required  point,  the  piston  q  was  worked  to 
stir  up  the  water;  this  it  did  by  drawing  the  water  through  the  holes 


"31 


FIG.  1. 


FIG.  2. 


at  c  I  and  the  perforated  diaphragm  s,  and  thence  up  through  the 
apparatus  to  return  on  the  outside.  When  the  whole  of  the  water  is 
at  a  nearly  uniform  temperature  the  stirring  is  stopped,  the  valve  op 
falls  into  place,  and  the  connection  of  the  water  in  the  outer  and  inner 
vessels  is  practically  closed  as  far  as  currents  are  concerned,  and  be- 
fore the  water  inside  can  cool  a  little  the  outer  water  must  have  cooled 
considerably. 


360  HENKY  A.  EOWLAND 

So  effective  was  this  arrangement  that,  although  some  of  the  ther- 
mometers read  to  0°-007  C.,  yet  they  would  remain  perfectly  stationary 
for  several  minutes,  even  when  at  40°  C.  At  very  high  temperatures, 
such  as  80°  or  90°  C.,  the  burner  was  kept  under  the  vessel  w  all  the 
time,  and  supplied  the  loss  of  the  outer  vessel  by  radiation.  The  inner 
vessel  would  under  these  circumstances  remain  at  a  very  constant  tem- 
perature. The  water  in  the  outer  vessel  never  differed  by  more  than 
a  small  fraction  of  a  degree  from  that  in  the  inner  one. 

To  get  the  0°  and  100°  points  the  upper  parts  of  the  vessel  above 
the  line  a  &  were  removed,  and  ice  placed  around  the  bulb  of  the  air 
thermometer,  and  left  for  several  hours,  until  no  further  lowering  took 
place.  For  the  100°  point  the  copper  vessel  shown  in  Fig.  3  was  used. 
The  portion  y  of  this  vessel  fitted  directly  over  the  bulb  of  the  air 
thermometer.  On  boiling  water  in  x,  the  steam  passed  through  the 
tube  to  the  air  thermometer.  It  is  with  considerable  difficulty  that 
the  100°  point  is  accurately  reached,  and,  unless  care  be  taken,  the 
bulb  will  be  at  a  slightly  lower  temperature.  Not  only  must  the  bulb  be 
in  the  steam,  but  the  walls  of  the  cavity  must  also  be  at  100°.  To 
accomplish  this  in  this  case,  a  large  mass  of  cloth  was  heaped  over  the 
instrument,  and  then  the  water  in  x  vigorously  boiled  for  an  hour  or  so. 
After  fifteen  minutes  there  was  generally  no  perceptible  increase  of 
temperature,  though  an  hour  was  allowed  so  as  to  make  certain. 

The  external  appearance  of  the  apparatus  is  seen  in  Fig.  2.  The 
method  of  measuring  the  pressure  was  in  some  respects  similar  to  that 
used  in  the  air  thermometer  of  Jolly,  except  that  the  reading  was  taken 
by  a  cathetometer  rather  than  by  a  scale  on  a  mirror.  The  capillary 
stem  of  the  air  thermometer  leaves  the  water  vessel  at  a,  and  passes 
to  the  tube  &,  which  is  joined  to  the  three-way  cock  c.  The  lower  part 
of  the  cock  is  joined  by  a  rubber  tube  to  another  glass  tube  at  d,  which 
can  be  raised  and  lowered  to  any  extent,  and  has  also  a  fine  adjustment. 
These  tubes  were  about  1-5  cm.  diameter  on  the  inside,  so  that  there 
should  be  little  or  no  error  from  capillarity.  Both  tubes  were  exactly 
of  the  same  size,  and  for  a  similar  reason. 

The  three-way  cock  is  used  to  fill  the  apparatus  with  dry  air,  and 
also  to  determine  the  capacity  of  the  tube  above  a  given  mark.  In 
filling  the  bulb,  the  air  was  pumped  out  about  twenty  times,  and 
allowed  to  enter  through  tubes  containing  chloride  of  calcium,  sulphuric 
acid,  and  caustic  soda,  so  as  to  absorb  the  water  and  the  carbonic  acid. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


361 


The  Cathetometer 

The  cathetometer  was  one  made  by  Meyerstein,  and  was  selected 
because  of  the  form  of  slide  used.  The  support  was  round,  and  the 
telescope  was  attached  to  a  sleeve  which  exactly  fitted  the  support. 
The  greatest  error  of  cathetometers  arises  from  the  upright  support 
not  being  exactly  true,  so  that  the  telescope  will  not  remain  in  level 
at  all  heights.  It  is  true  that  the  level  should  be  constantly  adjusted, 
but  it  is  also  true  that  an  instrument  can  be  made  where  such  an  ad- 
justment is  not  necessary.  And  where  time  is  an  element  in  the 
accuracy,  such  an  instrument  should  be  used.  In  the  present  case  it 
was  absolutely  necessary  to  read  as  quickly  as  possible,  so  as  not  to 


FIG.  3. 


leave  time  for  the  column  to  change.  In  the  first  place  the  round 
column,  when  made,  was  turned  in  a  lathe  to  nearly  its  final  dimen- 
sions. The  line  joining  the  centres  of  the  sections  must  then  have 
been. very  accurately  straight.  In  the  subsequent  fitting  some  slight 
irregularities  must  have  been  introduced,  but  they  could  not  have  been 
great  with  good  workmanship.5  The  upright  column  was  fixed,  and 
the  telescope  moved  around  it  by  a  sleeve  on  the  other  sleeve.  Where 
the  objects  to  be  measured  are  not  situated  at  a  very  wide  angle  from 
each  other,  this  is  a  good  arrangement,  and  has  the  advantage  that  any 
side  of  the  column  can  be  turned  toward  the  object,  and  so,  even  if  it 

4  The  change  of  level  along  the  portion  generally  used  did  not  amount  to  more 
than  -1  of  a  division,  or  about  -Olmm.  at  the  mercury  column,  as  this  is  about  the 
smallest  quantity  which  could  be  observed  on  the  level. 


362  HENRY  A.  ROWLAND 

were  crooked,  we  could  yet  turn  it  into  such  a  position  as  to  nearly 
eliminate  error. 

It  was  used  at  a  distance  of  about  110  cm.  from  the  object,  and  no 
difficulty  was  found  after  practice  in  setting  it  on  the  column  to  j\  mm. 
at  least.  The  cross  hairs  made  an  angle  of  45°  with  the  horizontal,  as 
this  was  found  to  be  the  most  sensitive  arrangement. 

The  scale  was  carefully  calibrated,  and  the  relative  errors  c  for  the 
portion  used  were  determined  for  every  centimeter,  the  portion  of  the 
scale  between  the  0°  and  100°  points  of  the  air  thermometer  being 
assumed  correct.  There  is  no  object  in  determining  the  absolute  value 
of  the  scale,  but  it  should  agree  reasonably  well  with  that  on  the 
barometer;  for  let  H0,  Ht,  and  H1QO  be  the  readings  of  the  barometer, 
and  Ti0,  ht,  and  /t100  the  readings  of  the  cathetometer  at  the  temperatures 
denoted  by  the  subscript.  Then  approximately 


(.#100  +  /?100)  —  (fft>  +  ^o)        ^100  —  HQ  +  hlw  —  A0 

As  the  height  of  the  barometer  varies  only  very  slightly  during  an 
experiment,  the  value  of  this  expression  is  very  nearly 


"100  "0 

which  does  not  depend  on  the  absolute  value  of  the  scale  divisions. 

But  the  best  manner  of  testing  a  cathetometer  is  to  take  readings 
upon  an  accurate  scale  placed  near  the  mercury  columns  to  be  meas- 
ured. I  tried  this  with  my  instrument,  and  found  that  it  agreed  with 
the  scale  to  within  two  or  three  one-hundredths  of  a  millimeter,  which 
was  as  near  as  I  could  read  on  such  an  object. 

In  conclusion,  every  care  was  taken  to  eliminate  the  errors  of  this 
instrument,  as  the  possibility  of  such  errors  was  constantly  present  in 
my  mind;  and  it  is  supposed  that  the  instrumental  errors  did  not 
amount  to  more  than  one  or  two  one-hundredths  of  a  millimeter  on  the 
mercury  column.  The  proof  of  this  will  be  shown  in  the  results 
obtained. 

The  Barometer 

This  was  of  the  form  designed  by  Fortin,  and  was  made  by  James 
Green  of  New  York.  The  tube  was  2-0  cm.  diameter  nearly  on  the 
outside,  and  about  1-7  cm.  on  the  inside.  The  correction  for  capillarity 
is  therefore  almost  inappreciable,  especially  as,  when  it  remains  con- 

6  These  amounted  to  less  than  -016mm.  at  any  part. 


Ox  THE  MECHAXICAL  EQUIVALENT  OF  HEAT  3f>3 

stant,  it  is  exactly  eliminated  from  the  equation.  The  depression  for 
this  diameter  is  about  -08  mm.,  but  depends  upon  the  height  of  the 
meniscus.  The  height  of  the  meniscus  was  generally  about  1-3  mm.; 
but  according  as  it  was  a  rising  or  falling  meniscus,  it  varied  from 
1-4  to  1-2  mm.  These  are  the  practical  values  of  the  variation,  and 
would  have  been  greater  if  the  barometer  had  not  been  attached  to  the 
wall  a  little  loosely,  so  as  to  have  a  slight  motion  when  handled.  Also 
in  use  the  instrument  was  slightly  tapped  before  reading.  The  varia- 
tion of  the  height  of  the  meniscus  from  1-2  to  1-4  mm.  would  affect 
the  reading  only  to  the  extent  of  -01  to  -02  mm. 

The  only  case  where  any  correction  for  capillarity  is  needed  is  in 
finding  the  temperatures  of  the  steam  at  the  100°  point,  and  will  then 
affect  that  temperature  only  to  the  extent  of  about  0°-005. 

The  scale  of  the  instrument  was  very  nearly  standard  at  0°  C.,  and 
was  on  brass. 

At  the  centre  of  the  brass  tube  which  surrounded  the  barometer,  a 
thermometer  was  fixed,  the  bulb  being  surrounded  by  brass,  and  there- 
fore indicating  the  temperature  of  the  brass  tube. 

In  order  that  it  should  also  indicate  the  temperature  of  the  barome- 
ter, the  whole  tube  and  thermometer  were  wrapped  in  cloth  until  a 
thickness  of  about  5  or  6  cm.  was  laid  over  the  tube,  a  portion  being 
displaced  to  read  the  thermometers.  This  wrapping  of  the  barometer 
was  very  important,  and  only  poor  results  were  obtained  before  its 
use;  and  this  is  seen  from  the  fact  that  1°  on  the  thermometer  indi- 
cates a  correction  of  -12  mm.  on  the  barometer,  and  hence  makes  a 
difference  of  0°-04  on  the  air  thermometer. 

As  this  is  one  of  the  most  important  sources  of  error,  I  have  now 
devised  means  of  almost  entirely  eliminating  it,  and  making  continual 
reading  of  the  barometer  unnecessary.  This  I  intend  doing  by  an 
artificial  atmosphere,  consisting  of  a  large  vessel  of  air  in  ice,  and 
attached  to  the  open  tube  of  the  manometer  of  the  air  thermometer. 

The  Thermometers 

The  standard  thermometers  used  in  my  experiments  are  given  in 
the  following  table  on  the  next  page. 

The  calibration  of  the  first  four  thermometers  has  been  described. 
The  calibration  of  the  Kew  standard  was  almost  perfect,  and  no  cor- 
rection was  thought  necessary.  The  scale  divided  on  the  tube  was  to 
half-degrees  Fahrenheit;  but  as  the  32°  and  212°  points  were  not  cor- 
rect, it  was  in  practice  used  as  a  thermometer  with  arbitrary  divisions. 


364 


HEXKY  A.  EOWLAND 


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ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


365 


The  interval  between  the  0°  and  100°  points,  as  Welsh  found  it,  was 
180° -12,  usinff  barometer  at  30  inches,  or  180° -05  as  corrected  to 
760  mm.  of  mercury.8  At  the  present  time  it  is  179° -68,*  showing  a 
change  of  1  part  in  486  in  twenty-five  years.  This  fact  shows  that 
the  ordinary  method  of  correcting  for  change  of  zero  is  not  correct,  and 
that  the  coefficient  of  expansion  of  glass  changes  with  time.10 

I  have  not  been  able  to  find  any  reference  to  the  kind  of  glass  used 
in  this  thermometer.     But  in  a  report  by  Mr.  Welsh  we  find  a  com- 

TABLE  VI. — COMPARISON  BY  WELSH,  1852. 


Mean  of 
Kew  Standards 
Nos.  4  and  14. 

Fastr6  231, 
Regnault. 

J 
Kew. 

Troughton  and 
Simms 
(Royal  Society). 

A 

Kew. 

32°00 

32°00                    0 

32°00                    0 

38-71 

38-72                +-01 

38-70 

—  •01 

45-04 

45-03 

01 

45-03 

—  •01 

49-96 

49-96 

•00 

49-96 

•00 

55-34 

55-37 

+  •03 

55-34 

•00 

60-07 

60-05 

—  •02 

60-06 

—  •01 

65-39 

65-41 

+  •02 

65-36 

—  •03 

69-93 

69-95 

+  •02 

69-93 

•00 

74-69 

74-69           |          -00 

74-72 

+  •03 

80-05 

80-06 

+  •01 

80-14 

+  •09 

85-30 

85-33 

+  •03 

85-44 

+  •14 

90-50 

90-51 

+  •01 

90-56 

+  •06 

95-26 

95-24 

—  •02 

95-40 

+  •14 

101-77 

101-77 

•00 

101-94 

+  •15 

109-16 

109-15               —-01 

109-25 

+  •08 

212-00 

212-00 

•00 

212-00 

•00 

parison,  made  on  March  19,  1852,  of  some  of  his  thermometers  with 
two  other  thermometers, — one  by  Fastre,  examined  and  approved  by 
Eegnault,  and  the  other  by  Troughton  and  Simms.  The  thermometer 
which  I  used  was  made  a  little  more  than  a  year  after  this;  and  it  is 

8  Boiling  point,       "Welsh,        Aug.  17,  1853,     212° -17;  barometer    30  in. 
Freezing  point,          "  "  "          32° -05. 

Boiling  point,     Rowland,     June  22,  1878,     212° -46;  barometer  760  mm. 
Freezing  point,  «  "  "  32°-78. 

The  freezing  point  was  taken  before  the  boiling  point  in  either  case. 
9 179° -70,  as  determined  again  in  January,  1879. 

10  The  increase  shown  here  is  1  in  80  nearly  !  It  is  evidently  connected  with  the 
change  of  zero ;  for  when  glass  has  been  heated  to  100°,  the  mean  coefficient  of  ex- 
pansion between  0  and  100°  often  changes  as  much  as  1  in  50.  Hence  it  is  not 
strange  that  it  should  change  1  in  80  in  twenty-five  years.  I  believe  this  fact  has 
been  noticed  in  the  case  of  standards  of  length. 


366  HENRY  A.  ROWLAND 

reasonable  to  suppose  that  the  glass  was  from  the  same  source  as  the 
standards  Nos.  4  and  14  there  used.  We  also  know  that  Regnault  was 
consulted  as  to  the  methods,  and  that  the  apparatus  for  calibration 
was  obtained  under  his  direction. 

I  reproduce  the  table  on  preceding  page  with  some  alterations,  the 
principal  one  of  which  is  the  correction  of  the  Troughton  and  Simms 
thermometers,  so  as  to  read  correctly  at  32°  and  212°,  the  calibration 
being  assumed  correct,  but  the  divisions  arbitrary. 

It  is  seen  that  the  Kew  standards  and  the  Fastre  agree  perfectly,  but 
that  the  Troughton  and  Simms  standard  stands  above  the  Kew  ther- 
mometers at  100°  F. 

The  Geissler  standard  was  made  by  Geissler  of  Bonn,  and  its  scale 
was  on  a  piece  of  milk  glass,  enclosed  in  a  tube  with  the  stem.  The 
calibration  was  fair,  the  greatest  error  being  about  0°-015  C.,  at  50°  C.; 
but  no  correction  for  calibration  was  made,  as  the  instrument  was  only 
used  as  a  check  for  the  other  thermometers. 

3.  EESULTS  OF  COMPARISON 
Calculation  of  Air  Thermometw 

This  has  already  been  described,  and  it  only  remains  to  discuss  the 
formula  and  constants,  and  the  accuracy  with  which  the  different, 
quantities  must  be  known. 

The  well-known  formula  for  the  air  thermometer  is 

ff-ft+4 

m _J 


*  V 


i 

-  fl 


V\    'l  +  a?       "1  +  0*  J 

Solving  with  reference1  to  T,  and  placing  in  a  more  convenient  form, 
we  have 

H-h'  +   *H-.—, 


T=  -    -  _  nearlv, 

a  A'      «     _L_  __*_ 
v 

where  '  — 


and  r  =  a  —  £=  -00364. 

For  the  first  bulb,  v 

For  the  second  bulb,  v_ 

V 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


367 


To  discuss  the  error  of  T  due  to  errors  in  the  constants,  we  must 
replace  «  by  its  experimental  value,  seeing  that  it  was  determined 
with  the  same  apparatus  as  that  by  which  T  was  found.  As  it  does 
not  change  very  much,  we  may  write  approximately 


^=100 


H—  h 


I     /Hloo  —  H\_bmHlw-bH\ 


~m-rt\ 


From  this  formula  we  can  obtain  by  differentiation  the  error  in 
each  of  the  quantities,  which  would  make  an  error  of  one-tenth  of 
one  per  cent  in  T.  The  values  are  for  T  =  400  nearly;  £  =  20°; 
H  wo  —  h  =  270  mm.  ;  and  h  =  750  mm.  If  x  is  the  variable, 

,    dx   *rp dx      T      _  04  dx 

~~dT         ~oTT  1000  ~        ~dT ' 

TABLE  VII. — ERRORS  PRODUCING  AN  ERROR  IN  T  OF  1  IN  1000  AT  40°  C. 


foinn 

ft 

bioo 

bioo-b 

H. 

f/ioo  or  h. 

JL 

a 

a 

a 

a 

' 

7> 

Jhnn           i      .     OinnrO         _4,   A 

bioo    „ 

a 

a             sani. 

a 

Absolute 

value, 

•llmm. 

•27  mm. 

•005 

•00074 

•00087 

•0047 

•00087 

Ax 

Relative 

value, 

0-9 

•10 

•12 

•62 

Ax 

X 

From  this  table  it  would  seem  that  there  should  be  no  difficulty  in 
determining  the  40°  point  on  the  air  thermometer  to  at  least  1  in  2000; 
and  experience  has  justified  this  result.  The  principal  difficulty  is  in 
the  determination  of  H,  seeing  that  this  includes  errors  in  reading  the 
barometer  as  well  as  the  cathetometer.  For  this  reason,  as  mentioned 
before,  I  have  designed  another  instrument  for  future  use,  in  which 
the  barometer  is  nearly  dispensed  with  by  use  of  an  artificial  atmos- 
phere of  constant  pressure. 

The  value  of  -^.does  not  seem  to  affect  the  result  to  any  great  extent; 

and  if  it  was  omitted  altogether,  the  error  would  be  only  about  1  in 
1000,  assuming  that  the  temperature  t  was  the  same  at  the  determina- 
tion of  the  zero  point,  the  40°  point,  and  the  100°  point.  It  seldom 
varied  much. 

The  coefficient  of  expansion  of  the  glass  influences  the  result  very 
slightly,  especially  if  we  know  the  difference  of  the  mean  coefficients 


368 


HENRY  A.  ROWLAND 


between  0°  and  100°,  and  say  — 10°  and  -f  10°.  This  difference  I  at 
first  determined  from  Regnault's  tables,  but  afterwards  made  a  deter- 
mination of  it,  and  have  applied  the  correction.11 

The  table  given  by  Regnault  is  for  one  specimen  of  glass  only;  and 
I  sought  to  better  it  by  taking  the  expansion  at  100°  from  the  mean 
of  the  five  specimens  given  by  Regnault  on  p.  231  of  the  first  volume 
of  his  Relation  des  Experiences,  and  reducing  the  numbers  on  page  237 
in  the  same  proportion.  I  thus  found  the  values  given  in  the  second 
column  of  the  following  table. 

TABLE  VIII. — COEFFICIENT    OF   EXPANSION   OF    THE    GLASS   OF    THE   AIR  THER- 
MOMETER, ACCORDING  TO  THE  AIR  THERMOMETER. 


Tempera- 
ture ac- 
cording to 
Air  Ther- 
mometer. 

Values  of  b 
used  for  a  first 
Calculation. 

b  from 
Regnault's 
Table, 
Glass  No.  5. 

Experimental  Results. 

Apparent 
Coefficient  of 
Expansion  of 
Mercury. 

5,  using 
Regnault's 
Value  for 
Mercury.12 

ft,  using 
Recknagel's 
Value  for 
Mercury.13 

b,  using 
Wttllner's 
Value  for 
Mercury.14 

0 
20° 
40° 
60° 
80° 
100° 

•0000252 
•0000253 
•0000256 
•0000259 
•  0000262 
•0000264 

•  0000263 
•0000264 
•0000267 
•  0000270 
•  0000273 
•0000276 

•00015410 
•00015395 
•00015391 

•0000254 
•0000258 
•0000261 

.0000264 
•0000266 
•0000267 

•0000273 
•0000276 
•0000278 

•00015381 

•0000277 

.0000277 

•0000287 

The  second  column  contains  the  values  which  I  have  used,  and  one 
of  the  last  three  columns  contains  my  experimental  results,  the  last 
being  probably  the  best.  The  errors  by  the  use  of  the  second  column 
compared  with  the  last  are  as  follows: — 

TTiinrfrom  using  &100  — 640  =  -0000008  instead  of  -0000011; 
TD3rjr  from  using  &100  =  -0000264  instead  of  -0000287; 

or,  ^Vrr  for  both  together. 

As  the  error  is  so  small,  I  have  not  thought  it  worth  while  to  entirely 
recalculate  the  tables,  but  have  calculated  a  table  of  corrections  (see 
opposite  page),  and  have  so  corrected  them. 

11  This  was  determined  by  means  of  a  large  weight  thermometer  in  which  the  mer- 
cury had  been  carefully  boiled.     The  glass  was  from  the  same  tube  as  that  of  the  air 
thermometer,  and  they  were  cut  from  it  within  a  few  inches  of  each  other. 

12  Relations  des  Experiences,  i,  328. 
13 Fogg.  Ann.,  cxiii,  135. 
"Experimental  Physik,  Wiillner,  i,  67. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


369 


T=  T  {1  +  373  (b(w  -  M  -  (273+  T}(V  -  b)\, 
T=  T'  {I  —  .000858  +  (273+7v)(&  —  b')\t 

T=  -99975  T  approximately  between  0  and  40°.  The  last  is  true 
within  less  than  -j-gVir  °f  a  degree. 

The  two  bulbs  of  the  air  thermometer  used  were  from  the  same  piece 
of  glass  tubing,  and  consequently  had  nearly,  if  not  quite,  the  same 
coefficient  of  expansion. 

In  the  reduction  of  the  barometer  and  other  mercurial  columns  to 
zero,  the  coefficient  -000162  was  used,  seeing  that  all  the  scales  were 
of  brass. 

In  the  tables  the  readings  of  the  thermometers  are  reduced  to 
volumes  of  the  tube  from  the  tables  of  calibration,  and  they  are  cor- 
rected for  the  pressure  of  water,  which  increased  their  reading,  except 
at  0°,  by  about  0°-01C. 

TABLE  IX. — TABLE  OF  CORRECTIONS. 


T 

T 

Correction. 

Calculated 
Temperature. 

Corrected 
Temperature. 

0 

0 

0 

0 

0 

10 

9-9971 

—  •0029 

20 

19-9946 

—  •0054 

30 

29-9924 

0076 

40 

39-9907 

—  •0093 

50 

49-9894 

—  0106 

60 

59-9865 

—  •0135 

80 

79-9880 

—  •0120 

100 

100- 

0 

The  order  of  the  readings  was  as  follows  in  each  observation: — 1st, 
barometer;  2d,  cathetometer;  3d,  thermometers  forward  and  backward; 
4th,  cathetometer;  5th,  barometer,  &c., — repeating  the  same  once  or 
twice  at  each  temperature.  In  the  later  observations,  two  series  like 
the  above  were  taken,  and  the  water  stirred  between  them. 

The  following  results  were  obtained  at  various  times  for  the  value  of 
a  with  the  first  bulb : — 

•0036664 

•0036670 

•0036658 

•0036664 

•0036676 


Mean  a  =  -00366664 


24 


370 


HEXRY  A.  KOWLAXD 


obtained  by  using  the  coefficient-  of  expansion  of  glass  -0000264:  at 
100°,  or  a—  -0036698,  using  the  coefficient  -0000287. 

The  thermometers  Nos.  6163,  6165,  6166,  were  always  taken  out  of 
the  bath  when  the  temperature  of  40°  was  reached,  except  on  Novem- 
ber 14,  when  they  remained  in  throughout  the  whole  experiment. 

The  thermometer  readings  are  reduced  to  volumes  by  the  tables  of 
calibration. 

TABLE  X.— IST  SERIES,  Nov.  14,  1877. 


Relative 
Weight. 

Air 
Thermometer. 

V 
6163. 

V 
6166. 

V 

6167. 

Temperature 
by  6167. 

J 

4 

0 

115-33 

21-25 

6-147 

0 

0 

4 

17°  -1425 

422-84 

255-80 

15-685 

17°-661 

•236 

4 

23°  -793 

534-71 

341   05 

19-157 

24°  -089 

•296 

5 

30°  -582 

653-49 

431-71 

22-833 

30°  •  896 

•314 

2 

38°  -569 

793  •  1  8 

•47-175 

3  8°  -93  5 

•366 

2 

51°  -040 

33-864 

51°  -320 

•280 

4 

59°  -137 

38-256 

59°  -452 

•315 

The  first  four  series,  Tables  X  to  XIII,  were  made  with  one  bulb 
to  the  air  thermometer.     A  new  bulb  was  now  made,  whose  capacity 

was  192-0  c.  cm.,  that  of  the  old  being  201-98  c.  cm.     The  value  of   L. 


for  the  new  bulb  was  -0058. 
follows : — 

June  8th 
June  22d 
June  25th 

]\Iean 


The  values  of  li'  and  a  were  obtained  as 


•00366790 
•00366977 
•00366779 

•0036685 


ft' 

753-876 
753-805 
753-837 

753-84 


This  value  of  «  is  calculated  with  the  old  coefficient  for  glass.     The 
new  would  have  given  -0036717. 

It  now  remains  to  determine  from  these  experiments  the  most  prob- 
able values  of  the  constants  in  the  formula,  comparing  the  air  with 
the  mercurial  thermometer.  The  formula  is,  as  we  have  found, 

but  I  have  generally  used  it  in  the  following  form: 

t=CV-f0  —  mt  (100  —  /)  (1  —  n  (100  -f  #)) , 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


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376  HENET  A.  EOWLAND 

And  the  following  relations  hold  among  the  constants : 

C  =  G'  (1  +  m  (60  —  8400  »)) ,  nearly , 
a  =  mn, 

b  =  ~— 100°, 
n 

T=CV—t9, 
i  —t  ® 

*t  —  l  o  n' ' 

In  these  formulae  t  is  the  temperature  on  the  air  thermometer;  V  is 
the  volume  of  the  stem  of  the  mercurial  thermometer,  as  determined 
from  the  calibration  and  measured  from  any  arbitrary  point;  and  C", 
f  0,  m,  and  n  are  constants  to  be  determined. 

The  best  way  of  finding  these  is  by  the  method  of  least  squares. 
C"  must  be  found  very  exactly;  t0  is  only  to  be  eliminated  from  the 
equations;  m  must  be  found  within  say  ten  per  cent,  and  n  need  only 
be  determined  roughly.  To  find  them  only  within  these  limits  is  a 
very  difficult  matter. 

Determination  of  n 

As  this  constant  needs  a  wide  range  of  temperatures  to  produce  much 
effect,  it  can  only  be  determined  from  thermometer  No.  6167,  which 
was  of  the  same  glass  as  6163,  6165,  and  6166.  It  is  unfortunate  that 
it  was  broken  on  November  21,  and  so  we  only  have  the  experiments 
of  the  first  and  second  series.  From  these  I  have  found  w  =  -003 
nearly.  This  makes  b  =  233°,  which  is  not  very  far  from  the  values 
found  before  from  experiments  above  100°  by  Eegnault  on  ordinary 
glass." 

Determination  of  C  and  m 

I  shall  first  discuss  the  determination  of  these  for  thermometers 
Nos.  6163,  6165,  and  6166,  as  these  were  the  principal  ones  used. 

As  No.  6163  extended  from  0°  to  40°,  and  the  others  only  from 
0°  to  30°,  it  was  thought  best  to  determine  the  constants  for  this  one 
first,  and  then  find  those  for  6165  and  6166  by  comparison.  As  this 
comparison  is  deduced  from  the  same  experiments  as  those  from  which 
we  determine  the  constants  of  6163,  very  nearly  the  same  result  is 

15  Some  experiments  with  Baudin  thermometers  at  high  temperatures  have  given 
me  about  240°, — a  remarkable  agreement,  as  the  point  must  be  uncertain  to  10°  or 
more. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  377 

found  as  if  we  obtained  the  constants  directly  by  comparison  with  the 
air  thermometer. 

The  constants  of  6163  can  be  found  either  by  comparison  with  6167, 
or  by  direct  comparison  with  the  air  thermometer.  I  shall  first  deter- 
mine the  constants  for  No.  6167. 

The  constants  C  and  t0  for  this  thermometer  were  found  directly 
by  observation  of  the  0°  and  100°  points;  and  we  might  assume  these, 
and  so  seek  only  for  m.  In  other  words,  we  might  seek  only  to  ex- 
press the  difference  of  the  thermometers  from  the  air  thermometer 
by  a  formula.  But  this  is  evidently  incorrect,  seeing  that  we  thus 
give  an  infinite  weight  to  the  observations  at  the  0°  and  100°  points. 
The  true  way  is  obviously  to  form  an  equation  for  each  temperature, 
giving  each  its  proper  weight.  Thus  from  the  first  series  we  find  for 
No.  6167,— 

Weight.  Equations  of  Condition. 

4  0       =   6-147  C  —  t0, 

4  17° -427  =  15-685  C  — 10  —  930m, 

4  23°-793  =  19-157  C  —  t0  —  1140m, 
&c.  &c.  &c. 

5  100°       =60-156  C  —  t0, 

which  can  be  solved  by  the  method  of  least  squares.  As  t0  is  unim- 
portant, we  simply  eliminate  it  from  the  equations.  I  have  thus 
found, — 

Weight. 

1  Nov.  14  (7  =  1-85171         m=  -000217 

2  Nov.  20, 21         (7  =  1-85127         m= -000172 


Mean  0  =  1-85142         m= -000187 

The  difference  in  the  values  of  m  is  due  to  the  observations  not  being 
so  good  as  were  afterwards  obtained.  However,  the  difference  only 
signifies  about  0°-03  difference  from  the  mean  at  the  50°  point.  After 
November  20  the  errors  are  seldom  half  of  this,  on  account  of  the 
greater  experience  gained  in  observation. 

The  ratio  of  C  for  6167  and  6163  is  found  in  the  same  way. 

Weight. 

1  Nov.  14       -0310091 

2  Nov.  20        -0309846 

Mean        -0309928 


378  HENRY  A.  BOWLAND 

Hence  for  6163  we  have  in  this  way 

C  =  -057381  C"  =  -056995  m  =  -000187. 

By  direct  comparison  of  No.  6163  with  the  air  thermometer.,  we  find 
the  following: 

m. 

•000239 
•000166 
•000226 
•000155 
•000071 
.000115 


Date. 

Weight. 

C'. 

Nov.  14 

1 

•056920 

Nov.  20 

2 

•056985 

Jan.  25 

3 

•056986 

Feb.  11 

4 

•056997 

June    8 

3 

•056961 

June  22 

2 

•056959 

Mean  -056976  ±  -000004  -000154  ±  -000010 

The  values  of  C"  agree  with  each  other  with  great  exactness,  and 
the  probable  error  is  only  ±0-°003  C.  at  the  40°  point. 

The  great  differences  in  the  values  of  m,  when  we  estimate  exactly 
what  they  mean  in  degrees,  also  show  great  exactness  in  the  experi- 
ments. The  mean  value  of  m  indicates  a  difference  of  only  0°-05 
between  the  mercurial  and  air  thermometer  at  the  20°  point,  the  0° 
and  40°  points  coinciding.  The  probable  error  of  m  in  degrees  is  only 
±0°.003C. 

There  is  one  more  method  of  finding  m  from  these  experiments;  and 
that  is  by  comparing  the  values  of  C'  with  No.  6167,  the  glass  of  6167 
being  supposed  to  be  the  same  as  that  of  6163. 

We  have  the  formula 

C  =  C"(l  +  34-8??i). 

Hence 

C—C' 


m  = 


3i-SC' 


We  thus  obtain  the  following  results: 


Date. 

Weight. 

Value  of  m 

Nov.  14 

1 

•000236 

Nov.  20 

2 

•000218 

Jan.  25 

3 

•000217 

Feb.  11 

4 

•000197 

June    8 

3 

•000215 

June  22 

2 

•000216 

Mean         -000213 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  379 

The  results  for  m  are  then  as  follows : 

From  direct  comparison  of  Xo.  6167  with  the  air  thermometer  -000187 
From  direct  comparison  of  Xo.  G163  with  the  air  thermometer  -000154 
From  comparison  of  Xo.  6163  with  Xo.  6167  -000213 

The  first  and  last  are  undoubtedly  the  most  exact  numerically,  but 
they  apply  to  Xo.  6167,  and  are  also,  especially  the  first,  derived  from 
somewhat  higher  temperatures  than  the  20°  point,  where  the  correc- 
tion is  the  most  important.  The  value  of  m,  as  determined  in  either 
of  these  ways,  depends  upon  the  determination  of  a  difference  of  tem- 
perature amounting  to  0°-30,  and  hence  should  be  quite  exact. 

The  value  of  m,  as  obtained  from  the  direct  comparison  of  Xo.  6163 
with  the  air  thermometer,  depends  upon  the  determination  of  a  differ- 
ence of  about  0°-05  between  the  mercurial  and  the  air  thermometer. 
At  the  same  time,  the  comparison  is  direct,  the  temperatures  are  the 
same  as  we  wish  to  use,  and  the  glass  is  the  same.  I  have  combined 
the  results  as  follows: 

m  from  Xo.  6167  -000200 

m  from  Xo.  6163  -000154 


Mean  •  00018  1§ 

It  now  remains  to  deduce  from  the  tables  the  ratios  of  the  constants 
for  the  different  thermometers. 

The  proper  method  of  forming  the  equations  of  condition  are  as 
follows,  applying  the  method  to  the  first  series : 

Weight. 

4  21-25  Cllt  =  115-33  C l  —  i\ 

4  255-80  Cllt  =  422-84  C,  —  r, 

4  34 1  -05  Cllt  =  534-71  Ct  —  r. 

5  431-71  Cllt  =  653-49  Ct  — i\ 

where  (?„,  is  the  constant  for  Xo.  6166,  C,  is  that  for  Xo.  6163,  and 
r0  is  a  constant  to  be  eliminated.     Dividing  by  Clt  the  equations  can 

be  solved  for  £jw.     The  following  table  gives  the  results : 
"t 

16  See  Appendix  to  Thermometry,  where  it  is  finally  thought  best  to  reject  the 
value  from  No.  6167  altogether. 


380 


HENEY  A.  EOWLAND 


TABLE  XVI.— RATIOS  OF  CONSTANTS. 


Date. 

Weight. 

6163 

6167 

6166 

6167 

6166 
6163 

6165 
6163 

6165 
6166 

Nov.    14 
Nov.    20 
Jan.     25 
Feb.     11 
June      8 
June    22 

1 
2 
3 
4 
3 
2 

•031009 
•030985 

•040658 
•  040670 

1-3111 
1-3128 
1-3122 
1-3115 
1-3108 
1-3122 

8-0588 
8-0605 
8-0588 

6-1449 
6-1469 
6-1428 

Mean 

.030993 
±.00005 

.040666 
±  •  000003 

1.31175 
±   -0004 

8  .  0594 
±    .0002 

6.1451 
±.0004 

From  these  we  have  the  following,  as  the  final  most  probable  results : 

Cn  =  8-0601  Clt 
<7,,,  =  1-31175  0,, 

C,    =    -031003  <7iv, 
£„  =    -24991  <7iv, 
0,,,=    -040661  0IT, 

of  which  the  last  three  are  only  used  to  calculate  the  temperatures  on 
the  mercurial  thermometer,  and  hence  are  of  little  importance  in  the 
remainder  of  this  paper. 

The  value  of  C'  which  we  have  found  for  the  old  value  of  the  coeffi- 
cient of  expansion  of  glass  was 

C'  =  -056976; 

and  hence,  corrected  to  the  new  coefficient,  it  is,  as  I  have  shown, 

C,    =.056962. 
Hence,  G n  =  '45912  , 

<7y//  = -074720. 

And  we  have  finally  the  three  following  equations  to  reduce  the  ther- 
mometers to  temperatures  on  the  air  thermometer: 

Thermometer  No.  5163: 
T  =  -056962  V  — 1'0  —  -00018  T  (40  —  T)  (1  —  -003  (T  -f  40)). 

Thermometer  "No.  6165: 
T=  -45912  V"  —  V  — -00018  T  (T  —  40)  (1  —  -003  (T  +  40)). 

Thermometer  No.  6166: 
T=  -074720  V'"  —  V"— ' 00018  T  (T  —  40)  (1  — -003  (T+40)); 

where  V,  V" ',  and  V"  are  the  volumes  of  the  tube  obtained  by  cali- 
bration; t0',  t0",  and  t0"f  are  constants  depending  on  the  zero  point,  and 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  381 

of  little  importance  where  a  difference  of  temperature  is  to  be  meas- 
ured; and  T  is  the  temperature  on  the  air  thermometer. 

On  the  mercurial  thermometer,  using  the  0°  and  100°  points  as  fixed, 
we  have  the  following  by  comparison  with  No.  6167: 

Thermometer  No.  6163;  £=  -057400  V  —  t0; 
Thermometer  No.  6165;  £=  -46265  V  —  10; 
Thermometer  No.  6166;  £=  -075281  V  —  10. 

The  Kew  Standard 

The  Kew  standard  must  be  treated  separately  from  the  above,  as  the 
glass  is  not  the  same.  This  thermometer  has  been  treated  as  if  its 
scale  was  arbitrary. 

In  order  to  have  variety,  I  have  merely  plotted  all  the  results  with 
this  thermometer,  including  those  given  in  the  Appendix,  and  drawn 
a  curve  through  them.  Owing  to  the  thermometer  being  only  divided 
to  -J°  F.,  the  readings  could  not  be  taken  with  great  accuracy,  and  so 
the  results  are  not  very  accordant;  but  I  have  done  the  best  I  could, 
and  the  result  probably  represents  the  correction  to  at  least  0°-02  or 
0°-03  at  every  point. 

(d)  Reduction  to  the  Absolute  Scale 

The  correction  to  the  air  thermometer  to  reduce  to  the  absolute 
scale  has  been  given  by  Joule  and  Thomson,  in  the  Philosophical 
Transactions  for  1854;  but  as  the  formula  there  used  is  not  correct, 
I  have  recalculated  a  table  from  the  new  formula  used  by  them  in  their 
paper  of  1862. 

That  equation,  which  originated  with  Rankine,  can  be  placed  in  the  form 


where  p,  v,  and  /j.  are  the  pressure,  volume,  and  absolute  temperature 
of  a  given  weight  of  the  air;  D  is  its  density  referred  to  air  at  0°  C. 
and  760  mm.  pressure;  fa  is  the  absolute  temperature  of  the  freezing 
point;  and  m  is  a  constant  which  for  air  is  0°-33  C. 
For  the  air  thermometer  with  constant  volume 

T  =  100    P'~P° 


or,  since  D  =  1, 

tt  -  /,,  =  T-  -00088  T 


from  which  I  have  calculated  the  following  table  of  corrections: 


382 


HENRY  A".  ROWLAND 


TABLE  XVII. — REDUCTION  OF  AIR  THERMOMETER  TO  ABSOLUTE  SCALE. 


T 
Air  Thermometer. 

M  —  ("0 

Absolute  Temperature. 

A 

or  Correction  to  Air 
Thermometer. 

0 

0 

0 

0 

10 

9-9972 

—  •0028 

20 

19-9952 

—  •0048 

30 

29-9939 

—  •0061 

40 

39-9933 

—  •0067 

50 

49-9932 

0068 

60 

59-9937 

0063 

70 

69-9946 

—  •0054 

80 

79-9956 

—  •0044 

90 

89-9978 

—  •0022 

100 

100-000 

0 

200 

200-037 

+  -037 

300 

300-092 

+  -092 

400 

400-157 

-1-  -157 

500 

500-228 

+  -228 

It  is  a  curious  circumstance,  that  the  point  of  maximum  difference 
occurs  at  about  the  same  point  as  in  the  comparison  of  the  mercurial 
and  air  thermometers. 

From  the  previous  formula,  and  from  this  table  of  corrections,  the 
following  tables  were  constructed. 

TABLE  XVIII.— THERMOMETER  No.  6163. 


Reading  In 
Millimeters  on 
Stem. 

Temperature 
on  Mercurial 
Thermometer, 
0°  and  100°  fixed. 

Temperature 
on  Mercurial 
Thermometer  0° 
and  40°  fixed  by 
Air  Thermom. 

Temperature 
on  Air  Ther- 
mometer. 

Temperature 
on  Absolute 
Scale  from  0°  C. 

Reading  In 
Millimeters  on 
Stem. 

Temperature  • 
ou  Mercurial 
Thermometer, 
0°andlOU°nxed. 

Temperature 
on  Mercurial 
Thermom.,  0° 
and  40°  fixed  by 
Air  Thermom. 

Temperature 
ou  Air  Ther- 
mometer. 

Temperature 
on  Absolute 
Scale  fromO°C. 

50 

—  •923 

-  —  917 

_°911 

-•911 

240 

20-557 

20-409 

20-350 

20°345 

58-1 

0 

0 

0 

0 

250 

21-670 

21.515 

21-457 

21-452 

60 

+  -217 

+  -215 

+  -214 

+  •214 

260 

22-776 

22-616 

22  •  559  22  •  554 

70 

1-356 

1-336 

1-328 

1  •  328 

270 

23-884 

23-713 

23-657 

23.652 

80 

2-494 

2-475 

2-461 

2-460 

280 

24-989 

24-810 

24-755 

24-750 

90 

3-631 

3-604 

3-584 

3-583 

290 

26-093   25-907 

25-854 

25  •  848 

100 

4-767 

4-733 

4-707 

4-706 

300 

27-200   27-006 

26-956 

26-950 

110 

5-903 

5-860 

5-829 

5-827 

310 

28-311 

28-108 

28-060 

28  •  056 

120 

7-036 

6-986 

6-950 

6-948 

320 

29-425 

29-214 

29-169 

39-163 

130 

8-170 

8-111 

8-071 

8-069 

330 

30-541 

30-324 

30-282 

30  -276 

140 

9-304 

9-237 

9-193 

9-190 

340 

31-662 

31-436 

31-398 

31-392 

150 

10-436 

10.361 

10-314 

10-311 

350 

32.782 

32-548 

32,-  51  4 

32-508 

160 

11-568 

11-485 

11-435 

11-432 

360 

33-903 

33-660 

33-630 

33-624 

170 

12-700 

12-608 

12-556 

12-553 

370 

35-023 

34-773 

34-748 

34-742 

180 

13-829 

13-730 

13-676 

13-672 

380 

36-143 

35-884 

35-864 

35-857 

190 

14-957 

14-850 

14-794 

14-790 

390 

37-261 

36-994 

36-979 

36-972 

200 

16-081 

15-966 

15-909 

15-905 

400 

38-377 

38-103 

38-094 

38-087 

210 

17-203 

17-080 

17-022 

17-018 

410 

89-493 

39-210 

39-206 

39  •  199 

220 

18-322 

18-191 

18-132 

18-127 

420 

40-604 

40-314 

40-316 

40-309 

230 

19-440 

19-301 

19-242 

19-237 

TABLE  XIX.— THERMOMETER  No.  6165. 


Reading  In 
Millimeters  on 

Htom. 

Temperature 
on  Mercurial, 
Thermometer, 
0*  and  100°  fixed. 

Temperature 
on  Mercurial 
Thermom.,  0° 
and  40°  fixed  by 
Air  Thermom. 

O    1                        S)  m  ^ 
U  u     .                 U.  *  o 

S*2         HI 

«  tH    <Q                     CO   O    "> 
fc-  ^   S                   I*   03   O 
0  b  •                0>  .Q  *-t 

o,—  o           a<*~1 

o  a             5  fl<3 
H  o              H  0$ 

Reading  In 
Millimeters  on 
Stem. 

Temperature 
on  Mercurial 
Thermometer, 
0°  and  10U°  fixed. 

Temperature 
on  Mercurial 
Thermom.,  0° 
and  40°  fixed  by 
Air  Thermom. 

Temperature 
on  Air  Ther- 
mometer. 

Temperature 
on  Absolute 
Scale  from  0°  C. 

30 

464 

—  •460 

o                    o 
—  .457      —-457 

230 

17-198 

17-067 

17-009 

17-005 

35 

0 

0 

0                 0 

240 

18-056 

17-920 

17-861 

17-8.57 

40 

+  •463 

+  -460 

+  •457      +-457 

250 

18-917 

18-773 

18-714 

18-709 

50 

1-387 

1-376 

1-368        1-368 

260 

19-771 

19-621  j  19-562 

19-557 

60 

2-307 

2-290 

2-276        2-275 

270 

20-621 

20-465  !  20-406 

20-401 

70 

3-216       3-192 

3-174        3-173 

280 

21-469 

21-306  1  21-247 

21-242 

80 

4-122        4-092 

4-069       4-068 

290 

22-308 

22-139     22-081 

22-076 

90 

5-022 

4-984 

4-957        4-955 

300 

23-144 

22-969 

22-912 

22-907 

100 

5-916 

5-872 

5  •  841        5  •  839 

310 

23-974 

23-792 

23-736 

23-731 

110 

6-804 

6-753 

6-714        6.712 

320 

24  •  796 

24-607      24.552 

24-547 

120 

7-685 

7-628 

7-590        7-588 

330 

25-618 

25-424     25-370 

25-365 

130 

8-564 

8-500 

8-459        8.456 

340 

26-433 

26-232     26-180 

26-174 

140 

9-439        9.368 

9-324       9-321 

350 

27-245 

27-038 

26-987 

26-981 

150 

10-309      10-232 

10-186      10-183 

360 

28-049 

27-837      27-788 

27-782 

160 

11-174      11-091 

11-042      11-039 

370 

28-856 

28-637     28-590 

28  •  584 

170 

12-038      11.947 

11-896      11-893 

380 

29-651 

29-426     29-382 

29-376 

180 

12-900      12-802 

12.749      12.746 

390 

30-449 

30-218      30-176 

30-170 

190 

13-760     13-655 

13-601      13-598 

400 

31-249 

31-011   ;  30-971 

30-965 

200 

14-619      14-508 

14-453      14-450 

410 

32-073 

31-829     31-782 

31-786 

210 

15-479      15-362 

15-305      15-302 

420 

32-861 

32-611 

32-577 

32-581 

220 

16-340 

16-215 

16-157      16-153 

TABLE  XX.  —  THERMOMETER  No.  6166. 


a 

in—  iT1? 

-•6 

m  i 

0 

a 

--o   ffi_  .--d 

«>  _  d 

Reading  In 
Millimeters  c 
Stem. 

Temperatun 
ou  Mercurla 
Thermomete] 
0°aud  100°  flxe 

Temperature 
on  Mercurla 
Thermometel 
0°  and  40°  flxe 

Temperatun 
on  Air  Ther- 
mometer. 

Temperaturi 
on  Absolute 
Scale  from  0° 

Reading  In 
Millimeters  o 
Stem. 

Temperatur 
on  Mercurla 
Thermomete 
0°  and  100°  flxe 

Temperatur 
on  Mercurla 
Thermomete 
0°  and  40°  flxe 

Temperatur 
on  Air  Ther 
mometer. 

Temperatur 
on  Absolute 
Scale  from  t>° 

20 

—  036 

—  •036 

034 

034 

230 

16-478 

16-356 

16-298 

16-294 

30 

+  •770 

+  •764 

+  •  759 

+  •759 

240 

17-259 

17-132 

17-074 

17-070 

40 

1-574 

1-562 

1-553 

1-553 

250 

18-042 

17-908 

17-849 

17-845 

50 

2  •  368 

2-350 

2-336 

2-335 

260 

18-825 

18-686 

18-627 

18-622 

60 

3-156 

3-133 

3-115 

3-114 

270 

19-609 

19-464 

19-405 

19-400 

70 

3-941 

3-911 

3  •  889 

3-888 

280 

20-392 

20-241 

20-182 

20-177 

80 

4-726 

4-691 

4-665 

4-664 

290 

21-176 

21-019 

20-960 

20-955 

90 

5  •  509 

5-468 

5-438 

5-436 

300 

21  •  735 

21-793 

21-735 

21  •  730 

100 

6-293 

6-246 

6-212 

6-210  j 

310 

22-511 

22  •  569 

22-511 

22-506 

110 

7-076 

7-024 

6  -988 

6-986 

320 

23-292 

23-349 

23-292 

23-287 

120 

7-862 

7-804 

7  •  765 

7-763 

330 

24-075 

24-131 

24  •  075 

24-070 

130 

8-649 

8-585 

8-544 

8-542 

340 

24-855 

24-910 

24-855 

24-850 

140 

9-437 

9-367 

9  •  323 

9-321 

350 

25-634 

25-687 

25  •  634 

25-628 

150 

10-228 

10-151 

10-105 

10-102 

360 

26-415 

26-466 

26-412 

26-406 

160 

11-017 

10-935 

10-887 

10-884 

370 

27-441 

27-245 

27-195 

27-189 

170 

11-805 

11-717 

11-667 

11-664 

380 

28  •  240 

28-030 

27-982 

27-976 

180 

12-589 

12-496 

12-444 

12-441 

390 

29-030 

28-814 

28-768 

28-762 

190 

13-370 

13-271 

13-217 

13-214 

400 

29-819 

29-597 

29-550 

29-544 

200 

14-148 

14-043 

13-988 

13-984 

410 

30-608 

30-381 

30-339 

30-333 

210 

14-923 

14-812 

14-756 

14-753 

420 

31-396 

31-162 

31-123 

31-117 

220 

15-  699 

15  •  583 

15-526 

15-522 

430 

32-189 

31-950 

31-914 

31-908 

384 


HENRY  A.  BOWLAND 


In  using  these  tables  a  correction  is  of  course  to  be  made  should  the 
zero  point  change. 

TABLE  XXI. — CORRECTION  OF  KEW  STANDARD  TO  THE  ABSOLUTE  SCALE. 


Temperature  C. 

Correction  in 
degrees  C. 

0° 

0 

10° 

—  03 

20° 

—  05 

30° 

—  06 

40° 

—  •07 

50° 

—  07 

60° 

—  06 

70° 

—  •04 

80° 

—  •02 

90° 

—  01 

100° 

0 

Appendix  to  Thermometry 

The  last  of  January,  1879,  Mr.  S.  W.  Holman,  of  the  Massachusetts 
Institute  of  Technology,  came  to  Baltimore  to  compare  some  thermom- 
eters with  the  air  thermometer;  and  by  his  kindness  I  will  give  here 
the  results  of  the  comparison  which  we  then  made  together. 

As  in  this  comparison  some  thermometers  made  by  Fastre  in  1851 
were  used,  the  results  are  of  the  greatest  interest. 

The  tables  are  calculated  with  the  newest  value  for  the  coefficient  of 
expansion  of  glass.  The  calibration  of  all  the  thermometers,  except 
the  two  by  Casella,  has  been  examined,  and  found  good.  The  Casella 
thermometers  had  no  reservoir  at  the  top,  and  could  not  thus  be  readily 
calibrated  after  being  made.  The  G-eissler  also  had  none,  but  I  suc- 
ceeded in  separating  a  column. 

The  absence  of  a  reservoir  at  the  top  should  immediately  condemn 
a  standard,  for  there  is  no  certainty  in  the  work  done  with  it. 

From  these  tables  we  would  draw  the  inference  that  No.  6163  repre- 
sents the  air  thermometer  with  considerable  accuracy.  At  the  same 
time,  both  tables  would  give  a  smaller  value  of  ra  than  I  have  used, 
and  not  very  far  from  the  value  found  before  by  direct  comparison, 
namely,  -00015. 

The  difference  from  using  m=  -00018  would  be  a  little  over  0°-01  C. 
at  the  20°  point. 

All  the  other  thermometers  stand  above  the  air  thermometer,  between 
0°  and  100°,  by  amounts  ranging  between  about  0°-05  and  0°-35C., 


. 


385 


TABLE  XXII.— SEVENTH  SERIES. 


Air 

Ther- 
mome- 
ter. 

Original  Readings. 

Reduced  Readings. 

6163. 

7334 
Baudln. 

Kew 
Stand- 
ard 
No.  104. 

32374 
Casella. 

Gelss- 
ler. 

6163 
Reduced 
to  Air 
Ther- 
mome- 
ter. 

7334 
Baudln. 

Kew 
Stand- 
ard 
No.  104. 

32374 
Casella. 

Gelss- 
ler. 

6 

is-43 
6-08 
12-68 
20-49 
24-55 
29-51 
39-45 
39-15 
51-17 
61-12 
70-74 
80-09 
80-39 
89-95 
89-92 
100-00 

"58-83 
63-5 
113-0 
171-55 
242-0 
278-8 
323-9 
413-1 
410-7 

—  •11 

32-68 
33-60 
43-65 
55-47 
69-55 
76-90 
85-88 
103-72 
103-23 
124-84 
142-73 
159-87 
176-50 
177-23 
194-35 
194-22 
212-37 

+  •20 
•71 
6-33 
12-91 
20-77 
24-80 
29-80 
39-76 
39-48 
51-49 
61-47 
71-00 
80-31 
80-74 
90-22 
90-18 
100-06 

+  •69 

13-42 
21-29 
25-33 
30-32 
40-22 
39-98 
51-83 
61-69 
71-14 
80-25 
80-66 
90-11 
90-06 
99-32 

8 

•52 
6-08 
12-65 
20-49 
24-54 
29  52 
39-47 
39-20 

8 

o 

0 
•52 
6-11 
12-68 
20-57 
24-61 
29-61 
39-53 
39-26 
51-29 
61-24 
70-78 
80-04 
80-44 
89-97 
89-90 
100-00 

8 
•51 
6-13 
12-70 
20-56 
24-59 
29-58 
39-54 
39-26 
51-26 
61-23 
70-76 
80-06 
80-49 
89-97 
89-93 
100-00 

8 

12-73 
20-63 
24-66 
29-66 
39-62 
39-34 
51-32 
61-29 
70-83 
80-02 
80-43 
89-93 
89-89 
100-00 

12-59 
20-48 
24-50 
29-49 
39-43 
39-15 
51-10 
61-05 
70-57 
79-74 
80-15 
89-63 
89-59 
99-69 

12-82 
20-74 
24-81 
29-83 
39-80 
39-56 
51-49 
61-41 
70-92 
80-10 
80-51 
90-03 
89-98 
100-00 



TABLE  XXIII. — EIGHTH  SERIES. 


Air 
Ther- 
mome- 
ter. 

Original  Readings. 

Reduced  Readings. 

6163. 

378 
Fastre. 

7316 
Baudln. 

368 
Fastr6. 

3235 
Casella. 

6163 
Reduced 
to  Air 
Ther- 
mome- 
ter. 

376 

Fastrfi. 

7316 
Baudln. 

368 

Fastre. 

3236 
Casella. 

6 
3.67 
11-55 
20-72 
32-19 
39-36 
50-71 
60-10 
73-82 
86-50 

"  58°  60 
90-7 
161-6 
243-7 
347-4 
411-85 

111-3 
130-0 
170-9 
217-9 
276-9 
313-85 
372-0 
420-0 
490-6 
555-25 
550-2 
624-93 

—  •23 

11-40 
20-59 
32-09 
39-26 
50-57 
59-92 
73-59 
86-16 
85-21 
99-70 

87-6 
106-25 
147-2 
194-2 
253-2 
290-1 
248-2 
396-45 
466-85 
531-22 
525-95 
600-58 

32-80 
39-35 
53-70 
70-15 
90-80 
103-68 
123-65 
140-80 
165-68 
188-20 
186-42 
212-45 

o 
0 

3-61 
11-56 
20-70 
32-17 
39-36 

o 
0 
3-64 
11-60 
20-75 
32-24 
39-43 
50-75 
60-10 
73-84 
86-48 
86-45 
100-00 

§ 

8 

3-64 
11-62 
20-80 
32-28 
39-48 
50-80 
60-21 
73-93 
86-56 
85-45 
100-00 

8 

3-65 
11-63 
20-79 
32-29 
39-45 
50-57 
60-12 
73-97 
86-56 
85-51 
100-00 

11-64 
20-84 
32-34 
39-52 
50-84 
60-19 
73-87 
86-51 
85-50 
100-00 

100-00  

none  standing  below.     Indeed,  no  table  has  ever  been  published  show- 
ing any  thermometer  standing  below  the  air  thermometer  between  0° 

17  The  original  readings  in  ice  were  58-68  and  58-45,  to  which   -15  was  added  to 
allow  for  the  pressure  of  water  in  the  comparator.     This,  of  course,  gives  the  same 
final  result  as  if  -15  were  subtracted  from  each  of  the  other  temperatures.     No  cor- 
rection was  made  to  the  others. 

18  Probably  some  error  of  reading. 

25 


386 


HENEY  A.  ROWLAND 


and  100°.  By  inference  from  experiments  above  100°  on  crystal  glass 
by  Regnault,  thermometers  of  this  glass  should  stand  below,  but  it 
never  seems  to  have  been  proved  by  direct  experiment.  The  Fastre 
thermometers  are  probably  made  of  this  glass,  and  my  Baudin's  cer- 
tainly contain  lead;  and  yet  these  stand  above,  though  only  to  a  small 
amount,  in  the  case  of  the  Fastre's. 

The  Geissler  still  seems  to  retain  its  pre-eminence  as  having  the 
greatest  error  of  the  lot. 

The  Baudin  thermometers  agree  well  together,  but  are  evidently 
made  from  another  lot  of  glass  from  the  No.  6167  used  before.  These 
last  two  depart  less  from  the  air  thermometer.  The  explanation  is 
plain,  as  Baudin  had  manufactured  more  than  one  thousand  ther- 
mometers between  the  two,  and  so  had  probably  used  up  the  first  stock 
of  glass.  And  even  glass  of  the  same  lot  differs,  especially  as  Regnault 
has  shown  that  the  method  of  working  it  before  the  blow-pipe  affects 
it  very  greatly. 

It  is  very  easy  to  test  whether  the  calorimeter  thermometers  are  of 
the  same  glass  as  any  of  the  others,  by  testing  whether  they  agree  with 
No.  6163  throughout  the  whole  range  of  40°.  The  difference  in  the 
values  of  m  for  the  two  kinds  of  glass  will  then  be  about  -003  of  the 
difference  between  them  at  20°,  the  0°  and  40°  points  agreeing.  The 
only  difficulty  is  in  calibrating  or  reading  the  100°  thermometers  accur- 
ately enough. 

The  Baudin  thermometers  were  very  well  calibrated,  and  were 
graduated  to  ^°  C.,  and  so  were  best  adapted  to  this  kind  of  work. 
Hence  I  have  constructed  the  following  tables,  making  the  0°  and  40° 
points  agree. 

TABLE  XXIV. — COMPARISON  OF  6163  AND  THE  BATJDIN  STANDARDS. 


6163 
Mercurial 
0°  and  40° 
fixed. 

7334.19 

Difference. 

6163 
Mercurial 
0°  and  40° 
fixed. 

7316.19 

Difference. 

0 

0 

0 

0 

0 

0 

12-699 

12-673 

+  •026 

11-609 

11-584 

+  •025 

20-547 

20-553 

—  •006 

20-762 

20-746 

+  •016 

24-604 

24-567 

+  •037 

32-203 

32-211 

—  •008 

29-564 

29-550 

+  •014 

39-358 

39-358 

0 

39-337 

39-337 

0 

19  A  correction  of  0°-01  was  made  to  the  zero  points  of  these  thermometers  on  ac- 
count of  the  pressure  of  the  water. 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  387 

Taking  the  average  of  the  two,  it  would  seem  that  No.  6163  stood 
about  -015  higher  than  the  mean  of  7334  and  7316  at  the  20°  point, 
or  6163  has  a  higher  value  of  ra  by  -000045  than  the  others. 

These  differ  about  -17  from  the  air  thermometer  at  40°,  which  gives 
the  value  of  m  about  -000104.  Whence  m  for  6163  is  -00015,  as  we 
have  found  before  by  direct  comparison  with  the  air  thermometer. 

I  am  inclined  to  think  that  the  former  value,  -00018,  is  too  large, 
and  to  take  -00015,  which  is  the  value  found  by  direct  comparison,  as 
the  true  value.  As  the  change,  however,  only  makes  at  most  a  differ- 
ence of  0°-01  at  any  one  point,  and  as  I  have  already  used  the  previous 
value  in  all  calculations,  I  have  not  thought  it  worth  while  to  go  over 
all  my  work  again,  but  will  'refer  to  the  matter  again  in  the  final 
results,  and  then  reduce  the  final  results  to  this  value. 

m.— CALOKIMETKY 
(a)  Specific  Heat  of  Water 

The  first  observers  on  the  specific  heat  of  water,  such  as  De  Luc, 
completed  the  experiment  with  a  view  of  testing  the  thermometer;  and 
it  is  curious  to  note  that  both  De  Luc  and  Flaugergues  found  th£  tem- 
perature of  the  mixture  less  than  the  mean  of  the  two  equal  portions 
of  which  it  was  composed,  and  hence  the  specific  heat  of  cold  water 
higher  than  that  of  warm. 

The  experiments  of  Flaugergues  were  apparently  the  best,  and  he 
found  as  follows :  " 

3  parts  of  water  at  0°  and  1  part  at  80°  R.  gave  19° -86  K. 
2  parts  of  water  at  0°  and  2  parts  at  80°  R.  gave  39° -81  R. 
1  part  of  water  at  0°  and  3  parts  at  80°  R.  gave  59° -87  R. 

But  it  is  not  at  all  certain  that  any  correction  was  made  for  the 
specific  heat  of  the  vessel,  or  whether  the  loss  by  evaporation  or  radia- 
tion was  guarded  against. 

The  first  experiments  of  any  accuracy  on  this  subject  seem  to  have 
been  made  by  F.  E.  Neumann  in  1831.21  He  finds  that  the  specific 
heat  of  water  at  the  boiling  point  is  1-0127  times  that  at  about  28°  C. 
(22°  R.). 

The  next  observer  seems  to  have  been  Regnault,22  who,  in  1840, 

MGehler,  Phys.  Worterbuch,  i,  641. 
"Pogg.  Ann.,  xxiii,  40. 
22 Ibid.,  li,  72. 


388  HENRY  A.  EOWLAND 

found  the  mean  specific  heat  between  100°  C.  and  16°  C.  to  be  1-00709 
and  1-00890  times  that  at  about  14°. 

But  the  principal  experiments  on  the  subject  were  published  by 
Eegnault  in  1850,23  and  these  have  been  accepted  to  the  present  time. 
It  is  unfortunate  that  these  experiments  were  all  made  by  mixing  water 
above  100°  with  water  at  ordinary  temperatures,  it  being  assumed  that 
water  at  ordinary  temperatures  changes  little,  if  any.  An  interpolation 
formula  was  then  found  to  represent  the  results;  and  it  was  assumed 
that  the  same  formula  held  at  ordinary  temperature,  or  even  as  low 
as  0°  C.  It  is  true  that  Eegnault  experimented  on  the  subject  at 
points  around  4°  C.  by  determining  the  specific  heat  of  lead  in  water 
at  various  temperatures;  but  the  results  were  not  of  sufficient  accuracy 
to  warrant  any  conclusions  except  that  the  variation  was  not  great. 

Boscha  has  attempted  to  correct  Eegnault's  results  so  as  to  reduce 
them  to  the  air  thermometer;  but  Eegnault,  in  Comptes  Rendus,  has 
not  accepted  the  correction,  as  the  results  were  already  reduced  to  the 
air  thermometer. 

Him  (Comptes  Rendus,  Ixx,  592,  831)  has  given  the  results  of  some 
experiments  on  the  specific  heat  of  water  at  low  temperatures,  which 
give  the  absurd  result  that  the  specific  heat  of  water  increases  about 
six  or  seven  per  cent  between  zero  and  13°!  The  method  of  experi- 
ment was  to  immerse  the  bulb  of  a  water  thermometer  in  the  water 
of  the  calorimeter,  until  the  water  had  contracted  just  so  much,  when 
it  was  withdrawn.  The  idea  of  thus  giving  equal  quantities  of  heat 
to  the  water  was  excellent,  but  could  not  be  carried  into  execution 
without  a  great  amount  of  error.  Indeed,  experiments  so  full  of  error 
only  confuse  the  physicist,  and  are  worse  than  useless. 

The  experiments  of  Jamin  and  Amaury,  by  the  heating  of  water  by 
electricity,  were  better  in  principle,  and,  if  carried  out  with  care,  would 
doubtless  give  good  results.  But  no  particular  care  seems  to  have 
been  taken  to  determine  the  variation  of  the  resistance  of  the  wire 
with  accuracy,  and  the  measurement  of  the  temperature  is  passed  over 
as  if  it  were  a  very  simple,  instead  of  an  immensely  difficult  matter. 
Their  results  are  thus  to  be  rejected;  and,  indeed,  Eegnault  does  not 
accept  them,  but  believes  there  is  very  little  change  between  5°  and  25°. 

In  PoggendorfFs  Annalen  for  1870  a  paper  by  Pfaundler  and  Platter 
appeared,  giving  the  results  of  experiments  around  4°  C.,  and  deducing 
the  remarkable  result  that  water  from  0°  to  10°  C.  varied  as  much  as 

"Pogg.  Ann.,  Ixxix,  241;   also,  Rel.  d.  Exp.,  i,  729. 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  389 

twenty  per  cent  in  specific  heat,  and  in  a  very  irregular  manner, — first 
decreasing,  then  increasing,  and  again  decreasing.  But  soon  after  an- 
other paper  appeared,  showing  that  the  results  of  the  previous  experi- 
ments were  entirely  erroneous. 

The  new  experiments,  which  extended  up  to  13°  C.,  seemed  to  give 
an  increase  of  specific  heat  up  to  about  6°,  after  which  there  was  appar- 
ently a  decrease.  It  is  to  be  noted  that  Geissler's  thermometers  were 
used,  which  I  have  found  to  depart  more  than  any  other  from  the  air 
thermometer. 

But  as  the  range  of  temperature  is  very  small,  the  reduction  to  the 
air  thermometer  will  not  affect  the  results  very  much,  though  it  will 
somewhat  decrease  the  apparent  change  of  specific  heat. 

In  the  Journal  de  Physique  for  November,  1878,  there  is  a  notice  of 
some  experiments  of  M.  von  Miinchausen  on  the  specific  heat  of  water. 
The  method  was  that  of  mixture  in  an  open  vessel,  where  evaporation 
might  interfere  very  much  with  the  experiment.  No  reference  is  made 
to  the  thermometer,  but  it  seems  not  improbable  that  it  was  one  from 
Geissler;  in  which  case  the  error  would  be  very  great,  as  the  range  was 
large,  and  reached  even  up  to  70 °C.  The  error  of  the  Geissler  would 
be  in  the  direction  of  making  the  specific  heat  increase  more  rapidly 
than  it  should.  The  formula  he  gives  for  the  specific  heat  of  water  at 
the  temperature  t  is 

1  -f  -000302  i. 

Assuming  that  the  thermometer  was  from  Geissler,  the  formula,  re- 
duced to  the  air  thermometer,  would  become  approximately 

1  — -00009  t+  -0000015  t2. 

Had  the  thermometer  been  similar  to  that  of  Kecknagel,  it  would 
have  been  1  -f  -000045  t  -f  -000001  t2. 

It  is  to  be  noted  that  the  first  formula  would  actually  give  a  decrease 
of  specific  heat  at  first,  and  then  an  increase. 

As  all  these  results  vary  so  very  much  from  each  other,  we  can 
hardly  say  that  we  know  anything  about  the  specific  heat  of  water 
between  0  and  100°,  though  Kegnault's  results  above  that  temperature 
are  probably  very  nearly  correct. 

It  seems  to  me  probable  that  my  results  with  the  mechanical  equiv- 
alent apparatus  give  the  variation  of  the  specific  heat  of  water  with 
considerable  accuracy;  indeed,  far  surpassing  any  results  which  we 
can  obtain  by  the  method  of  mixture.  It  is  a  curious  result  of  those 
experiments,  that  at  low  temperatures,  or  up  to  about  30°  C.,  the  spe- 


390  HENKY  A.  EOWLAXD 

cific  heat  of  water  is  about  constant  on  the  mercurial  thermometer  made 
by  Baudin,  but  decreases  to  a  minimum  at  about  30°  when  the  reduction 
is  made  to  the  air  thermometer  or  the  absolute  scale,  or,  indeed,  the  Kew 
standard. 

As  this  curious  and  interesting  result  depends  upon  the  accurate 
comparison  of  the  mercurial  with  the  air  thermometer,  I  have  spent 
the  greater  part  of  a  year  in  the  study  of  the  comparison,  but  have  not 
been  able  to  find  any  error,  and  am  now  thoroughly  convinced  of  the 
truth  of  this  decrease  of  the  specific  heat.  But  to  make  certain,  I  have 
instituted  the  following  independent  series  of  investigations  on  the 
specific  heat  of  water,  using,  however,  the  same  thermometers. 

The  apparatus  is  shown  in  Fig.  4.  A  copper  vessel,  A,  about  20  cm. 
in  diameter  and  23  cm.  high,  rests  upon  a  tripod.  In  its  interior  is  a 
three-way  stopcock,  communicating  with  the  small  interior  vessel  B, 
the  vessel  A,  and  the  vulcanite  spout  C.  By  turning  it,  the  vessel  B 
could  be  filled  with  water,  and  its  temperature  measured  by  the  ther- 
mometer D,  after  which  it  could  be  delivered  through  the  spout  into 
the  calorimeter.  As  the  vessel  B,  the  stopcock,  and  most  of  the  spout, 
were  within  the  vessel  A,  and  thus  surrounded  by  water,  and  as  the 
vulcanite  tube  was  very  thin,  the  water  could  be  delivered  into  the 
calorimeter  without  appreciable  change  of  temperature.  The  proof  of 
this  will  follow  later. 

The  calorimeter,  E,  was  of  very  thin  copper,  nickel-plated  very 
thinly.  A  hole  in  the  back  at  F  allowed  the  delivery  spout  to  enter, 
and  two  openings  on  top  admitted  the  thermometers.  A  wire  attached 
to  a  stirrer  also  passed  through  the  top.  The  calorimeter  had  a  capac- 
ity of  about  three  litres,  and  weighed  complete  about  388-3  grammes. 
Its  calorific  capacity  was  estimated  at  35-4  grammes.  It  rested  on 
three  vulcanite  pieces,  to  prevent  conduction  to  the  jacket.  Around 
the  calorimeter  on  all  sides  was  a  water-jacket,  nickel-plated  on  its 
interior,  to  make  the  radiation  perfectly  definite. 

The  calorific  capacity  of  the  thermometers,  including  the  immersed 
stem  and  the  mercury  of  the  bulb,  was  estimated  as  follows :  14  cm.  of 
stem  weighed  about  3-8  gr.,  and  had  a  capacity  of  -8  gr.;  10  gr.  of 
mercury  had  a  capacity  of  -3  gr.;  total,  1-1  gr. 

Often  the  vessel  B  was  removed,  and  the  water  allowed  to  flow 
directly  into  the  calorimeter. 

The  following  is  the  process  followed  during  one  experiment  at  low 
temperatures.  The  vessel  A  was  filled  with  clean  broken  ice,  the  open- 
ing into  the  stopcock  being  covered  with  fine  gauze  to  prevent  any 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


391 


small  particles  of  ice  from  flowing  out.  The  whole  was  then  covered 
with  cloth,  to  prevent  melting.  The  vessel  was  then  filled  with  water, 
and  the  two  thermometers  immersed  to  get  the  zero  points.  The 
calorimeter  being  about  two-thirds  filled  with  water,  and  having  been 
weighed,  was  then  put  in  position,  the  holes  corked  up,  and  one  ther- 
mometer placed  in  it,  the  other  being  in  the  melting  ice.  An  obser- 
vation of  its  temperature  was  then  taken  every  minute,  it  being  fre- 
quently stirred. 


FIG.  4. 


When  enough  observations  had  been  obtained  in  this  way,  the  cork 
was  taken  out  of  the  aperture  F  and  the  spout  inserted,  and  the  water 
allowed  to  run  for  a  given  time,  or  until  the  calorimeter  was  full.  It 
was  then  removed,  the  cork  replaced,  and  the  second  thermometer 
removed  from  the  ice  to  the  calorimeter.  Observations  were  then 
taken  as  before,  and  the  vessel  again  weighed. 

Two  thermometers  were  used  in  the  way  specified,  so  that  one  might 
approach  the  final  temperature  from  above  and  the  other  from  below. 
But  no  regular  difference  was  ever  observed,  and  so  some  experiments 


392  HENRY  A.  EOWLAND 

were  made  with  both  thermometers  in  the  calorimeter  during  the  whole 
experiment. 

The  principal  sources  of  error  are  as  follows : 

1st.  Thermometers  lag  behind  their  true  reading.  This  was  not 
noticed,  and  would  probably  be  greater  in  thermometers  with  very  fine 
stems  like  Geissler's.  At  any  rate,  it  was  almost  eliminated  in  the 
experiment  by  using  two  thermometers. 

2d.  The  water  may  be  changed  in  temperature  in  passing  through 
the  spout.  This  was  eliminated  by  allowing  the  water  to  run  some 
time  before  it  went  into  the  calorimeter.  The  spout  being  very  thin, 
and  made  of  vulcanite,  covered  on  the  outside  with  cloth,  it  is  not 
thought  that  there  was  any  appreciable  error.  It  will  be  discussed 
more  at  length  below,  and  an  experiment  given  to  prove  this. 

3d.  The  top  of  the  calorimeter  not  being  in  contact  with  the  water, 
its  temperature  may  be  uncertain.  To  eliminate  this,  the  calorimeter 
was  often  at  the  temperature  of  the  air  to  commence  with.  Also  the 
water  was  sometimes  violently  agitated  just  before  taking  the  final 
reading,  previous  to  letting  in  the  cold  water.  Even  if  the  tempera- 
ture of  this  part  was  taken  as  that  of  the  air,  the  error  would  scarcely 
ever  be  of  sufficient  importance  to  vitiate  the  conclusions. 

4th.  The  specific  heat  of  copper  changes  with  the  temperature. 
Unimportant. 

5th.  Some  water  might  remain  in  the  spout  whose  temperature  might 
be  different  from  the  rest.  This  was  guarded  against. 

6th.  Evaporation.     Impossible,  as  the  calorimeter  was  closed. 

7th.  The  introduction  of  cold  water  may  cause  dew  to  be  deposited  on 
the  calorimeter.  The  experiments  were  rejected  where  this  occurred. 

The  corrections  for  the  protruding  thermometer  stem,  for  radiation, 
&c.,  were  made  as  usual,  the  radiation  being  estimated  by  a  series  of 
observations  before  and  after  the  experiment,  as  is  usual  in  determin- 
ing the  specific  heat  of  solids. 

June  14,  1878. — First  Experiment 
Time.  Ther.  6163.     Ther.  6166.         0  Points. 

41  296-75  6163,  57-9  Air,  21°  C. 

42  296-7  6165,  34-8  Jacket  about  25°  C. 

43  296-7  6166,  20-5* 

44  296-65 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


393 


Time.  Ther.  6163.     Ther.  6166. 

44i-44f  Water  running. 

46*  218-7  251-7 

47*  218-8  251-8 

48*  218-9  252-0 


Temperature  before  296-6 
Correction  for  0      +  -2 


296-8=26°-597 

Correction  for  stem  +  '019 

Initial  temperature  of 

calorimeter  26°-616 

218-6  +  -2  =  218-8  =  17°-994 
Correction  for  stem       — -006 


0  Points. 

Calorimeter  before  2043-0 

"           after  2853'3 

Water  at  0°  added  810-3 

Thermometer  1-1 

Total  at  0°  8114 

Calorimeter  before  2043'0 

Weight  of  Vessel  388-3 

Water  1654-7 

Capacity  of  calorimeter  35-4 

"            thermometer  1*1 

Total  capacity  1691-2 

251-6  -  1  =  251-5  =  17°-962- 

Correction  for  stem  — -006 


17°-956 


17°-988 
Mean  temperature  of  mixture,  17° -972. 

Mean  specific  heat  0°  —  18°  _  1691-2  X  8°-644  _ 
Mean  specific  heat  18°  —27°  ~~  811-4  X  17°'972 

June  lit. — Second  Experiment 

Calorimeter  before  2016-3;  temperature  361-4  by  No.  6163. 
Calorimeter  after  3047-0;  temperature  244-5  and  288-7. 

Air,  21°  C.;  jacket  about  27°. 

361-4+  -2  =  361-6  =  33°-803,  or  33°-863  when  corrected  for  stem. 
244-5  -|_  -2  =  244-7  =  20°-865;  no  correction  for  stem. 
288-7 — •  1  =  288-6  =  20° -846;  no  correction  for  stem. 

Mean,  20° -855. 

Mean  specific  heat  between  0°  and  21°  _  ^.QQgg 
Mean  specific  heat  between  21°  and  34° 

June  l-'f. — Third  Experiment 

Calorimeter  before  1961-8;  temperature  293-6  by  No.  6166. 
Calorimeter  after  3044-6;  temperature  243-7  and  213-0. 

Air  and  jacket,  about  18°  C. 


394  HENET  A.  EOWLAND 

393-6— -l  =  393-5  =  29°-036,  or  29°-077  when  corrected  for  stem. 
243-7— -1  =  243 -6  =  17° -349;  no  correction  for  stem. 
213-0  +  -2  =  213-2  =  17° -374;  no  correction  for  stem. 

Mean,  17° -361. 

Mean  specific  heat  between  0°  and  17°  1-0024 

Mean  specific  heat  between  17°  and  29°  ~ 

It  is  to  he  observed  that  thermometer  No.  6166  in  all  cases  gave 
temperatures  about  0°-02  or  0°-03  below  No.  6163.  This  difference 
is  undoubtedly  in  the  determination  of  the  zero  points,  as  on  June  15 
the  zero  points  were  found  to  be  20-4  and  58-0.  As  one  has  gone  up 
and  the  other  down,  the  mean  of  the  temperatures  needs  no  correction. 

June  15 

Calorimeter  before  2068-2;  temperature  364-6  by  No.  6166. 
Calorimeter  after  2929-2;  temperature  249-7  and  217-7. 

Air  and  jacket  at  about  22°  C. 

264-6  =  26°-766,  or  26°-782  when  corrected  for  stem. 
249-7  =  H° -822,  or  17°-812  when  corrected  for  stem. 
217-7+  -l  =  217-8=17°-884,  or  17°-874  when  corrected  for  stem. 

Bejected  on  account  of  great  difference  in  final  temperatures  by  the 
two  thermometers,  which  was  probably  due  to  some  error  in  reading. 

June  21 

Calorimeter  before  2002-7;  temperature  330-3  by  No.  6163. 
Calorimeter  after  3075-2;  temperature  221-9  and  256-6. 

Air  and  jacket,  21°  C. 

330-3  +  -1  =  330-4  =  30°-321,  or  30°-359  when  corrected  for  stem. 
221-9+ -1=222-0  =  18°-349,  or  18°-343  when  corrected  for  stem. 
256-6+  -0  =  256-6  =  18°-358,  or  18°-352  when  corrected  for  stem. 

Mean,  18° -347. 

Specific  heat  between  0°  and  18°  __ 
Specific  heat  between  18°  and  30°  ~~ 

June  21 

Calorimeter  before  2073-8;  temperature  347-8  by  No.  6166. 
Calorimeter  after  2986-8:  temperature  234-5  and  206-6. 

Air  and  jacket,  about  21°  C. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  395 

347-8+  -0  =  347-8  =  25° -457,  or  25°-471  when  corrected  for  stem. 
234-5  +  -0  =  234-5  =  16°-643,  or  16°-636  when  corrected  for  stem. 
206-6  +  -1  =  206-7  =  16°-651,  or  16°-644  when  corrected  for  stem. 

Mean,  16° -640. 

Specific  heat  between  0°  and  17°  _  .99971 
Specific  heat  between  17°  and  25°  ~~ 

Eejected  because  dew  was  formed  on  the  calorimeter. 

A  series  was  now  tried  with  both  thermometers  in  the  calorimeter 
from  the  beginning. 

June  25 

Calor.  before  2220-3;  temperat.  325-6  by  No.  6166;  309-9  by  No.  6165. 
Calor.  after  3031-4;  temperat.  233-4  by  No.  6166;  224-6  by  No.  6165. 

Air,  24° -2  C.;  jacket,  23° -5. 

325-6  +  -0  =  325-6  =  23°-725,  or  23°-726  when  corrected  for  stem. 

309-9  +  -2  =  310-1  =  23°-739,  or  23°-740  when  corrected  for  stem. 

233-4+  -0  =  233-4  =  16°-558,  or  16°-545  when  corrected  for  stem. 

224-6+ -2  =  224-8  =  16°-562,  or  16°-549  when  corrected  for  stem. 

Means,  23° -733  and  16° -547. 

Specific  heat  between  0°  and  l'»°  _ 
Specific  heat  between  16°  and  24°  ~ 

June  25 

Calor.  before  2278-6;  temperat.  340-35  by  No.  6166;  324-1  by  No.  6165. 
Calor.  after  3130-2;  temperat.  242-5  by  No.  6166;  232-8  by  No.  6165. 

Air,  23° -5  C.;  jacket,  22° -5. 

340-35  +  -0  =  340-35  =  24° -877,  or  24° -881  when  corrected  for  stem. 
324-1  +-2  =  324-3  =  24° -899,  or  24° -903  when  corrected  for  stem. 
242-5  +  -0  =  242-5  =17° -264,  or  17° -253  when  corrected  for  stem. 
232-8  +  -2  =  233-0  =17° -261,  or  17° -250  when  corrected  for  stem. 

Specific  heat  between  0°  and  17°  _  i  . 
Specific  heat  between  17°  and  25° 


Calor.  before  2316-35;  temperat.  386-1  by  No.  6166;  368-4  by  No.  6165. 
Calor.  after  2966-90;  temperat.  295-4  by  No.  6166;  281-7  by  No.  6165. 

Air,  23°-5C.;  jacket,  22° -5. 


396  HENKY  A.  KOWLAND 

386-1+  -0  =  386-1  =  28°-455,  or  2S°-465  when  corrected  for  stem. 

268-4+  -2  =  368-6  =  28°-472,  or  28°-482  when  corrected  for  stem. 

295-4+  -0  =  295-4  =  21°-374,  or  21°-368  when  corrected  for  stem. 

281-7  +  -2  =  281-9  =  21°-400,  or  21°-394  when  corrected  for  stem. 

Means,  28°  -473  and  21°  -381. 


Specific  heat  between  0°  and  21 
"~ 


_  -. 

~ 


Specific  heat  between  2r°"and~28"0" 

Two  experiments  were  made  on  June  23  with  warm  water  in  vessel 
A,  readings  being  taken  of  the  temperature  of  the  water,  as  it  flowed 
out,  by  one  thermometer,  which  was  then  transferred  to  the  calorimeter 
as  before. 

June  23 

Water  in  A  while  running,  314-15  by  No.  6163. 

Calor.  before  1530-9;  temperat.  281-1  by  No.  6166. 

Calor.  after  2996-3;  temperat.  328-4  by  No.  6166;  272-7  by  No.  6163. 

314-15  +  -1  =  314-25  =  28°-526,  or  28°-552  when  corrected  for  stem. 
281-1  +-0  =  281-1  =20°  -262,  or  20°  -258  when  corrected  for  stem. 
328-4  +-0  =  328-4  =23°  -945,  or  23°  -950  when  corrected  for  stem. 
272-7  +  -1  =  272-8  =23°  -960,  or  23°  -966  when  corrected  for  stem. 

Specific  heat  between  20°  and  24°  _  .QQDQ 
Specific  heat  between  24°  and  29°  ~ 

June  23 
Water  in  A  while  running,  383-9  by  No.  6163. 

Calor.  before  1624-9;  temperat.  286-75  by  6166. 

Calor.  after  3048-2;  temperat.  392-45  by  6166,  and  318-1  by  6163. 

383-9  +  -1  =  384-0  =36°-303,  or  36°-357  when  corrected  for  stem. 
286-75+  -0  =  286-  75  =  20°  -702,  or  20°  -700  when  corrected  for  stem. 
392-45+  -0  =  392-45  =  28°  -954,  or  28°  -980  when  corrected  for  stem. 
318-1  +-1  =  318-2  =28°  -964,  or  28°  -992  when  corrected  for  stem. 

Specific  heat  between  21°  and  29°   _  . 
Specific  heat  between  29°  and  36 

To  test  the  apparatus,  and  also  to  check  the  estimated  specific  heat 
of  the  calorimeter,  the  water  was  almost  entirely  poured  out  of  the 
calorimeter,  and  warm  water  placed  in  the  vessel  A,  which  was  then 
allowed  to  flow  into  the  calorimeter. 


ON  THE  MECHANICAL  EQUIVALENT  or  HEAT  397 

Water  in  A  while  running,  309-0  by  No.  6163. 

Calor.  before  391-3;  temperat.  314-5  by  6166. 

Calor.  after  3129-0;  temperat.  308-3  by  6166,  and  378-5  by  6163. 

Air  about  21°  C. 

Therefore,  water  lost  0°-078,  and  calorimeter  gained  5°.  Hence  the 
capacity  of  the  calorimeter  is  39. 

Another  experiment,  more  carefully  made,  in  which  the  range  was 
greater,  gave  35. 

The  close  agreement  of  these  with  the  estimated  amount  is,  of 
course,  only  accidental,  for  they  depend  upon  an  estimation  of  only 
0°-08  and  0°-12  respectively.  But  they  at  least  show  that  the  water  is 
delivered  into  the  calorimeter  without  much  change  of  temperature. 

A  few  experiments  were  made  as  follows  between  ordinary  tempera- 
tures and  100°,  seeing  that  this  has  already  been  determined  by  Reg- 
nault. 

Two  thermometers  were  placed  in  the  calorimeter,  the  temperature 
of  which  was  about  5°  below  that  of  the  atmosphere.  The  vessel  B 
was  then  filled,  and  the  water  let  into  the  calorimeter,  by  which  the 
temperature  was  nearly  brought  to  that  of  the  atmosphere;  the  opera- 
tion was  then  immediately  repeated,  by  which  the  temperature  rose 
about  5°  above  the  atmosphere.  The  temperature  of  the  boiling  water 
was  given  by  a  thermometer  whose  100°  was  taken  several  times. 

As  only  the  rise  of  temperature  is  needed,  the  zero  points  of  the 
thermometers  in  the  calorimeter  are  unnecessary,  except  to  know  that 
they  are  within  0°-02  of  correct. 

June  18 
Temperature  of  boiling  water,  99° -9. 

Calor.  before  2684-7;  temperat.  259-2  by  6166,  and  248-3  by  6165. 
Calor.  after  2993-2;  temperat.  381-0  by  6166,  and  363-4  by  6165. 

259-3  =  18°-568,  or  18°-555  when  corrected  for  stem. 
248- 3  =  18° -564,  or  18° -551  when  corrected  for  stem. 
381-0  =  28°-054,  or  28°-065  when  corrected  for  stem. 
363-4  =  28° -055,  or  28° -066  when  corrected  for  stem. 

Specific  heat  28°  —  100°  _  ,  .Of)24 
Specific  heat  18°  -    28°  ~ 

Other  experiments  gave  1-0015  and  1-0060,  the  mean  of  all  of  which 


398  HENEY  A.  EOWLAXD 

is  1-0033.     Regnault's  formula  gives  1-005;  but  going  directly  to  his 
experiments,  we  get  about  1-004,  the  other  quantity  being  for  110°. 

The  agreement  is  very  satisfactory,  though  one  would  expect  my 
small  apparatus  to  lose  more  of  the  heat  of  the  boiling  water  than 
Regnault's.  Indeed,  for  high  temperatures  my  apparatus  is  much 
inferior  to  Regnault's,  and  so  I  have  not  attempted  any  further  experi- 
ments at  high  temperatures. 

My  only  object  was  to  confirm  by  this  method  the  results  deduced 
from  the  experiments  on  the  mechanical  equivalent;  and  this  I  have 
done,  for  the  experiments  nearly  all  show  that  the  specific  heat  of  water 
decreases  to  about  30°,  after  which  it  increases.  But  the  mechanical 
equivalent  experiments  give  by  far  the  most  accurate  solution  of  the 
problem;  and,  indeed,  give  it  with  an  accuracy  hitherto  unattempted  in 
experiments  of  this  nature. 

But  whether  water  increases  or  decreases  in  specific  heat  from  0°  to 
30°  depends  upon  the  determination  of  the  reduction  to  the  air  ther- 
mometer. According  to  the  mercurial  thermometers  Nos.  6163,  6165  and 
6166,  treating  them  only  as  mercurial  thermometers,  the  specific  heat  of 
water  up  to  30°  is  nearly  constant,  ~bui  by  the  air  thermometer,  or  ~by  the 
Kew  standard  or  Fastre,  it  decreases. 

Full  and  complete  tables  of  comparison  are  published,  and  from  them 
any  one  can  satisfy  himself  of  the  facts  in  the  case. 

I  am  myself  satisfied  that  I  have  obtained  a  very  near  approximation 
to  absolute  temperatures,  and  accept  them  as  the  standard.  And  by 
this  standard  the  specific  heat  of  water  undoubtedly  decreases  from  0° 
to  about  30°. 

To  show  that  I  have  not  arrived  at  this  result  rashly,  I  may  mention 
that  I  fought  against  a  conclusion  so  much  at  variance  with  my  precon- 
ceived notions,  but  was  forced  at  last  to  accept  it,  after  studying  it  for 
more  than  a  year,  and  making  frequent  comparisons  of  thermometers, 
and  examinations  of  all  other  sources  of  error. 

However  remarkable  this  fact  may  be,  being  the  first  instance  of  the 
decrease  of  the  specific  heat  with  rise  of  temperature,  it  is  no  more 
remarkable  than  the  contraction  of  water  to  4°.  Indeed,  in  both  cases 
the  water  hardly  seems  to  have  recovered  from  freezing.  The  specific 
heat  of  melting  ice  is  infinite.  Why  is  it  necessary  that  the  specific 
heat  should  instantly  fall,  and  then  recover  as  the  temperature  rises? 
Is  it  not  more  natural  to  suppose  that  it  continues  to  fall  even  after  the 
ice  is  melted,  and  then  to  rise  again  as  the  specific  heat  approaches  infin- 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  399 

ity  at  the  boiling  point?    And  of  all  the  bodies  which  we  should  select  as 
probably  exhibiting  this  property,  water  is  certainly  the  first. 

(&.)  Heat  Capacity  of  Calorimeter 

During  the  construction  of  the  calorimeter,  pieces  of  all  the  material 
were  saved  in  order  to  obtain  the  specific  heat.  The  calorimeter  which 
Joule  used  was  put  together  with  screws,  and  with  little  or  no  solder. 
But  in  my  calorimeter  it  was  necessary  to  use  solder,  as  it  was  of  a  much 
more  complicated  pattern.  The  total  capacity  of  the  solder  used  was 
only  about  -$fa  of  the  total  capacity  including  the  water;  and  if  we 
should  neglect  the  whole,  and  call  it  copper,  the  error  would  be  only 
about  y-gVfr-  Hence  it  was  considered  sufficient  to  weigh  the  solder 
before  and  after  use,  being  careful  to  weigh  the  scraps.  The  error  in 
the  weight  of  solder  could  not  possibly  have  been  as  great  as  ten  per 
cent,  which  would  affect  the  capacity  only  1  part  in  12,000. 

To  determine  the  nickel  used  in  plating,  the  calorimeter  was  weighed 
before  and  after  plating;  but  it  weighed  less  after  than  before,  owing 
to  the  polishing  of  the  copper.  But  I  estimated  the  amount  from  the 
thickness  of  a  loose  portion  of  the  plating.  I  thus  found  the  approxi- 
mate weight  of  nickel,  but  as  it  was  so  small,  I  counted  it  as  copper. 
The  following  are  the  constituents  of  the  calorimeter: — 

Thick  sheet  copper 25-1  per  cent. 

Thin  sheet  copper 45-7        " 

Cast  brass 17-9        " 

Boiled  or  drawn  brass 5-7        " 

Solder    4-0 

Steel  1-6        " 


100-0 
Mckel    -3        " 

To  determine  the  mean  specific  heat,  the  basket  of  a  Regnault's 
apparatus  was  filled  with  the  scraps  in  the  above  proportion,  allowing 
the  basket  of  brass  gauze,  which  was  very  light,  to  count  toward  the 
drawn  brass.  The  specific  heat  was  then  determined  between  20°  and 
100°,  and  between  about  10°  and  40°.  Between  20°  and  100°  the 
ordinary  steam  apparatus  was  used,  but  between  10°  and  40°  a  special 
apparatus  filled  with  water  was  used,  the  water  being  around  the  tube 
containing  the  basket,  in  the  same  manner  as  the  steam  is  in  the 


400  HENRY  A.  EOWLAND 

original  apparatus.  In  the  calorimeter  a  stirrer  was  used,  so  that  the 
basket  and  water  should  rapidly  attain  the  same  temperature.  The  water 
was  weighed  before  and  after  the  experiment,  to  allow  for  evaporation. 
A  correction  of  about  1  part  in  1000  was  made,  on  account  of  the  heat 
lost  by  the  basket  in  passing  from  the  apparatus  to  the  calorimeter,  in 
the  100°  series,  but  no  correction  was  made  in  the  other  series.  The 
thermometers  in  the  calorimeter  were  Nos.  6163  and  6166  in  the  dif- 
ferent experiments. 

The  principal  difficulty  in  the  determination  is  in  the  correction  for 
radiation,  and  for  the  heat  which  still  remains  in  the  basket  after  some 
time.  After  the  basket  has  descended  into  the  water,  it  commences  to 
give  out  heat  to  the  water;  this,  in  turn,  radiates  heat;  and  the  tempera- 
ture we  measure  is  dependent  upon  both  these  quantities. 

Let  T  =  temperature  of  the  basket  at  the  time  t 

i(        IT"    _  «  «  (I  ((  0 

«        JW —  «  «  «  «  <-£ 

"     0    —  "  "       water         «  t 

«        Ql      __  «  «  «  «  Q 

(I  Q'l        __  («  ((  ((  «  QO 

6"  =  T". 
We  may  then  put  approximately 

T—T"  =  (T  -  T")e-~z, 
where  c  is  a  constant.     But 

rpl  rpn  rpi  rp 

0"  —  0'     '  '    Q  —  tf    ' 

hence 


To  find  c  we  have 

1          0"  —  0' 

t         3    ff'  —  0 

where  6"  can  be  estimated  sufficiently  accurately  to  find  C"  approxi- 
mately. 

These  formulae  apply  when  there  is  no  radiation.     When  radiation 
takes  place,  we  may  write,  therefore,  when  t  is  not  too  small, 


0—0'  =  (0"  —  #')(!  -  e-~T) 

where  0  is  a  coefficient  of  radiation,  and  t0  is  a  quantity  which  must  be 
subtracted  from  t,  as  the  temperature  of  the  calorimeter  does  not  rise 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  401 

instantaneously.     To  estimate  t0,  Ta  being  the  temperature  of  the  air, 
we  have,  according  to  Newton's  law  of  cooling, 

t 

C(t-  Q  =    „  °_  T    C(0  —  Ta}  dt  nearly, 

~        a  «/ 

0"  —  0' 
t»  =  c  tf,  _T  nearly, 

ri 

where  it  is  to  be  noted  that  -,,     _   is  nearly  a  constant  for  all  values  of 

"  •*-  a 

0"—  Ta    according  to  Newton's  law  of  cooling. 

The  temperature  reaches  a  maximum  nearly  at  the  time 

0"—o't 

and  if  6m  is  the  maximum  temperature,  we  have  the  value  of  0"  as 
follows : 

0"  =  T"  =  0^  +  C(tm  +  c—L): 

\.    m      '  v/    7 


and  this  is  the  final  temperature  provided  there  was  no  loss  of  heat. 

When  the  final  temperature  of  the  water  is  nearly  equal  to  that  of 
the  air,  C  will  be  small,  but  the  time  im  of  reaching  the  maximum 
will  be  great.  If  a  is  a  constant,  we  can  put  C  =  a  (6"  —  Ta),  and 
G(tn  +  c  —  £0)  will  be  a  minimum,  when 


or       a  =  »- 


ac 

That  is,  the  temperature  of  the  air  must  be  lower  than  the  tempera- 
ture of  the  water,  so  that  Ta  =  6"  as  nearly  as  possible  ;  but  the  for- 
mula shows  that  this  method  makes  the  corrections  greater  than  if  we 
make  Ta  =  d',  the  reason  being  that  the  maximum  temperature  is  not 
reached  until  after  an  infinite  time.  It  will  in  practice,  however,  be 
found  best  to  make  the  temperature  of  the  water  at  the  beginning 
about  that  of  the  air.  It  is  by  far  the  best  and  easiest  method  to 
make  all  the  corrections  graphically,  and  I  have  constructed  the  follow- 
ing graphical  method  from  the  formula?. 

First  make  a  series  of  measurements  of  the  temperature  of  the  water 
of  the  calorimeter,  before  and  after  the  basket  is  dipped,  together  with 
the  times.  Then  plot  them  on  a  piece  of  paper  as  in  Fig.  5,  making 
the  scale  sufficiently  large  to  insure  accuracy.  Five  or  ten  centimeters 
to  a  degree  are  sufficient. 

nab  c  d  is  the  plot  of  the  temperature  of  the  water  of  the  calori- 
26 


402 


HENRY  A.  EOWLAND 


meter,  the  time  being  indicated  by  the  horizontal  line.  Continue  the 
line  d  c  until  it  meets  the  line  I  a.  Draw  a  horizontal  line  through 
the  point  I.  At  any  point,  &,  of  the  curve,  draw  a  tangent  and  also  a 
vertical  line  bg;  the  distance  eg  will  be  nearly  the  value  of  the  con- 
stant c  in  the  formula?.  Lay  off  I  f  equal  to  c,  and  draw  the  line  fJiTc 
through  the  point  h,  which  indicates  the  temperature  of  the  atmos- 
phere or  of  the  vessel  surrounding  the  calorimeter.  Draw  a  vertical 
line,  j  Ic,  through  the  point  Tc.  From  the  point  of  maximum,  c,  draw 
a  line,  j  c,  parallel  to  d  m,  and  where  it  meets  Ic  j  will  be  the  required 
point,  and  will  give  the  value  of  6".  Hence,  the  rise  of  temperature, 
corrected  for  all  errors,  will  be  Ic  j. 

This  method,  of  course,  only  applies  to  cases  where  the  final  tem- 
perature of  the  calorimeter  is  greater  than  that  of  the  air;  otherwise 
there  will  be  no  maximum. 


FIG.  5. 

In  practice,  the  line  d  m  is  not  straight,  but  becomes  more  and  more 
nearly  parallel  to  the  base  line.  This  is  partly  due  to  the  constant 
decrease  of  the  difference  of  temperature  between  the  calorimeter  and 
the  air,  but  is  too  great  for  that  to  account  for  it.  I  have  traced  it  to 
the  thin  metal  jacket  surrounding  the  calorimeter,  and  I  must  condemn, 
in 'the  strongest  possible  manner,  all  such  arrangements  of  calorimeters 
as  have  such  a  thin  metal  jacket  around  them.  The  jacket  is  of  an 
uncertain  temperature,  between  that  of  the  calorimeter  and  the  air. 
When  the  calorimeter  changes  in  temperature,  the  jacket  follows  it  but 
only  after  some  time;  hence,  the  heat  lost  in  radiation  is  uncertain. 
The  true  method  is  to  have  a  water  jacket  of  constant  temperature,  and 
then  the  rate  of  decrease  of  temperature  will  be  nearly  constant  for  a 
long  time. 

The  following  results  have  been  obtained  by  Mr.  Jacques,  Fellow  of 
the  University,  though  the  first  was  obtained  by  myself.  Corrections 
were,  of  course,  made  for  the  amount  of  thermometer  stem  in  the  air. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  403 

Temperature.  Mean  Specific  Heat. 

24°  to  100°  -0915 

26°  to  100°  -0915 

25°  to  100°  -0896 

13°  to     39°  -0895 

14°  to     38°  -0885 

9°  to     41°  -0910 

To  reduce  these  to  the  mean  temperature  of  0°  to  40°,  I  have  used 
the  rate  of  increase  found  by  Bede  for  copper.  They  then  become,  for 
the  mean  from  0°  to  40°, — 

•0897 
•0897 
•0878 
•0893 
•0883 
•0906 


Mean  -0892   ±  -00027 

As  the  capacity  of  the  calorimeter  is  about  four  per  cent  of  that  of 
the  total  capacity,  including  the  water,  this  probable  error  is  about  -g-oW 
of  the  total  capacity,  and  may  thus  be  considered  as  satisfactory. 

I  have  also  computed  the  mean  specific  heat  as  follows,  from  other 
observers : — 

Copper  between  20°  and  100°  nearly. 

•0949  Dulong. 

•0935  Eegnault. 

•0952  Eegnault. 

•0933  Bede. 

•0930  Kopp. 


•0940 

This  reduced  to  between  0°  and  40°  by  Bede's  formula  gives  -0922. 
Hence  we  have  the  following  for  the  calorimeter: 2* — 

24  The  cast  brass  was  composed  of  28  parts  of  copper,  2  of  tin,  1  of  zinc,  and  1  of 
lead.  The  rolled  brass  was  assumed  to  have  the  same  composition.  The  solder  was 
assumed  to  be  made  of  equal  parts  of  tin  and  lead. 


404  HEXRY  A.  ROWLAND 

Per  cent.  Specific  Heat  between  0°  and  40°  C. 

Copper  91-4  -0922 

Zinc  -7  -0896 

Tin  3-6  -0550 

Lead  2-7  -0310 

Steel  1-6  -1110 


Mean  -0895 

The  close  agreement  of  this  number  with  the  experimental  result 
can  only  be  accidental,  as  the  reduction  to  the  air  thermometer  would 
decrease  it  somewhat,  and  so  make  it  even  lower  than  mine.  However, 
the  difference  could  not  at  most  amount  to  more  than  0-5  per  cent, 
which  is  very  satisfactory. 

The  total  capacity  of  the  calorimeter  is  reckoned  as  follows : — 

Weight  of  calorimeter 3-8712  kilogrammes. 

Weight  of  screws  .  . .  . -0016  kilogrammes. 

Weight  of  part  of  suspending  wires.  .    -0052  kilogrammes. 
Total  weight 3-8780  kilogrammes. 

Capacity  =  3-878  X  '0892  =  -3459  kilogrammes. 

To  this  must  be  added  the  capacity  of  the  thermometer  bulb  and 
several  inches  of  the  stem,  and  of  a  tube  used  as  a  safety  valve,  and  we 
must  subtract  the  capacity  of  a  part  of  the  shaft  which  was  joined  to 
-the  shaft  turning  the  paddles.  Hence, 

•3459 
-f-  -0011 
4-  -0010 
—  •0010 


Capacity  =-3470 

As  this  is  only  about  four  per  cent  of  the  total  capacity,  it  is  not 
necessary  to  consider  the  variation  of  this  quantity  with  the  tempera- 
ture through  the  range  from  0°  to  40°  which  I  have  used. 

IV.— DETERMINATION  OF  EQUIVALENT 
(o.)  Historical  Remarks 

The  history  of  the  determination  of  the  mechanical  equivalent  of  heat 
is  that  of  thermodynamics,  and  as  such  it  is  impossible  to  give  it  at 
length  here. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  405 

I  shall  simply  refer  to  the  few  experiments  which  a  priori  seem  to 
possess  the  greatest  value,  and  which  have  been  made  rather  for  the 
determination  of  the  quantity  than  for  the  illustration  of  a  method, 
and  shall  criticise  them  to  the  best  of  my  ability,  to  find,  if  possible,  the 
cause  of  the  great  discrepancies. 

1.    GENERAL  REVIEW  OF  METHODS 

Whenever  heat  and  mechanical  energy  are  converted  the  one  into 
the  other,  we  are  able  by  measuring  the  amounts  of  each  to  obtain  the 
ratio.  Every  equation  of  thermodynamics  proper  is  an  equation 
between  mechanical  energy  and  heat,  and  so  should  be  able  to  give  us 
the  mechanical  equivalent.  Besides  this,  we  are  able  to  measure  a 
certain  amount  of  electrical  energy  in  both  mechanical  and  heat  units, 
and  thus  to  also  get  the  ratio.  Chemical  energy  can  be  measured  in 
heat  units,  and  can  also  be  made  to  produce  an  electric  current  of  known 
mechanical  energy.  Indeed,  we  may  sum  up  as  follows  the  different 
kinds  of  energy  whose  conversion  into  one  another  may  furnish  us  with 
the  mechanical  equivalent  of  heat.'  And  the  problem  in  general  would 
be  the  ratio  by  which  each  kind  of  energy  may  be  converted  into  each  of 
the  others,  or  into  mechanical  or  absolute  units. 

a.  Mechanical  energy. 

6.  Heat. 

c.  Electrical  energy. 

d.  Magnetic  energy. 

e.  Gravitation  energy. 

f.  Radiant  energy. 

g.  Chemical  energy. 
h.  Capillary  energy. 

Of  these  different  kinds  of  energy,  only  the  first  five  can  be  measured 
other  than  by  their  conversion  into  other  forms  of  energy,  although  Sir 
William  Thomson,  by  the  introduction  of  such  terms  as  "  cubic  mile  of 
sunlight,"  has  made  some  progress  in  the  case  of  radiation.  Hence  for 
these  five  only  can  the  ratio  be  known. 

Mechanical  energy  is  measured  by  the  force  multiplied  by  the  dis- 
tance through  which  the  force  acts,  and  also  by  the  mass  of  a  body  multi- 
plied by  half  the  square  of  its  velocity.  Heat  is  usually  referred  to  the 
quantity  required  to  raise  a  certain  amount  of  water  so  many  degrees, 
though  hitherto  the  temperature  of  the  water  and  the  reduction  to  the 
air  thermometer  have  been  almost  neglected. 


406  HENRY  A.  ROWLAND 

The  energy  of  electricity  at  rest  is  the  quantity  multiplied  by  half  the 
potential ;  or  of  a  current,  it  is  the  strength  of  current  multiplied  by  the 
electro-motive  force,  and  by  the  time ;  or  for  all  attractive  forces  varying 
inversely  as  the  square  of  the  distance,  Sir  William  Thomson  has  given 
the  expression 


TF/**' 


where  R  is  the  resultant  force  at  any  point  in  space,  and  the  integral  is 
taken  throughout  space. 

These  last  three  kinds  of  energy  are  already  measured  in  absolute 
measure  and  hence  their  ratios  are  accurately  known.  The  only  ratio, 
then,  that  remains  is  that  of  heat  to  one  of  the  others,  and  this  must  be 
determined  by  experiment  alone. 

But  although  we  cannot  measure  f,  g,  h  in  general,  yet  we  can  often 
measure  off  equal  amounts  of  energy  of  these  kinds.  Thus,  although  we 
cannot  predict  what  quantities  of  heat  are  produced  when  two  atoms  of 
different  substances  unite,  yet,  when  the  same  quantities  of  the  same 
.  substances  unite  to  produce  the  same  compound,  we  are  safe  in  assuming 
that  the  same  quantity  of  chemical  energy  comes  into  play. 

According  to  these  principles,  I  have  divided  the  methods  into  direct 
and  indirect. 

Direct  methods  are  those  where  &  is  converted  directly  or  indirectly 
into  a,  c,  d,  or  e,  or  vice  versa. 

Indirect  methods  are  those  where  some  kind  of  energy,  as  g,  is  con- 
verted into  &,  and  also  into  a,  c,  d,  or  e. 

In  this  classification  I  have  made  the  arrangement  with  respect  to 
the  kinds  of  energy  which  are  measured,  and  not  to  the  intermediate 
steps.  Thus  Joule's  method  with  the  magneto-electric  machine  would 
be  classed  as  mechanical  energy  into  heat,  although  it  is  first  converted 
into  electrical  energy.  The  table  does  not  pretend  to  be  complete,  but 
gives,  as  it  were,  a  bird's-eye  view  of  the  subject.  It  could  be  extended 
by  including  more  complicated  transformations;  and,  indeed,  the  sym- 
metrical form  in  which  it  is  placed  suggests  many  other  transformations. 
As  it  stands,  however,  it  includes  all  methods  so  far  used,  besides  many 
more. 

In  the  table  of  indirect  methods,  the  kind  of  energy  mentioned  first  is 
to  be  eliminated  from  the  result  by  measuring  it  both  in  terms  of  heat 
and  one  of  the  other  kinds»of  energy,  whose  value  is  known  in  absolute 
or  mechanical  units. 


ON  THE  MECHANICAL  EQUIVALENT  or  HEAT 


407 


It  is  to  be  noted  that,  although  it  is  theoretically  possible  to  measure 
magnetic  energy  in  absolute  units,  yet  it  cannot  be  done  practically  with 
any  great  accuracy,  and  is  thus  useless  in  the  determination  of  the 
equivalent.  It  could  be  thus  left  out  from  the  direct  methods  without 
harm,  as  also  out  of  the  next  to  last  term  in  the  indirect  methods. 


TABLE  XXV.— SYNOPSIS  OF  METHODS  FOR  OBTAINING  THE 
MECHANICAL  EQUIVALENT  OF  HBAT. 


j  Mechanical  Energy 
J.  Gravltatlon 


4    ft.  Heat,  Electric  Energy  . 


y.  Heat,  Magnetic  Energy 


1.  Reversible  process 


I  2.  Irreversible 
cess 


pro- 


l.  Reversible  process 


2.  Irreversible 
cess 


pro- 


f  a.  Expansion  or  compression  ac- 
cording to  adlabatlc  curve. 
6.  Expansion  or  compression  ac- 
cording to  Isothermal  curve. 

c.  Expansion  or  compression  ac- 

cording to  any  curve  with  re- 
generator. 

d.  Electro-magnetic  engine  driven 

by  thermo-electric  pile  In  a 
circuit  of  no  resistance. 

a.  Friction,  percussion,  etc. 

6.  Heat  from  magneto-electric  cur- 
rents, or  electric  machine. 

a.  Thermo-electric  currents. 

ft.  Pyro-electric  phenomena  (prob- 
ably). 

a.  Heating  of  wire  by  current,  or 
heat  produced  by  discharge 
of  electric  battery. 


(  a.  Thermo-electric   current    mag- 

1.  Reversible  process    '.          netizlng  a  magnet  in  a  circuit 

of  no  resistance. 

2.  Irreversible      pro-  (  a.  Heating   of   magnet  when   de- 

cess  I          magnetized. 


a.  Radiant  Energy,  Heat 

(Radiant  energy    absorbed 
by  blackened  eurface.) 


0.  Chemical  Energy,  Heat 

(Combustion,  etc.) 


y.  Capillary  energy,  Heat 

(Heat  produced  when  a  liq- 
uid Is  absorbed  by  a  po- 
rous solid.) 


S.  Electrical  energy,  Heat 

(Heat  generated  in  a  wire 
by  an  electrical  current.) 


e.  Magnetic  Energy,  Heat 

(Heat  generated  on  demag- 
netizing a  magnet.) 


Gravitation  Energy,  Heat — 
(Heat  generated  by  a  tail- 
ing body.) 


Crooke's  radiometer. 
Thermo-electric  pile. 
Thermo-electric  pile  with  electro- 
magnet In  circuit. 

1.  Cannon. 

2.  Electro-magnet  machine  run  by 

galv.  battery. 
Current  from  battery. 
Electro-magnet   magnetized  by  a 

battery  current. 


a.  Mechanical  Energy. 

5.  Electrical         " 

c.  Magnetic  " 

d.  Gravitation     " 

a.  Mechanical  Energy 

6.  Electrical         " 

c.  Magnetic          "         •? 

d.  Gravitation      " 

a.  Mechanical  Energy.      Movement  of  liquid  by  capillarity. 
.    _.  „         j  Electrical  currents  from  capillary 

"•  *•'  {          action  at  surface  of  mercury. 

c.  Magnetic  " 

d.  Gravitation      "  Raising  of  liquid  by  capillarity. 

agneto-electric  or   electro-mag- 
netic   machine.    Electric    at- 
traction. 
Electro-magnet. 


a.  Mechanical  Energy 

6.  Magnetic          " 
c.  Gravitation      " 


j  M 


a.  Mechanical  Energy 


6.  Electrical 
c.  Gravitation 


Armature  attracted  by  a  perma- 
nent Magnet. 

Induced  current  on  demagnetizing 
a  magnet. 


a.  Mechanical  Energy.  J  Velocity   Imparted    to    a    falling 
6.  Electrical         "          I         body. 


c.  Magnetic 


408 


HENRY  A.  ROWLAND 


TABLE  XXVI. — HISTORICAL  TABLE  OF  EXPERIMENTAL  RESULTS. 


Method 
in 
General. 

Method  in  Particular. 

Observer. 

Date. 

Result. 

A 
A 

A 
A 

/: 
S 

a 
a 

a 

ft 

;-' 
ft 

1 

2 

9 

'3 

n 
b 

a 

b 

or 
c 

a 

b 
a 

2 
1 

Compression  of  air  

Joule" 
Joule" 

1845         443-8 
1845         437-8 

Expansion         "        

Theory  of  gases  (see  below)  .    

"          vapors  (see  below)  

Experiments  on  steam-engine  

Hirnv" 
Hirnv" 

Edlund*1" 

Rumfordix 
Joule1" 
Joulelv 
Joulev 
Joulevi 
Joulevl 
Joulevi 
Him™1 
Favrelx 
Him1"1 
Him''11 
HirnT« 
Him*11 
HirnT" 
Puluj*1" 
Joule 

Joule"1 

Vioile* 

Quintus 
Icilius*1 
also  Weber 
Lenz,  also 
Weber 
Joule*1" 
H.  F.  Weber*1' 

Joule"1 
FavreIV 

Weber, 
Boscha, 
Favre,  and 
Silbermann 

Joule 
Boscha*11 

1857 
1860-1 

1865  J 

1798 
1843 
1845 
1847 
1850 
1850 
1850 
1857 
1858 
1858 
1858 
1860-1 
1860-1 
1860-1 
1876' 
1878 

1843 
1870  J 

(.1857 

J1859J 

1867 

1878 

1843 

1858 

Il857 
J1859 

413-0 
420-432 
443-6 
430-1 
428-3 
940ft.lbs. 
424-6 
488-3 
428-9 
423-9 
424-7 
425-2 
371-6 
413-2 
400-450 
425-0 
432-0 
432-0 
425-0 
426-6 
423-9 

460-0 
435.2 
434-9 
435-8 
437  '4 

399-7 

396-4 
478-2 
429-5 
428-15 

499-0 
443-0 

432-1 
419-5 

ti               ti             11 

Expansion  and  contraction  of  metals.  .  . 
Boring  of  cannon  

Friction  of  water  in  tubes  

"                 «'      in  calorimeter  

<*                 "      in  calorimeter  

"                 "      in  calorimeter  

Friction  of  mercury  in  calorimeter  

"           plates  of  iron           

«           metals       

"           metals  in  mercury  calor.  .  .  . 
"           metals.  .  .•  

Boring  of  metals  .        

Water  in  balance  afrottement  

Flow  of  liquids  under  strong  pressure.  . 
Crushing  of  lead  

Water  in  calorimeter  

Heating  by  magneto-electric  currents.  .  . 

Heat  generated  in  a  disc  between  the  ) 
poles  of  a  magnet       f 

Heat  developed  in  wire  of  known  ab-  \ 
solute  resistance  ") 

Do.                do.                do. 

Do.                do.               do. 
Do.                do.                do. 

Diminishing  of  the  heat  produced  in  a  1 
battery   circuit   when    the    current  V 
produces  work        ) 

Do.                do.               do. 

Heat  due  to  electrical  current,  electro-  "| 
chemical    equivalent     of     water  = 
•009379,  absolute  resistance  electro-  i 
motive  force  of  Daniell   cell,  heat  [ 
developed  by  action  of  zinc  on  sul.  | 
of  copper  J 

Heat  developed  in  Daniell  cell  

Electro-motive  force  of  Daniell  cell.  .  .  . 

Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


409 


2.    KESULTS  OF  BEST  DETERMINATIONS  ' 

On  the  basis  of  this  table  of  methods  I  have  arranged  the  following 
table,  showing  the  principal  results  so  far  obtained. 

In  giving  the  indirect  results,  many  persons  have  only  measured  one 
of  the  transformations  required;  and  as  it  would  lengthen  out  the  table 
very  much  to  give  the  complete  calculation  of  the  equivalent  from  these 
selected  two  by  two,  I  have  sometimes  given  tables  of  these  parts.  As 
the  labor  of  looking  up  and  reducing  these  is  very  great,  it  is  very 
possible  that  there  have  been  some  omissions. 

I  have  taken  the  table  published  by  the  Physical  Society  of  Berlin,1  as 
the  basis  down  to  1857,  though  many  changes  have  been  made  even 
within  this  limit. 

I  shall  now  take  up  some  of  the  principal  methods,  and  discuss  them 
somewhat  in  detail. 


Method  from  Theory  of  Gases 

As  the  different  constants  used  in  this  method  have  bf en  obtained  by 
many  observers,  I  first  shall  give  their  results. 

TABLE  XXVII. — SPECIFIC  HEAT  OF  GASES. 


Limit  to 
Temperature. 

Approximate 
Temperature 
of  Water. 

Temperature 
reduced  to 

Specific  Heat. 

Air  

, 

Mercurial 

i    -2669      I 

Delaroche  and 

20°  to  210° 

-iZ  { 

Thermometer 

Air 
Thermometer 

y          ( 

i    •  23751"' 

Berard. 
Regnault. 

20°  to  100° 

20°        j 

Mercurial 
Thermometer 

j    -2389"" 

E.Wiedemann. 

Hydrogen..  . 

.  .j 

Mercurial 

\3-2936      -( 

Delaroche  and 

15°  to  200° 

1 

12°-2   | 

Thermometer 

Air 
Thermometer 

/                    t 
1  3  -4090"1 

Berard. 
Regnault. 

21°  to  100° 

21°        | 

Mercurial 
Thermometer 

13-410"" 

E.Wiedemann. 

25  Taking  mean  results  on  page  101  of  Rel.  des  Exp.,  torn,  ii., 


410  HENRY  A.  KOWLAND 

TABLE    XXVIII. — COEFFICIENT    OF    EXPANSION    OF    AlR    UNDER    CONSTANT    VOLUME 


Taking  Expansion  of  Mercury 
according-  to  Regnault. 

Taking  Expansion  of  Mercury 
according  to  Wiillner's  Re- 
calculation   of    Regnault's 
Experiments. 

Regnault  

•  0036655 

•0036687 

Magnus     

•0036678 

•0036710 

Jolly  

•  0036695 

•0036727 

Rowland  

•0036675 

•0036707 

Mean      

•0036676 

•0036708 

TABLE  XXIX.— RATIO  OF  SPECIFIC  HEATS  OF  AIR. 


Method. 

Observer. 

Date. 

Ratio 
of  Specific 
Heats. 

Method  of  Clement  &  Desormes,  ) 
globe  20  litres  I 

Clement  &                       | 
Desormes""'  J 

1812 
Published  in 

t    1-354 

Never  fully  published  

Gay-Lussac  et  Welter1'1. 

1819 

1-3748 

Method  of  C16ment  &  Desormes.  . 
Using  Breguet  thermometer  

Delaroche  et  Berard*11  .  . 
Favre  &  Silbermann""'. 

1853 

1-249 
1-421 

Clement  &  Desormes,  globe  39  ) 

Masson"  

1858 

1-4196 

Clement  &  Desormes  

Weisbach"1.  .  .  .  '.  

1859 

1  •  4025 

C16ment  &  Desormes,  globe  10  ) 

Hirnxxli          

1861 

1-3845 

litres  ) 

Passage  of  gas  from  one  vessel  ) 

Cazin"lv  

1862 

1-41 

into  another,  globes  60  litres  j 
Pressure  in  globe  changed  by  ) 

1863 

aspirator,  globe  25  litres.  .  .  .  ) 
Heating  of  gas  by  electric  cur-  ) 

Jamin  &  Richard1""1  .  .  . 

1864 

1-41 

Clement  &  D6sormes  

Tresca  et  Laboulaye"'1. 

1864 

Barometer  under  air-pump  re-  ) 

Kohlrausch1"'  

1869 

1-302 

ceiver  of  6  litres  ) 

Compression  and  expansion  of  ) 

Regnault  

1871    J 

Results  lost 
in  the  siege 

C16ment&D6sormes  with  metal-  ) 

R6ntgen"v"  

I 

1873 

of  Paris. 
1-4053 

lie  manometer,  globe  70  litres  ) 
Compression  of  gas  by  piston. 

AmagatXXI  

1874 

1-397 

ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


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412  HENRY  A.  KOWLAND 

References.     (Tables  XXVI  to  XXX.) 

j  Physical  Society  of  Berlin,  Fort,  tier  Phys.,  1858. 
"  Joule,    Phil.    Mag.,    ser.   3,    TO!,    xxvi.        See    also    Mec.    Warmeaquivalent, 

Gesammelte  Abhandlungen  von  J.  P.  Joule,  Braunschweig,  1872. 
111  Joule,  Phil.  Mag.,  ser.  3,  vol.  xxiii.     See  also  2  above. 
iv      <i         «         u         u          u      xxvi.    .          "  " 

v         u  u  u  u  u        xxvii.  "  " 

»i         «  u  «  u  u        Xxxi.  "  " 

vii  Hirn,  Theorie  Mec.  de  la  Chaleur,  ser.  1,  3me  ed. 
Tiii  Edlund,  Pogg.  Ann.,  cxiv.  I,  1865. 

ix  Favre,  Comptes  Rend.,  Feb.  15,  1858;  also  Phil.  Mag.,  xv.  406. 
x  Violle,  Ann.  de  Chim.,  ser.  4,  xxii.  64. 
xi  Quintus  Icilius,  Pogg.  Ann.,  ci.  69. 
xli  Boscha,  Pogg.  Ann.,  cviii.  162. 
xiii  Joule,  Report  of  the  Committee  on  Electrical  Standards  of  the  B.  A.,  London, 

1873,  p.  175. 

xiv  H.  F.  Weber,  Phil.  Mag.,  ser.  5,  v.  30. 
xv  Favre,  Comptes  Rend.,  xlvii.  599. 
XTi  Regnault,  Rel.  des  Experiences,  torn.  ii. 
xvil  E.  Wiedemann,  Pogg.  Ann.,  clvii.  1. 

xvl11  Clement  et  Desormes,  Journal  de  Physique,  Ixxxix.  333,  1819. 
xlx  Laplace,  Mec.  Celeste,  v.  125. 

xx  Masson,  Ann.  de  Chim.  et  de  Phys.,  ser.  3,  torn.  liii. 
xxi  Weisbach,  Der  Civilingenieur,  Neue  Folge,  Bd.  v.,  1859. 
xxii  Hirn,  Theorie  Mec.  de  la  Chaleur,  i,  111. 
xxiii  Favre  et  Silbermann,  Ann.  de  Chim.,  ser.  3,  xxxvii.  1851. 
xxiv  Cazin,  Ann.  de  Chim.,  ser.  3,  torn.  Ixvi. 
xxv  Dupr6,  Ann.  de  Chim.,  3me  ser.,  Ixvii.  359,  1863. 
xxvi  Kohlrausch,  Pogg.  Ann.,  cxxxvi.  618. 
xsvii  Rontgen,  Pogg.  Ann.,  cxlviii.  603. 
xxvlil  Jamin  et  Richard,  Comptes  Rend.,  Ixxi.  336. 
xxix  Tresca  et  Laboulaye,  Comptes  Rend.,  Iviii.  358.     Ann.   du  Conserv.  des  Arts 

et  Metiers,  vi.  365. 

xxx  Amagat,  Comptes  Rend.,  Ixxvii.  1325. 
xxxi  Mem.  de  1'Acad.  des  Sci.,  1738,  p.  128. 
xxxii  Benzenberg,  Gilbert's  Annalen,  xlii.  1. 
xxxm  Goldingham,  Phil.  Trans.,  1823,  p.  96. 

xxxiv  Ann.  de  Chim.,  1822,  xx.  210  also,  (Euvres  de  Arago,  Mem.  Sci.,  ii.  1. 
xxxv  Stampfer  und  Von  Myrbach,  Pogg.  Ann.,  v.  496. 
xxxvi  Moll  and  Van  Beek,  Phil.  Trans.,  1824,  p.  424.     See  also  Shroder  van  der  Kolk, 

Phil.  Mag.,  1865. 
xxxvii  parry  an(j  Foster,  Journal  of  the  Third  Voyage,  1824-5,  Appendix,  p.  86.  Phil. 

Trans.,  1828,  p.  97. 

xxxviii  Savart,  Ann.  de  Chim.;  ser.  2,  Ixxi.  20.     Recalculated. 
XMIX  Bravais  et  Martins,  Ann.  de  Chim.,  ser.  3,  xiii.  5. 
11  Regnault,  Rel.  des  Exp.,  iii.  533. 

xli  Delaroche  et  Berard,  Ann.  de  Chim.,  Ixxxv.  72  and  113. 
xl"  Puluj,  Pogg.  Ann.,  clvii.  656. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  413 

Estimating  the  weight  rather  arbitrarily,  I  have  combined  them  as 
follows : 

No. 

1 
2 
3 

4 
5 
6 
7 
8 
9 
10 


Velocity  at  0°-  C. 
Dry  Air. 

Estimated  Weight 
of  Observation. 

332-6 

2 

332-7 

2 

330-9 

2 

330-8 

4 

332-5 

3 

332-8 

7 

.332-0 

1 

331-8 

1 

332-4 

4 

330-7 

10 

Mean       331-75 

Or,  corrected  for  the  normal  carbonic  acid  in  the  atmosphere,  it  be- 
comes 331-78  metres  per  second  in  dry  pure  air  at  0°  C. 

From  Eegnault's   experiments   on   the  velocity  in  pipes   I  find  by 
graphical  means  331-4  m.  in  free  air,  which  is  very  similar  to  the  above. 

Calculation  from  Properties  of  Gases 

K=  specific  heat  of  gas  at  constant  pressure. 
lc  =  specific  heat  of  gas  at  constant  volume. 
p  =  pressure  in  absolute  units  of  a  unit  of  mass. 
v  =  volume  in  absolute  units  of  a  unit  of  mass. 
H  =  absolute  temperature. 
J=  Joule's  equivalent  in  absolute  measure. 
=K 

General  formula  for  all  bodies: 

_  1 

~~  l_j^_(dp_\  (dv_\  ' 

V1  I  dv  \ 

r  =  —  -7-i-r-i 


T  _    /*   (  dp  \  /  dv  \       f 
*'•  7?  \7fc).\dJ )  F^T' 


414  HENEY  A.  ROWLAND 

Also, 

J=    ~  ~^(!*L\    ~^L' 
\  dp  ),,,      V 

Application  to  gases;  Rankine's  formula  is,— 

(4L)SBA/1+*,*L    *.}, 

\  d/j.  h       ii  \  ;j.     v  J 


dp- 1  —       -  -,  -  —  .  1  + 

If  a.v  is  the  coefficient  of  expansion  between  0°  and  100°,  then 

AI,  =  —  (1  +  -00635m), 
whence 


where   a'p  and   a,  are  the  true  coefficients  of  expansion  at  the  given 
temperature; 

+  5m  *.*•. 


According  to  Thomson  and  Joule's  experiments  m  =  0°-33  C.  for  air 
and  about  2°-0  for  C02  .  Hence  //„=  272°  -99. 

The  equations  should  be  applied  to  the  observations  directly  at  the 
given  temperature,  but  it  will  generally  be  sufficient  to  use  them  after 
reduction  to  0°  C.  Using  K  =  -2375  according  to  Regnault  for  air,  we 
have  for  the  latitude  of  Baltimore,  — 

From  Rontgen's  value  r  =  1-4053          —  =  430-3.33 

J 

"    Amagat's       "  1-397  —  =  436-6. 

"    velocity  of  sound  331-78m.  per  sec.—  =  429'6. 

*/ 

33R6ntgen  gives  the  value  428-1  for  the  latitude  of  Paris  as  calculated  by  a  formula 
of  Shroder  v.  d.  Kolk,  and  427-3  from  the  formula  for  a  perfect  gas,  and  these  both 
agree  more  nearly  with  my  result  than  that  calculated  from  my  own  formula. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  415 

Using  Wiedemann's  value  for  K,  -2389,  these  become 

—  =  427-8 ;       -^  =  434-0 ;       —  =  427-1 . 
999 

As  Wiedemann,  however,  used  the  mercurial  thermometer,  and  as 
the  reduction  to  the  air  thermometer  would  increase  these  figures  from 
•2  to  -8  per  cent,  it  is  evident  that  Eegnault's  value  for  K  is  the  more 
nearly  correct.  I  take  the  weights  rather  arbitrarily  as  follows : 

Weight.  J. 

Eontgen  3  430-3 

Amagat  1  436-6 

Velocity  of  sound        4  429-6 


Mean  430-7 

And  this  is  of  course  the  value  referred  to  water  at  14°  C.  and  in  the 
latitude  of  Baltimore.     My  value  at  this  point  is  427-7. 

This  determination  of  the  mechanical  equivalent  from  the  properties 
of  air  is  at  most  very  imperfect,  as  a  very  slight  change  in  either  f  or 
the  velocity  of  sound  will  produce  a  great  change  in  the  mechanical 
equivalent. 

From  Theory  of  Vapors 

Another  important  method  of  calculating  the  mechanical  equivalent 
of  heat  is  from  the  equation  for  a  body  at  its  change  of  state,  as  for 
instance  in  vaporization.  Let  v  be  the  volume  of  the  vapor,  and  v'  the 
volume  of  the  liquid,  H  the  heat  required  to  vaporize  a  unit  of  mass  of 
the  water;  also  let  p  be  the  pressure  in  absolute  units,  and  //  the  absolute 
temperature.  Then 

JH 


The  quantity  H  and  the  relation  of  p  to  //  have  been  determined  with 
considerable  accuracy  by  Regnault.  To  determine  J  it  is  only  required 
to  measure  the  volume  of  saturated  steam  from  a  given  weight  of  water; 
and  the  principal  difficulty  of  the  process  lies  in  this  determination, 
though  the  other  quantities  are  also  difficult  of  determination. 

This  volume  can  be  calculated  from  the  density  of  the  vapor,  but  this 
is  generally  taken  in  the  superheated  state. 


416  HENRY  A.  KOWLAND 

The  experiments  of  Fairbairn  and  Tate34  are  probably  the  best  direct 
experiments  on  the  density  of  saturated  vapor,  but  even  those  do  not 
pretend  to  a  greater  accuracy  than  about  1  in  100.  With  Eegnault's 
values  of  the  other  quantities,  they  give  about  Joule's  value  for  the 
equivalent,  namely  425.  Him,  Herwig,  and  others  have  also  made  the 
determination,  but  the  results  do  not  agree  very  well.  Herwig  even 
used  a  Geissler  standard  thermometer,  which  I  have  shown  to  depart 
very  much  from  the  air  thermometer. 

Indeed,  the  experiments  on  this  subject  are  so  uncertain,  that  physi- 
cists have  about  concluded  to  use  this  method  rather  for  the  deter- 
mination of  the  volume  of  saturated  vapors  than  for  the  mechanical 
equivalent  of  heat. 

From  the  Steam-Engine  and  Expansion  of  Metals 

The  experiments  of  Hirn  on  the  steam-engine  and  of  Edlund  on  the 
expansion  and  contraction  of  metals,  are  very  excellent  as  illustrating 
the  theory  of  the  subject,  but  cannot  have  any  weight  as  accurate  deter- 
minations of  the  equivalent. 

From  Friction  Experiments 

Experiments  of  this  nature,  that  is,  irreversible  processes  for  con- 
verting mechanical  energy  into  heat,  give  by  far  the  best  methods  for 
the  determination  of  the  equivalent. 

Rumford's  experiment  of  1798  is  only  valuable  from  an  historical 
point  of  view.  Joule's  results  since  1843  undoubtedly  give  the  best 
data  we  yet  have  for  the  determination  of  the  equivalent.  The  mean  of 
all  his  friction  experiments  of  1847  and  1850  which  are  given  in  the 
table  is  425-8,  though  he  prefers  the  smallest  number,  423-9,  of  1850. 
This  last  number  is  at  present  accepted  throughout  the  civilized  world, 
though  there  is  at  present  a  tendency  to  consider  the  number  too  small. 
But  this  value  and  his  recent  result  of  1878  have  undoubtedly  as  much 
weight  as  all  other  results  put  together. 

As  sources  of  error  in  these  determinations  I  would  suggest,  first, 
the  use  of  the  mercurial  instead  of  the  air  thermometer.  Joule  com- 
pared his  thermometers  with  one  made  by  Fastre.  In  the  Appendix 
to  Thermometry  I  give  the  comparison  of  two  thermometers  made  by 
Fastre  in  1850,  with  the  air  thermometer,  as  well  as  of  a  large  number 
of  others.  From  this  it  seems  that  all  thermometers  as  far  as  measured 

3*  Phil.  Mag.,  ser.  4,  xxi,  230. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  417 

stand  above  the  air  thermometer  between  0°  and  100°,  and  that  the 
average  for  the  Fastre  at  40°  is  about  0°-1  C.  Using  the  formula  given 
in  Thermometry  this  would  produce  an  error  of  about  3  parts  in  1000 
at  15°  C.,  the  temperature  Joule  used. 

The  specific  heat  of  copper  which  Joule  uses,  namely,  -09515,  is 
undoubtedly  too  large.  Using  the  value  deduced  from  more  recent 
experiments  in  calculating  the  capacity  of  my  calorimeter,  -0922, 
Joule's  number  would  again  be  increased  13  parts  in  10,000,  so  that 
we  have, — 

Joule's  value    423-9,  water  at  15°-7  C. 

Eeduction  to  air  thermometer -|-1'3 

Correction  for  specific  heat  of  copper.  . -f-  -5 
Correction  to  latitude  of  Baltimore.  .    . -f-  -5 


426-2 

It  does  not  seem  improbable  that  this  should  be  still  further  in- 
creased, seeing  that  the  reduction  to  the  air  thermometer  is  the  smallest 
admissible,  as  most  other  thermometers  which  I  have  measured  give 
greater  correction,  and  some  even  more  than  three  times  as  great  as 
the  one  here  used,  and  would  thus  bring  the  value  even  as  high  as  429. 

One  very  serious  defect  in  Joule's  experiments  is  the  small  range 
of  temperature  used,  this  being  only  about  half  a  degree  Fahrenheit, 
or  about  six  divisions  on  his  thermometer.  It  would  seem  almost  im- 
possible to  calibrate  a  thermometer  so  accurately  that  six  divisions 
should  be  accurate  to  one  per  cent,  and  it  would  certainly  need  a  very 
skillful  observer  to  read  to  that  degree  of  accuracy.  Further,  the  same 
thermometer  "  A  "  was  used  throughout  the  whole  experiment  with 
water,  and  so  the  error  of  calibration  was  hardly  eliminated,  the  tem- 
perature of  the  water  being  nearly  the  same.  In  the  experiment  on 
quicksilver  another  thermometer  was  used,  and  he  then  finds  a  higher 
result,  424-7,  which,  reduced  as  above,  gives  427-0  at  Baltimore. 

The  experiments  on  the  friction  of  iron  should  be  probably  rejected 
on  account  of  the  large  and  uncertain  correction  for  the  energy  given 
out  in  sound. 

The  recent  experiments  of  1878  give  a  value  of  772-55,  which  re- 
duced gives  at  Baltimore  426-2,  the  same  as  the  other  experiment. 

The  agreement  of  these  reduced  values  with  my  value  at  the  same 
temperature,  namely  427-3,  is  certainly  very  'remarkable,  and  shows 
what  an  accurate  experimenter  Joule  must  be  to  get  with  his  simple 
27 


418  HENRY  A.  EOWLAND 

apparatus  results  so  near  those  from  my  elaborate  apparatus,  which 
almost  grinds  out  accurate  results  without  labor  except  in  reduction. 
Indeed,  the  quantity  is  the  same  as  I  find  at  about  20°  C. 

The  experiments  of  Him  of  1860-61  seem  to  point  to  a  value  of  the 
equivalent  higher  than  that  found  by  Joule,  but  the  details  of  the 
experiment  do  not  seem  to  have  been  published,  and  they  certainly 
were  not  reduced  to  the  air  thermometer. 

The  method  used  by  Violle  in  1870  does  not  seem  capable  of  accur- 
acy, seeing  that  the  heat  lost  by  a  disc  in  rapid  rotation,  and  while 
carried  to  the  calorimeter,  must  have  been  uncertain. 

The  experiments  of  Him  are  of  much  interest  from  the  methods 
used,  but  can  hardly  have  weight  as  accurate  determinations.  Some 
of  the  methods  will  be  again  lef  erred  to  when  I  come  to  the  description 
of  apparatus. 

Method  by  Heat  Generated  by  Electric  Cwrent 

The  old  experiments  of  Quintus  Icilius  or  Lenz  do  not  have  any 
except  historical  value,  seeing  that  Weber's  measure  of  absolute  resist- 
ance was  certainly  incorrect  and  we  now  have  no  means  of  finding  its 
error. 

The  theory  of  the  process  is  as  follows.  The  energy  of  electricity 
being  the  product  of  the  potential  by  the  quantity,  the  energy  ex- 
pended by  forcing  the  quantity  of  electricity,  Q,  along  a  wire  of  re- 
sistance, R,  in  a  second  of  time,  must  be  QZR,  and  as  this  must  equal 
the  mechanical  equivalent  of  the  heat  generated,  we  must  have  JH  — 
QzRt,  where  H  is  the  heat  generated  and  t  is  the  time  the  current  Q 
flows. 

The  principal  difficulty  about  the  determination  by  this  method 
seems  to  be  that  of  finding  R  in  absolute  measure.  A  table  of  the 
values  of  the  ohm  as  obtained  by  different  observers,  was  published  by 
me  in  my  paper  on  the  'Absolute  Unit  of  Electrical  Besistance/  in 
the  American  Journal  of  Science,  Vol.  XV,  and  I  give  it  here  with 
some  changes. 

The  ratio  of  the  Siemens  unit  to  the  ohm  is  now  generally  taken  at 
•9536,  though  previous  to  1864  there  seems  to  have  been  some  doubt 
as  to  the  value  of  the  Siemens  unit. 

Since  1863-4,  when  units  of  resistance  first  began  to  be  made  with 
great  accuracy,  two  determinations  of  the  heat  generated  have  been 
made.  The  first  by  Joule  with  the  ohm,  and  the  second  by  H.  F. 
Weber,  of  Zurich,  with  the  Siemens  unit. 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


419 


Each  determination  of  resistance  with  each  of  these  experiments 
gives  one  value  of  the  mechanical  equivalent.  As  Lorenz's  result  was 
only  in  illustration  of  a  method,  I  have  not  included  it  among  the  exact 
determinations. 

TABLE  XXXI. 


Date. 

Observer. 

Value  of  Ohm. 

Remarks. 

1849 

Kirchhoff 

•88  to   -90 

Approximately. 

1851 

Weber 

•95  to   -97 

Approximately. 

1862 

Weber 

j  1-088 
j  1-075 

From  Thomson's  unit. 
From  Weber's  value  of  Siemens  unit. 

1863-4 

B.  A.  Committee 

j  1-0000 
}     -993 

Mean  of  all  results. 
Corrected   by   Rowland   to   zero    vel- 

ocity of  coil. 

1870 

Kohlrausch 

1-0193 

1873 

Lorenz 

•975 

Approximately. 

1876 

Rowland 

•99113s 

From  a  preliminary  comparison  with 

the  B.  A.  unit. 

1878 

H.  F.  Weber 

1-0014 

Using  ratio  of  Siemens  unit  to  ohm, 

•9536. 

The  result  found  by  Joule  was  J=  25187  in  absolute  measure  using 
feet  and  degrees  F.,  which  becomes  429-9  in  degrees  C.  on  a  mercurial 
thermometer  and  in  the  latitude  of  Baltimore,  compared  with  water 
at  18°-6C. 

TABLE  XXXII. — EXPERIMENTS  OF  JOULE. 


Observer. 

Value  of 
B.  A.  Unit. 

Mechanical  equivalent 
from  Joule's  Exp. 

Mechanical  equivalent 
reduced  to  Air  Ther- 
mometer   and    cor- 
rected for  8p.  Ht.  of 
Copper. 

B.  A.  Committee  

1-0000 

429-9 

431-4 

Ditto  corrected  by  Rowland 
Kohlrausch  

•993 
1-0193 

426-9 
438-2 

428-4 
439-7 

Rowland  

•9911 

426-1 

427-6 

H.  F.  Weber  

1-0014 

430-5 

432-0 

The  experiments  of  H.  F.  Weber36  gave  428-15  in  the  latitude  of 
Zurich  and  for  1°  C.  on  the  air  thermometer  and  at  a  temperature  of 
18°  C.  This  reduced  to  the  latitude  of  Baltimore  gives  428-45. 

My  own  value  at  this  temperature  is  426-8,  which  agrees  almost 
exactly  with  the  fourth  value  from  my  own  determination  of  the  abso~ 
lute  unit.37 

K  Given  -9912  by  mistake  in  the  other  tables. 
3«Phil.  Mag.,  1878,  5th  ser.,  v.  135. 

37  The  value  of  the  ohm  found  by  reversing  the  calculation  would  be  -992,  almost 
exactly  my  value. 


420 


HENEY  A.  ROWLAND 


There  can  be  no  doubt  that  Joule's  result  is  most  exact,  and  hence 
I  have  given  his  results  twice  the  weight  of  Weber's.  Weber  used  a 
wire  of  about  14  ohms'  resistance,  and  a  small  calorimeter  holding  only 
250  grammes  of  water.  This  wire  was  apparently  placed  in  the  water 
without  any  insulating  coating,  and  yet  current  enough  was  sent 
through  it  to  heat  the  water  15°  during  the  experiment.  No  precau- 
tion seems  to  have  been  taken  as  to  the  current  passing  into  the  water, 
which  Joule  accurately  investigated.  Again,  the  water  does  not  seem 
to  have  been  continuously  stirred,  which  Joule  found  necessary.  And 
further,  Newton's  law  of  cooling  does  not  apply  to  so  great  a  range 
as  15°,  though  the  error  from  this  source  was  probably  small.  Further- 

TABLE  XXXIII. 


EXPERIMENTS  OF  H.  F.  WEBER. 

Mean    of    Joule    and 
Weber,  giving  Joule 
twice  the  Weight  of 
Weber. 

Observer. 

Value  of 
B.  A.  Unit. 

Mechanical  equivalent 
of  Heat  from  Weber's 
Experiments. 

Mean    equivalent   re- 
duced  to  Air  Ther- 
mometer in  the  Lati- 
tude of  Baltimore. 

B.  A.  Committee  

1-000 
•993 
1-0193 
•9911 
1-0014 

427-9 
424-9 
436-2 
424-1 

428-5 

430-2 
427-2 
439-1 
426-4 
431-4 

Ditto  corrected  by  Rowland 
Kohlrausch  

H.  F.  Weber  

more,  I  know  of  no  platinum  which  has  an  increase  of  coefficient  of 
•001054  for  1°  C.,  but  it  is  usually  given  at  about  -003. 

There  can  be  no  doubt  that  experiments  depending  on  tKe  heating 
of  a  wire  give  too  small  a  value  of  the  equivalent,  seeing  that  the 
temperature  of  the  wire  during  the  heating  must  always  be  higher 
than  that  of  the  water  surrounding  it,  and  hence  more  heat  will  be 
generated  than  there  should  be.  Hence  the  numbers  should  be  slightly 
increased.  Joule  used  wire  of  platinum-silver  alloy,  and  Weber  plati- 
num wire,  which  may  account  for  Weber's  finding  a  smaller  value  than 
Joule,  and  Weber's  value  would  be  more  in  error  than  Joule's.  Undoubt- 
edly this  is  a  serious  source  of  error,  and  I  am  about  to  repeat  an 
experiment  of  this  kind  in  which  it  is  entirely  avoided.  Considering 
this  source  of  error,  these  experiments  confirm  both  my  value  of  the 
ohm  and  of  the  mechanical  equivalent,  and  unquestionably  show  a  large 
error  in  Kohlrausch's  absolute  value  of  the  Siemens  unit  or  ohm. 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  421 

The  experiments  of  Joule  and  Favre,  where  the  heat  generated  by 
a  current,  both  when  it  does  mechanical  work  and  when  it  does  not, 
are  very  interesting,  but  can  hardly  have  any  weight  in  an  estimation 
of  the  true  value  of  the  equivalent. 

The  method  of  calculating  the  equivalent  from  the  chemical  action 
in  a  battery,  or  the  electro-motive  force  required  to  decompose  any 
substance,  such  as  water,  is  as  follows: 

Let  E  be  such  electro-motive  force  and  c  be  the  quantity  of  chemical 
substance  formed  in  battery  or  decomposed  in  voltameter  per  second. 
Then  total  energy  of  current  of  energy  per  second  is  EQ,  where  Q  is 
the  current,  or  cQHJ,  where  H  is  the  heat  generated  by  unit  of  c,  or 
required  to  decompose  unit  of  c.  Hence,  if  the  process  is  entirely 
reversible,  we  must  have  in  either  case 

CHJ  =  E. 

But  the  process  is  not  always  reversible,  seeing  that  it  requires  more 
electro-motive  force  to  decompose  water  than  is  given  by  a  gas  battery. 
This  is  probably  due  to  the  formation  at  first  of  some  unstable  com- 
pound like  ozone.  The  process  with  a  battery  seems  to  be  best,  and  we 
can  thus  apply  it  to  the  Daniell  cell.  The  following  quantities  are 
mostly  taken  from  Kohlrausch. 

The  quantity  c  has  been  found  by  various  observers,  and  Kohlrausch  M 
gives  the  mean  value  as  -009421  for  water  according  to  his  units  (mg., 
mm.,  second  system).  Therefore  for  hydrogen  it  is  -001047. 

The  quantity  H  can  be  observed  directly  by  short-circuiting  the 
battery,  or  can  be  found  from  experiments  like  those  of  Favre  and 
Silbermann. 

The  electro-motive  force  E  can  be  made  to  depend  either  upon  the 
absolute  measure  of  resistance,  or  can  be  determined,  as  Thomson  has 
done,  in  electro-static  units.  In  electro-magnetic  units  it  is 

Absolute  Measure 

Siemens.  Ohms.  according  to  my 

Determination. 

After  Waltenhof  en  11-43  10-90  10-80  XlO10 

"     Kohlrausch39  11-71  H'17  11-07X1010 

After  Favre,  1  equivalent  of  zinc  developes  in  the  Daniell  cell  23993 
heat  units; 

.       /        E 


38  Fogg.  Ann.,  cxlix,  179. 

39  Given  by  Kohlrausch,  Pogg.  Ann.,  cxlix,  182. 


422  HEXRY  A.  ROWLAND 

On  the  rag.,  mm.,  second  system,  we  have  -#  =  10-935  X  1010,  c  = 
•001047,  H  =  23993,  g  =  9800-5  at  Baltimore. 

/.     —  =  444160  mm.  =  444-2  metres. 
9 

Using  Kohlrausch's  value  for  absolute  resistance,  he  finds  456-5, 
which  is  much  more  in  error  than  that  from  my  determination.  I  do 
not  give  the  calculation  from  the  Grove  battery,  because  the  Grove 
battery  is  not  reversible,  and  action  takes  place  in  it  even  when  no 
current  flows. 

Thomson  finds  the  difference  of  potential  between  the  poles  of  a 
Daniell  cell  in  electro-static  measure  to  be  -00374  on  the  cm.,  grm., 
second  system.40  Using  the  ratio  29,900,000,000  cm.  per  second,  as  I 
have  recently  found,  but  not  yet  published,  we  have  111,800,000  on 
the  electro-magnetic  system  or  11-18  X  1010  on  the  mm.,  mg.,  second 
system.  This  gives 

—  =  474.3  metres. 

g 

General  Criticism 

All  the  results  so  far  obtained,  except  those  of  Joule,  seem  to  be  of 
the  crudest  description;  and  even  when  care  was  apparently  taken  in 
the  experiment,  the  method  seems  to  be  defective,  or  the  determination 
is  made  to  rest  upon  the  determination  of  some  other  constant  whose 
value  is  not  accurately  known.  Again,  only  one  or  two  observers  have 
compared  their  thermometers  with  the  air  thermometer,  although  I 
have  shown  in  '  Thermometry '  that  an  error  of  more  than  one  per 
cent  may  be  made  by  this  method.  The  range  of  temperature  is  also 
small  as  a  general  rule  and  the  specific  heat  of  water  is  assumed  con- 
stant. 

Hence  a  new  determination,  avoiding  these  sources  of  erfor,  seems 
to  be  imperatively  demanded. 

(6.)  Description  of  Apparatus 
1.    PRELIMINARY  EEMARKS 

As  we  have  seen  in  the  historical  portion,  the  only  experiments  of  a 
high  degree  of  accuracy  to  the  present  time  are  those  of  Joule.  Looked 
at  from  a  general  point  of  view,  the  principal  defects  of  his  method 
were  the  use  of  the  mercurial  instead  of  the  air  thermometer,  and  the 
small  rate  at  which  the  temperature  of  his  calorimeter  rose. 

40  Thomson,  Papers  on  Electrostatics  and  Magnetism,  p.  246. 


ON  THE  MECHANICAL  EQUIVALEXT  OF  HEAT  423 

In  devising  a  new  method  a  great  rise  of  temperature  in  a  short  time 
was  considered  to  be  the  great  point,  combined,  of  course,  with  an  accu- 
rate measurement  of  the  work  done.  For  a  great  rise  of  temperature 
great  work  must  be  done,  which  necessitates  the  use  of  a  steam-engine 
or  other  motive  power.  For  the  measurement  of  the  work  done,  there 
is  only  one  principle  in  use  at  present,  which  is,  that  the  work  trans- 
mitted by  any  shaft  in  a  given  time  is  equal  to  2/r  times  the  product  of 
the  moment  of  the  force  by  the  number  of  revolutions  of  the  shaft  in 
that  time. 

In  mechanics  it  is  common  to  measure  the  amount  of  the  force 
twisting  the  shaft  by  breaking  it  at  the  given  point,  and  attaching  the 
two  ends  together  by  some  arrangement  of  springs  whose  stretching 
gives  the  moment.  Morin's  dynamometer  is  an  example.  Him41  gives 
a  method  which  he  seems  to  consider  new,  but  which  is  immediately 
recognized  as  Huyghens's  arrangement  for  winding  clocks  without  stop- 
ping them.  As  cords  and  pulleys  are  used  which  may  slip  on  each  other, 
it  cannot  possess  much  accuracy.  I  have  devised  a  method  by  cog- 
wheels which  is  more  accurate,  but  which  is  better  adapted  for  use  in 
the  machine-shop  than  for  scientific  experimentation. 

But  the  most  accurate  method  known  to  engineers  for  measuring  the 
work  of  an  engine  is  that  of  White's  friction  brake,  and  on  this  I  have 
based  my  apparatus.  Him  was  the  first  to  use  this  principle  in  deter- 
mining the  mechanical  equivalent  of  heat.  In  his  experiment  a  hori- 
zontal axis  was  turned  by  a  steam-engine.  On  the  axis  was  a  pulley 
with  a  flat  surface,  on  which  rested  a  piece  of  bronze  which  was  to  be 
heated  by  the  friction.  The  moment  of  the  force  with  which  the  fric- 
tion tended  to  turn  the  piece  of  bronze  was  measured,  together  with 
the  velocity  of  revolution.  This  experiment,  which  Him  calls  a  balance 
de  frottement,  was  first  constructed  by  him  to  test  the  quality  of  oils  used 
in  the  industrial  arts.  He  experimented  by  passing  a  current  of  water 
through  the  apparatus  and  observing  the  temperature  of  the  water  be- 
fore and  after  passing  through.  He  thus  obtained  a  rough  approxima- 
tion to  Joule's  equivalent. 

He  afterward  constructed  an  apparatus  consisting  of  two  cylinders 
about  30  cm.  in  diameter  and  100  cm.  long,  turning  one  within  the 
other,  the  annular  space  between  which  could  be  filled  with  water,  or 
through  which  a  stream  of  water  could  be  made  to  flow  whose  tempera- 
ture could  be  measured  before  and  after.  The  work  was  measured  by 
the  same  method  as  before. 

41  Exposition  de  la  Theorie  Mecanique  de  la  Chaleur,  3m«  6d.,  p.  18. 


424  HENRY  A.  BOWLAND 

But  in  neither  of  these  methods  does  Him  seem  to  have  recognized 
the  principle  of  the  work  transmitted  by  a  shaft  being  equal  to  the 
moment  of  the  force  multiplied  by  the  angle  of  rotation  of  the  shaft. 
In  designing  his  apparatus,  he  evidently  had  in  view  the  reproduction 
in  circular  motion  of  the  case  of  friction  between  two  planes  in  linear 
motion. 

Since  I  designed  my  apparatus,  Puluj42  has  designed  an  instrument 
to  be  worked  by  hand,  and  based  on  the  principle  used  by  Him.  He 
places  the  revolving  axis  vertical,  and  the  friction  part  consists  of  two 
cones  rubbing  together.  But  no  new  principle  is  involved  in  his  appa- 
ratus further  than  in  that  used  by  Him. 

In  my  apparatus  one  of  the  new  features  has  been  the  introduction 
of  the  Joule  calorimeter  in  the  place  of  the  friction  cylinders  of  Him 
or  the  cones  of  Puluj.  At  first  sight  the  currents  and  whirlpools  in 
such  a  calorimeter  might  be  supposed  to  have  some  effect;  but  when 
the  motion  is  steady,  it  is  readily  seen  that  the  torsion  of  the  calorimeter 
is  equal  to  that  of  the  shaft,  and  hence  the  principle  must  apply. 

This  change,  together  with  the  other  new  features  in  the  experi- 
ments and  apparatus,  has  at  once  made  the  method  one  of  extreme 
accuracy,  surpassing  all  others  very  many  fold. 

2.    GENEBAL  DESCRIPTION 

The  apparatus  was  situated  in  a  small  building,  entirely  separate 
from  the  other  University  buildings,  and  where  it  was  free  from  dis- 
turbances. 

Fig.  6  gives  a  general  view  of  the  apparatus.  To  a  movable  axis,  ab, 
a  calorimeter  similar  to  Joule's  is  attached,  and  the  whole  is  suspended 
by  a  torsion  wire,  c.  The  shaft  of  the  calorimeter  comes  out  from  the 
bottom,  and  is  attached  to  a  shaft,  ef,  which  receives  a  uniform  motion 
from  the  engine  by  mean's  of  the  bevel  wheels  g  and  Ji.  To  the  axis, 
ab,  an  accurate  turned  wheel,  M,  was  attached,  and  the  moment  of 
the  force  tending  to  turn  the  calorimeter  was  measured  by  the  weights 
o  and  p,  attached  to  silk  tapes  passing  around  the  circumference  of  the 
wheel  in  combination  with  the  torsion  of  the  suspending  wire.  To  this 
axis  was  also  attached  a  long  arm,  having  two  sliding  weights,  q  and  r, 
by  which  the  moment  of  inertia  could  be  varied  or  determined. 

42Pogg.  Ann.,  clvii,  437. 

"Joule's  latest  results  were  published  after  this  was  written,  and  I  was  not  aware 
that  he,  had  made  this  improvement  until  lately.  The  result  of  his  experiment,  how- 
ever, reached  me  soon  after,  and  I  have  referred  to  it  in  the  paper,  but  I  did  not  see 
the  complete  paper  until  much  later. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  425 


FIG.  6. 


426  HENRY  A.  EOWLAND 

The  number  of  revolutions  was  determined  by  a  chronograph,  which 
received  motion  by  a  screw  on  the  shaft  ef,  and  which  made  one  revo- 
lution for  102  of  the  shaft.  On  this  chronograph  was  recorded  the 
transit  of  the  mercury  over  the  divisions  of  the  thermometer. 

Around  the  calorimeter  a  water  jacket,  tu,  made  in  halves,  was 
placed,  so  that  the  radiation  could  be  estimated.  A  wooden  box  sur- 
rounded the  whole,  to  shield  the  observer  from  the  calorimeter. 

The  action  of  the  apparatus  is  in  general  as  follows:  As  the  inner 
paddles  revolve,  the  water  strikes  against  the  outer  paddles,  and  so 
tends  to  turn  the  calorimeter.  When  this  force  is  balanced  by  the 
weights  op,  the  whole  will  be  in  equilibrium,  which  is  rendered  stable 
by  the  torsion  of  the  wire  cd.  Should  any  slight  change  take  place  in 
the  velocity,  the  calorimeter  will  revolve  in  one  direction  or  the  other 
until  the  torsion  brings  it  into  equilibrium  again.  The  amount  of  tor- 
sion read  off  on  a  scale  on  the  edge  of  Tel  gives  the  correction  to  be 
added  to  or  subtracted  from  the  weights  op. 

One  observer  constantly  reads  the  circle  Tel,  and  the  other  constantly 
records  the  transits  of  the  mercury  over  the  divisions  of  the  ther- 
mometer. 

A  series  extending  over  from  one  half  to  a  whole  hour,  and  record- 
ing a  rise  of  15°  C.  to  perhaps  25°  C.,  and  in  which  a  record  was  made 
for  perhaps  each  tenth  of  a  degree,  would  thus  contain  several  hundred 
observations,  from  any  two  of  which  the  equivalent  of  heat  could  be 
determined,  though  they  would  not  all  be  independent.  Such  a  series 
would  evidently  have  immense  weight;  and,  in  fact,  I  estimate  that, 
neglecting  constant  errors,  a  single  series  has  more  weight  than  all  of 
Joule's  experiments  of  1849,  on  water,  put  together.44 

The  correction  for  radiation  is  inversely  proportional  to  the  ratio  of 
the  rate  of  work  generated  to  the  rate  at  which  the  heat  is  lost; 
and  this  for  equal  ranges  of  temperature  is  only  7V  as  great  in  my 
measures  as  in  Joule's;  for  Joule's  rate  of  increase  was  about  0°-62  C. 
per  hour,  while  mine  is  about  35°  C.  in  the  same  time,  and  can  be  in- 
creased to  over  45°  C.  per  hour. 

3.    DETAILS 
The  Calorimeter 

Joule's  calorimeter  was  made  in  a  very  simple  manner,  with  few 
paddles,  and  without  reference  to  the  production  of  currents  to  mix 

44  Forty  experiments,  with  an  average  rise  of  temperature  of  0°-56  F.,  equal  to 
0°-31  C.,  gives  a  total  rise  of  12° -4  C.,  which  is  only  about  two-thirds  the  average  of 
one  of  my  experiments.  As  my  work  is  measured  with  equal  accuracy,  and  my 
radiation  with  greater,  the  statement  seems  to  be  correct. 


N  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


427 


up  the  water.     Hence  the  paddles  were  made  without  solder,  and  were 
screwed  together.     Indeed,  there  was  no  solder  about  the  apparatus. 

But,  for  my  purpose,  the  number  of  paddles  must  be  multiplied,  so 
that  there  shall  be  no  jerk  in  the  motion,  and  that  the  resistance  may 
be  great;  they  must  be  stronger,  to  resist  the  force  from  the  engine, 
and  they  must  be  light,  so  as  not  to  add  an  uncertain  quantity  to  the 
calorific  capacity.  Besides  this,  the  shape  must  be  such  as  to  cause 
the  whole  of  the  water  to  run  in  a  constant  stream  past  the  thermom- 
eter, and  to  cause  constant  exchange  between  the  water  at  the  top  and 
at  the  bottom. 


FIG.  7. 


FIG.  8. 


Fig.  7  shows  a  section  of  the  calorimeter,  and  Fig.  8  a  perspective 
view  of  the  revolving  paddles  removed  from  the  apparatus,  and  with  the 
exterior  paddles  removed  from  around  it;  which  could  not,  however,  be 
accomplished  physically  without  destroying  them. 

To  the  axis  cb,  Fig.  7,  which  was  of  steel,  and  6  mm.  in  diameter,  a 
copper  cylinder,  ad,  was  attached,  by  means  of  four  stout  wires  at  e, 
and  four  more  at  f.  To  this  cylinder  four  rings,  g,  Ji,  i,  j,  were  attached, 
which  supported  the  paddles.  Each  one  had  eight  paddles,  but  each 
ring  was  displaced  through  a  small  angle  with  reference  to  the  one 
below  it,  so  that  no  one  paildle  came  over  another.  This  was  to  make 
the  resistance  continuous,  and  not  periodical.  The  lower  row  of  pad- 
dles were  turned  backwards,  so  that  they  had  a  tendency  to  throw  the 
water  outwards  and  make  the  circulation,  as  I  shall  show  afterwards. 


428  HENRY  A.  ROWLAND 

Around  these  movable  paddles  were  the  stationary  paddles,  consist- 
ing of  five  rows  of  ten  each.  These  were  attached  to  the  movable 
paddles  by  bearings,,  at  the  points  c  and  Jc,  of  the  shaft,  and  were  re- 
moved with  the  latter  when  this  was  taken  from  the  calorimeter. 
When  the  whole  was  placed  in  the  calorimeter,  these  outer  paddles  were 
attached  to  it  by  means  of  four  screws,  I  and  m,  so  as  to  be  immovable. 

The  cover  of  the  calorimeter  was  attached  to  a  brass  ring,  which 
was  nicely  ground  to  another  brass  ring  on  the  calorimeter,  and  which 
could  be  made  perfectly  tight  by  means  of  a  little  white-lead  paini 
The  shaft  passed  through  a  stuffing-box  at  the  bottom,  which  was 
entirely  within  the  outer  surface  of  the  calorimeter,  so  that  the  heat 
generated  should  all  go  to  the  water.  The  upper  end  of  the  shaft 
rested  in  a  bearing  in  a  piece  of  brass  attached  to  the  cover.  In  the 
cover  there  were  two  openings, — one  for  the  thermometer,  and  the 
other  for  filling  the  calorimeter  with  water. 


From  the  opening  for  the  thermometer,  a  tube  of  copper,  perforated 
with  large  holes,  descended  nearly  to  the  centre  of  the  calorimeter. 
The  thermometer  was  in  this  sieve-like  tube  at  only  a  short  distance 
from  the  centre  of  the  calorimeter,  with  the  revolving  paddles  outside 
of  it,  and  in  the  stream  of  water,  which  circulated  as  shown  by  the 
arrows. 

This  circulation  of  water  took  place  as  follows.  The  lower  paddles 
threw  the  water  violently  outwards,  while  the  upper  paddles  were  pre- 
vented from  doing  so  by  a  cylinder  surrounding  the  fixed  paddles. 
The  consequence  was,  that  the  water  flowed  up  in  the  space  between 
the  outer  shell  and  the  fixed  paddles,  and  down  through  the  central 
tube  of  the  revolving  paddles.  As  there  was  always  a  little  air  at  the 
top  to  allow  for  expansion,  it  would  also  aid  in  the  same  direction. 
•  These  currents,  which  were  very  violent,  could  be  observed  through 
the  opening's. 

The  calorimeter  was  attached  to  a  wheel,  fixed  to  the  shaft  db,  by 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  429 

the  method  shown  in  Fig.  9.  At  the  edge  of  the  wheel,  which  was  of 
the  exact  diameter  of  the  calorimeter,  two  screws  were  attached,  from 
which  wires  descended  to  a  single  screw  in  the  edge  of  the  calorimeter. 
Through  the  wheel,  a  screw  armed  with  a  vulcanite  point  pressed  upon 
the  calorimeter,  and  held  it  firmly.  Three  of  these  arrangements,  at 
distances  of  120°,  were  used.  To  centre  the  calorimeter,  a  piece  of 
vulcanite  at  the  centre  was  used.  By  this  method  of  suspension  very 
little  heat  could  escape,  and  the  amount  could  he  allowed  for  hy  the 
radiation  experiments. 

The  Torsion  System 

The  torsion  wire  was  of  such  strength  that  one  millimeter  on  the 
scale  at  the  edge  of  the  wheel  signified  11-8  grammes,  or  ahout  y^  of 
the  weights  op  generally  used.  There  were  stops  on  the  wheel,  so 
that  it  could  not  move  through  more  than  a  small  angle.  The  weights 
were  suspended  by  very  flexible  silk  tapes,  6  mm.  or  8  mm.  broad  and 
0-3  mm.  thick.  They  varied  from  4-5  k.  to  8-5  k.  taken  together.  The 
shaft,  ab,  was  of  uniform  size  throughout,  so  that  the  wire  c  suspended 
the  whole  system,  and  no  weight  rested  on  the  bearings. 

The  pulleys,  m,  n,  Fig.  6,  were  very  exactly  turned  and  balanced,  and 
the  whole  suspended  system  was  so  free  as  to  vibrate  for  a  considerable 
time.  However,  as  will  be  shown  hereafter,  its  freedom  is  of  little 
consequence. 

The  Water  Jacket 

Around  the  calorimeter,  a  water  jacket,  t  u,  was  placed,  so  that  the 
radiation  should  be  perfectly  definite.  During  the  preliminary  experi- 
ments a  simple  tin  jacket  was  used,  whose  temperature  was  determined 
by  two  thermometers,  one  above  and  the  other  below,  inserted  in  tubes 
attached  to  the  jacket. 

The  Driving  Gear 

The  cog-wheels,  g,  h,  were  made  by  Messrs.  Brown  and  Sharpe,  of 
Providence,  and  were  so  well  cut  that  the  motion  transmitted  to  the 
calorimeter  must  have  been  very  uniform. 

The  Chronograph 

The  cylinder  of  the  chronograph  was  turned  by  a  screw  on  the  shaft 
ef,  and  received  one  revolution  for  102  of  the  paddles;  155  revolutions 
of  the  cylinder,  or  15,810  of  the  paddles,  could  be  recorded,  though, 


430  HENRY  A.  EOWLAND 

when  necessary,  the  paper  could  be  changed  without  stopping,  and  the 
experiment  thus  continued  without  interruption. 

The  Frame  and  Foundation 

The  frame  was  very  massive  and  strong,  so  as  to  prevent  oscillation; 
and  the  whole  instrument  weighed  about  500  pounds  as  nearly  as  could 
be  estimated.  It  was  placed  on  a  solid  brick  pier,  with  a  firm  founda- 
tion in  the  ground.  The  trembling  was  barely  perceptible  to  the  hand 
when  running  the  fastest. 

The  Engine 

The  driving  power  was  a  petroleum  engine,  which  was  very  efficient 
in  driving  the  apparatus  with  uniformity. 

The  Balance 

For  weighing  the  calorimeter,  a  balance  capable  of  showing  the 
presence  of  less  than  T\  gramme  with  15,000  grammes  was  used.  The 
weights,  however,  by  Schickert,  of  Dresden,  were  accurate  among  them- 
selves to  at  least  5  mg.  for  the  larger  weights,  and  in  proportion  for 
the  smaller.  A  more  accurate  balance  would  have  been  useless,  as  will 
be  seen  further  on. 

Adjustments 

There  are  few  adjustments,  and  they  were  principally  made  in  the 
construction. 

In  the  first  place,  the  shafts  ab  and  ef  must  be  in  line.  Secondly, 
the  wheels  rrm  must  be  so  adjusted  that  their  planes  are  vertical,  and 
that  the  tapes  shall  pass  over  them  symmetrically,  and  that  their  edges 
shall  be  in  the  plane  of  the  wheel  Id. 

Deviation  from  these  adjustments  only  produced  small  error. 

(c.)  Theory  of  the  Experiment 
1.    ESTIMATION  OF  WORK  DONE 

The  calorimeter  is  constantly  receiving  heat  from  the  friction,  and 
is  giving  out  heat  by  radiation  and  conduction.  Now,  at  any  given 
instant  of  time,  the  temperature  of  the  whole  of  the  calorimeter  is  not 
the  same.  Owing  to  the  violent  stirring,  the  water  is  undoubtedly  at 
a  very  uniform  temperature  throughout.  But  the  solid  parts  of  the 
calorimeter  cannot  be  so.  The  greatest  difference  of  temperature  is 
evidently  soon  after  the  commencement  of  the  operation.  But  after 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  431 

some  time  the  apparatus  reaches  a  stationary  state,  in  which,  but  for 
the  radiation,  the  rise  of  temperature  at  all  points  would  be  the  same. 
This  steady  state  will  be  theoretically  reached  only  after  an  infinite 
time;  but  as  most  of  the  metal  is  copper,  and  quite  thin,  and  as  the 
whole  capacity  of  the  metal  work  is  only  about  four  per  cent  of  the 
total  capacity,  I  have  thought  that  one  or  two  minutes  was  enough  to 
allow,  though,  if  others  do  not  think  this  time  sufficient,  they  can 
readily  reject  the  first  few  observations  of  each  series.  When  there 
is  radiation,  the  stationary  state  will  never  be  reached  theoretically, 
though  practically  there  is  little  difference  from  the  case  where  there  is 
no  radiation. 

The  measurement  of  the  work  done  can  be  computed  as  follows. 
Let  M  be  the  moment  of  the  force  tending  to  turn  the  calorimeter,  and 
dd  the  angle  moved  by  the  shaft.  The  work  done  in  the  time  t  will 
be  fMdft.  If  the  moment  of  the  force  is  constant,  the  integral  is 
simply  Mti;  but  it  is  impossible  to  obtain  an  engine  which  runs  with 
perfect  steadiness,  and  although  we  may  be  able  to  calculate  the  inte- 
gral, as  far  as  long  periods  are  concerned,  by  observation  of  the  torsion 
circle,  yet  we  are  not  thus  able  to  allow  for  the  irregularity  during  one 
revolution  of  the  engine.  Hence  I  have  devised  the  following  theory. 
I  have  found,  by  experiments  with  the  instrument,  that  the  moment  of 
the  force  is  very  nearly,  for  high  velocities  at  least,  proportional  to  the 
square  of  the  velocity.  For  rapid  changes  of  the  velocity,  this  is  not 
exactly  true,  but  as  the  paddles  are  very  numerous  in  the  calorimeter, 
it  is  probably  very  nearly  true.  We  have  then 


where  C  is  a  constant.     Hence  the  work  done  becomes 

n  r  (dov,a    n  r/dff\',. 

W=  C   I        -jj-  \dO  =  C  I     (  —rr  \flt- 

J    \dt  )  J    \tltj 

As  we  allow  for  irregularities  of  long  period  by  readings  of  the  tor- 
sion circle,  we  can  assume  in  this  investigation  that  the  mean  velocity 
is  constant,  and  equal  to  t?0.  The  form  of  the  variation  of  the  velocity 
must  be  assumed,  and  I  shall  put,  without  further  discussion, 


dt 

We  then  find,  on  integrating  from  a  to  0, 


432  HENEY  A.  KOWLAND 

which  is  the  work  on  the  calorimeter  during  one  revolution  of  the 
engine. 

The  equation  of  the  motion  of  the  calorimeter,  supposing  it  to  be 
nearly  stationary,  and  neglecting  the  change  of  torsion  of  the  suspend- 
ing wire,  is 

m   dV       WD  ,   ntf-  2*  A2     A 

+  Cvl  (1  +  c  cos  -  -    =  0, 


TIT      —  ^— 

g    dt*          2  \  a 

where  m  is  the  moment  of  inertia  of  the  calorimeter  and  its  attach- 
ments, <p  is  the  angular  position  of  the  calorimeter,  W  is  the  sum  of 
the  torsion  weights,  and  D  is  the  diameter  of  the  torsion  wheel.  Hence, 

0  —  00  =  L  j  J/  \_Cvl  (I  + 

til     (_ 


When  WD  =  2CvQz  (I  -\-  -|c2),  the  calorimeter  will  merely  oscillate 
around  a  given  position,  and  will  reach  its  maximum  at  the  times  t  =  0, 
£  a,  a,  &c. 

The  total  amplitude  of  each  oscillation  will  be  very  nearly 

,,,_,,/  _  Cfrfra'c  =  WDga'c 
v*m  2x*m   ' 

If  x  is  the  amplitude  of  each  oscillation,  as  measured  in  millimetres, 
on  the  edge  of  the  wheel  of  "diameter  D,  we  have  <p  —  <p'  •=.  -?. 

Hence         .  c  =  ^, 

where  n  is  the  number  of  revolutions  of  the  engine  per  second. 
Having  found  c  in  this  way,  the  work  will  be,  during  any  time, 

w  =  TT  WDN(l  +  c2)  , 
where  N  is  the  total  number  of  revolutions  of  the  paddles. 

A  variation  of  the  velocity  of  ten  per  cent  from  the  mean,  or  twenty 
per  cent  total,  would  thus  only  cause  an  error  of  one  per  cent  in  the 
equivalent. 

Hence,  although  the  engine  was  only  single  acting,  yet  it  ran  easily, 
had  great  excess  of  power,  and  was  very  constant  as  far  as  long  periods 
were  concerned.  The  engine  ran  very  fast,  making  from  200  to  250 
revolutions  per  minute.  The  fly-wheel  weighed  about  220  pounds,  and 
had  a  radius  of  1£  feet.  At  four  turns  per  second,  this  gives  an  energy 
of  about  3400  foot-pounds  stored  in  the  wheel.  The  calorimeter  re- 
quired about  one-half  horse-power  to  drive  it;  and,  assuming  the  same 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  433 

for  the  engine  friction,  we  have  about  140  foot-pounds  of  work  re- 
quired per  revolution.  Taking  the  most  unfavorable  case,  where  all 
the  power  is  given  to  the  engine  at  one  point,  the  velocity  changes 
during  the  revolution  about  four  per  cent,  or  c  would  nearly  equal  .02, 
causing  an  error  of  1  part  in  2500  nearly.  By  means  of  the  shaking 
of  the  calorimeter,  I  have  estimated  c  as  follows,  the  value  of  m  being 
changed  by  changing  the  weight  on  the  inertia  bar,  or  taking  it  off 
altogether.  The  estimate  of  the  shaking  was  made  by  two  persons 
independently. 

m.  x  observed.  c  calculated. 

2,200,000  grms.  cm.a  -6  mm.  '016 

3,100,000          "  -36   "  -013 

11,800,000          "  -13   "  -017 

Mean,          c  =  '015 

causing  a  correction  of  1  part  in  5000. 

Another  method  of  estimating  the  irregularity  of  running  is  to  put 
on  or  take  off  weights  until  the  calorimeter  rests  so  firmly  against  the 
stops  that  the  vibration  ceases.  Estimated  in  this  way,  I  have  found 
a  little  larger  value  of  c,  namely,  about  -017. 

But  as  one  cannot  be  too  careful  about  such  sources  of  error,  I 
have  experimented  on  the  equivalent  with  different  velocities  and  with 
very  different  ways  of  running  the  engine,  by  which  c  was  greatly 
changed,  and  so  have  satisfied  myself  that  the  correction  from  this 
source  is  inappreciable  in  the  present  state  of  the  science  of  heat. 

Hence  I  shall  simply  put  for  the  work 

w  =  xNWD, 

in  gravitation  measure  at  Baltimore.     To  reduce  to  absolute  measure, 
we  must  multiply  by  the  force  of  gravity  given  by  the  formula 
g  =  9-78009  +  -0508  sms  ? , 

which  gives  9-8005  metres  per  second  at  Baltimore.  If  the  calorimeter 
moved  without  friction,  no  work  would  be  required  to  cause  it  to 
vibrate  back  and  forth,  as  I  have  described;  but  when  it  moves  with 
friction,  some  work  is  required.  When  I  designed  the  apparatus,  I  thus 
had  an  idea  that  it  would  be  best  to  make  it  as  immovable  as  possible 
by  adding  to  its  moment  of  inertia  by  means  of  the  inertia  bar  and 
weights.  But  on  considering  the  subject  further,  I  see  that  only  the 
excess  of  energy  represented  by  c2xNWD  can  be  used  in  this  way.  For, 
when  the  calorimeter  is  rendered  nearly  immovable  by  its  great  moment 
28 


^•a»as^=5r^=rR^cs=^^^j^s^xs^-Jua^ 


434  HENRY  A.  EOWLAXD 

of  inertia,  the  work  done  on  it  is,  as  we  have  seen,  TtNWD  (1  -f-  c2); 
but  if  it  had  no  inertia,  it  is  evident  that  the  work  would  be  only 
TiNWD.  If,  therefore,  the  calorimeter  is  made  partially  stationary, 
either  by  its  moment  of  inertia  or  by  friction,  the  work  will  be  some- 
where between  these  two,  and  the  work  spent  in  friction  will  be  only 
so  much  taken  from  the  error.  Hence  in  the  latter  experiments  the 
inertia  bar  was  taken  off,  and  then  the  calorimeter  constantly  vibrated 
through  about  half  a  millimeter  on  the  torsion  scale. 

Besides  this  quick  vibration,  the  calorimeter  is  constantly  moving  to 
the  extent  of  a  few  millimetres  back  and  forth,  according  to  the  vary- 
ing velocity  of  the  engine.  As  frequent  readings  were  taken,  these 
changes  were  eliminated.  In  very  rare  cases  the  weights  had  to  be 
changed  during  the  experiment;  but  this  was  very  seldom. 

The  vibration  and  irregular  motion  of  the  calorimeter  back  and  forth 
served  a  very  useful  purpose,  inasmuch  as  it  caused  the  friction  of  the 
torsion  apparatus  to  act  first  in  one  direction  and  then  in  the  other,  so 
that  it  was  finally  eliminated.  The  torsion  apparatus  moved  very 
freely  when  the  calorimeter  was  not  in  position,  and  would  keep 
vibrating  for  some  minutes  by  itself,  but  with  the  calorimeter  there 
was  necessarily  some  binding.  But  the  vibration  made  it  so  free  that 
it  would  return  quickly  to  its  exact  position  of  equilibrium  when  drawn 
aside,  and  would  also  quickly  show  any  small  addition  to  the  weights. 
This  was  tried  in  each  experiment. 

To  measure  the  heat  generated,  we  require  to  know  the  calorific 
capacity  of  the  whole  calorimeter,  and  the  rise  of  temperature  which 
would  have  taken  place  provided  no  heat  had  been  lost  by  radiation. 
The  capacity  of  the  calorimeter  alone  I  have  discussed  elsewhere,  find- 
ing the  total  amount  equal  to  -347  k.  of  water  at  ordinary  tempera- 
tures. The  total  capacity  of  the  calorimeter  is  then  A  -f-  -347,  where 
A  is  the  weight  of  water.  Hence  Joule's  equivalent  in  absolute  meas- 
ure is 

T_ 

~  ( 

where  n  is  the  number  of  revolutions  of  the  chronograph,  it  making 
one  revolution  to  102  of  the  paddles. 

The  corrections  needed  are  as  follows : 

1st.  Correction  for  weighing  in  air.  This  must  be  made  to  W,  the 
cast-iron  weights,  and  to  A  -f-  -347,  the  water  and  copper  of  the  calori- 
meter. If  /  is  the  density  of  the  air  under  the  given  conditions,  the 
correction  is  —  -835  A. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  435 

2d.  For  the  weight  of  the  tape  by  which  the  weights  are  hung. 

rm,-    •    "0006 
This  i 


3d.  For  the  expansion  of  torsion  wheel,  D'  being  the  diameter  at 
20°  C.     This  is  -000018  (t"  —  20°).     Hence, 

'  " 


where  t  —  i'  is  the  rise  of  the  temperature  corrected  for  radiation. 

2.    RADIATION 

The  correction  for  radiation  varies,  of  course,  with  the  difference  of 
temperature  between  the  calorimeter  and  jacket;  but,  owing  to  the 
rapid  generation  of  heat,  the  correction  is  generally  small  in  proportion. 
The  temperature  generated  was  generally  about  0°-6  per  minute.  The 
loss  of  temperature  per  minute  by  radiation  was  approximately  -00140° 
per  minute,  where  0  is  the  difference  of  the  temperature.  This  is  one 
per  cent  for  10°  -7,  and  four  per  cent  for  14°  -2.  Generally,  the  calori- 
meter was  cooler  than  the  jacket  to  start  with,  and  so  a  rise  of  about 
20°  could  be  accomplished  without  a  rate  of  correction  at  any  point 
of  more  than  four  per  cent,  and  an  average  correction  of  less  than  two 
per  cent.  An  error  of  ten  per  cent  is  thus  required  in  the  estimation 
of  the  radiation  to  produce  an  average  error  of  1  in  500,  or  1  in  250 
at  a  single  point.  The  coefficients  never  differ  from  the  mean  more 
than  about  two  per  cent.  The  observations  on  the  equivalent,  being 
at  a  great  variety  of  temperatures,  check  each  other  as  to  any  error  in 
the  radiation. 

The  losses  of  heat  which  I  place  under  the  head  of  radiation  include 
conduction  and  convection  as  well.  I  divide  the  losses  of  heat  into  the 
following  parts:  1st.  Conduction  down  the  shaft;  2d.  Conduction  by 
means  of  the  suspending  wires  or  vulcanite  points  to  the  wheel  above; 
3d.  True  radiation;  4th.  Convection  by  the  air.  To  get  some  idea  of 
the  relative  amounts  lost  in  this  way,  we  can  calculate  the  loss  by 
conduction  from  the  known  coefficients  of  conduction,  and  we  can  get 
some  idea  of  the  relative  loss  from  a  polished  surface  from  the  experi- 
ments of  Mr.  Nichol.  In  this  way  I  suppose  the  total  coefficient  of 
radiation  to  be  made  up  approximately  as  follows: 

Conduction  along  shaft     ............  -00011 

Conduction  along  suspending  wires.  .  .  .  -00006 

True  radiation    ....................  -00017 

Convection   ........................  -00106 

Total   .  -00140 


436  HENEY  A.  EOWLAND 

The  conduction  through  the  vulcanite  only  amounts  to  -0000002. 

From  this  it  would  seem  that  three-fourths  of  the  loss  is  due  to 
radiation  and  convection  combined. 

The  last  two  losses  depend  upon  the  difference  of  temperature  be- 
tween the  calorimeter  and  the  jacket,  but  the  first  two  upon  the  differ- 
ence between  the  calorimeter  and  frame  of  the  machine  and  the  wheel 
respectively.  The  frame  was  always  of  very  nearly  the  same  tempera- 
ture as  the  water  jacket,  but  the  wheel  was  usually  slightly  above  it. 
At  first  its  temperature  was  noted  by  a  thermometer,  and  the  loss  to 
it  computed  separately;  but  it  was  found  to  be  unnecessary,  and  finally 
the  whole  was  assumed  to  be  a  function  of  the  temperature  of  the 
calorimeter  and  of  the  jacket  only. 

At  first  sight  it  might  seem  that  there  was  a  source  of  error  in 
having  a  journal  so  near  the  bottom  of  the  calorimeter,  and  joined  to 
it  by  a  shaft.  But  if  we  consider  it  a  moment,  we  shall  see  that  the 
error  is  inappreciable;  for  even  if  there  was  friction  enough  in  the 
journal  to  heat  it  as  fast  as  the  calorimeter,  it  would  decrease  the 
radiation  only  seven  per  cent,  or  make  an  average  error  in  the  experi- 
ment of  only  1  in  700.  But,  in  fact,  the  journal  was  very  perfectly 
made,  and  there  was  no  strain  on  it  to  produce  friction;  besides  which, 
it  was  connected  to  a  large  mass  of  cast-iron  which  was  attached  to 
the  base.  Hence,  as  a  matter  of  fact,  the  journal  was  not  appreciably 
warmer  after  running  than  before,  although  tested  by  a  thermometer. 
The  difference  could  not  have  been  more  than  a  degree  or  so  at  most. 

The  warming  of  the  wheel  by  conduction  and  of  the  journal  by  fric- 
tion would  tend  to  neutralize  each  other,  as  the  wheel  would  be  warmer 
and  the  journal  cooler  during  the  radiation  experiment  than  the  fric- 
tion experiment. 

The  usual  method  of  obtaining  the  coefficient  of  radiation  would  be 
to  stop  the  engine  while  the  calorimeter  was  hot,  and  observe  the 
cooling,  stirring  the  water  occasionally  when  the  temperature  was  read. 
This  method  I  used  at  first,  reading  the  temperature  at  intervals  of 
about  a  half  to  a  whole  hour.  But  on  thinking  the  matter  over,  it 
became  apparent  that  the  coefficient  found  in  this  way  would  be  too 
small,  especially  at  small  differences  of  temperature;  for  the  layer 
next  to  the  outside  would  be  cooled  lower  than  the  mean  temperature, 
and  the  heat  could  only  get  to  the  outside  by  conduction  through  the 
water  or  by  convection  currents. 

Hence  I  arranged  the  engine  so  as  to  run  the  paddles  very  slowly, 
so  as  to  stir  the  water  constantly,  taking  account  of  the  number  of 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


437 


the  revolutions  and  the  torsion,  so  as  to  compute  the  work.  As  I  had 
foreseen,  the  results  in  this  case  were  higher  than  by  the  other  method. 
At  low  temperatures  the  error  of  the  first  method  was  fifteen  per  cent; 
but  at  high,  it  did  not  amount  to  more  than  about  three  to  five  per 
cent,  and  probably  at  very  high  temperatures  it  would  almost  vanish. 

I  do  not  consider  it  necessary  to  give  all  the  details  of  the  radiation 
experiments,  but  will  merely  remark  that,  as  the  calorimeter  was  nickel- 
plated,  and  as  seventy-five  per  cent  of  the  so-called  radiation  is  due 
to  convection  by  the  air,  the  coefficients  of  radiation  were  found  to  be 
very  constant  under  similar  conditions,  even  after  long  intervals  of 
time. 

The  experiments  were  divided  into  two  groups;  one  when  the  tem- 
perature of  the  jacket  was  about  5°  C.,  and  the  other  when  it  averaged 
about  20°  C. 

The  results  were  then  plotted,  and  the  mean  curve  drawn  through 
them,  from  which  the  following  coefficients  were  obtained.  These 
coefficients  are  the  loss  of  temperature  per  minute,  and  per  degree 
difference  of  temperature. 

TABLE  XXXV.*— COEFFICIENTS  OF  RADIATION. 


Difference  be- 
tween Jacket  and 
Calorimeter. 

Jacket  5°. 

Jacket  20°. 

o 

—5 

•00138 

•00134 

0 

•00135 

•00130 

+  5 

•00137 

•00132 

10 

•00142 

•00138 

15 

•00148 

•00144 

20 

•00154 

•00150 

25 

•00158 

.00154 

As  the  quantity  of  water  in  the  calorimeter  sometimes  varied  slightly, 
the  numbers  should  be  modified  to  suit,  they  being  true  when  the  total 
capacity  of  the  calorimeter  was  8-75  kil.  The  total  surface  of  the 
calorimeter  was  about  2350  sq.  cm.,  and  the  unit  of  time  one  minute. 
To  compare  my  results  with  those  of  McFarlane  and  of  Nichol  given 
in  the  Proc.  K.  S.  and  Proc.  R.  S.  E.,  I  will  reduce  my  results  so  that 
they  can  be  compared  with  the  tables  given  by  Professor  Everett  in  his 
'  Illustrations  of  the  Ccntimeter-Gramme-Second  System  of  Units/ 
pp.  50,  51. 


*  [There  is  no  table  numbered  XXXIV.] 


438 


HENRY  A.  ROWLAND 


The  reducing  factor  is  -0621,  and  hence  the  last  results  for  the  jacket 
at  20°  C.  become: 


TABLE  XXXVI. 


Difference  of 
Temperature. 

Coefficient  of  Radia- 
tion on  the  C.  G.  S. 

System. 

McFarlane's 
Value. 

Ratio. 

8 

•000081 

•000168 

2-07 

5 

•000082 

•000178 

2-17 

10 

•000086 

•000186 

2-16 

15 

•000089 

•000193 

2-17 

20 

•000093 

•000201 

2-16 

25 

•  000096 

•000207 

2.15 

The  variation  which  I  find  is  almost  exactly  that  given  by  McFar- 
lane, as  is  shown  by  the  constancy  of  the  column  of  ratios.  But  my 
coefficients  are  less  than  half  those  of  McFarlane.  This  may  possibly 
be  due  to  the  fact  that  the  walls  of  McFarlane's  enclosure  were  black- 
ened, and  to  his  surface  being  of  polished  copper  and  mine  of  polished 
nickel:  his  surface  may  also  have  been  better  adapted  by  its  form  to 
the  loss  of  heat  by  convection.  The  results  of  Nichol  are  also  much 
lower  than  those  of  McFarlane. 

The  fact  that  the  coefficients  of  radiation  are  less  with  increased 
temperature  of  jacket  is  just  contrary  to  what  Dulong  and  Petit  found 
for  radiation.  But  as  I  have  shown  that  convection  is  the  principal 
factor,  I  am  at  a  loss  to  check  my  result  with  any  other  observer. 
Dulong  and  Petit  make  the  loss  from  convection  dependent  only  upon 
the  difference  of  temperature,  and  approximately  upon  the  square  root 
of  the  pressure  of  the  gas.  Theoretically  it  would  seem  that  the  loss 
should  be  less  as  the  mean  temperature  rises,  seeing  that  the  air  be- 
comes less  dense  and  its  viscosity  increases.  Should  we  substitute 
density  for  pressure  in  Dulong's  law,  we  should  have  the  loss  by  con- 
vection inversely  as  the  square  root  of  the  mean  absolute  temperature, 
or  approximately  the  absolute  temperature  of  the  jacket.  This  would 
give  a  decrease  of  one  per  cent  in  the  radiation  for  about  6°,  which  is 
not  far  from  what  I  have  found. 

To  estimate  the  accuracy  with  which  the  radiation  has  been  obtained 
is  a  very  difficult  matter,  for  the  circumstances  in  the  experiment  are 
not  the  same  as  when  the  radiation  was  obtained.  In  the  first  place, 
although  the  water  is  stirred  during  the  radiation,  yet  it  is  not  stirred 
so  violently  as  during  the  experiment.  Further,  the  wheel  above  the 
calorimeter  is  warmer  during  radiation  than  during  the  experiment. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  439 

Both  these  sources  of  error  tend  to  give  too  small  coefficients  of  radia- 
tion, and  this  is  confirmed  by  looking  over  the  final  tables.  But  I  have 
not  felt  at  liberty  to  make  any  corrections  based  on  the  final  results,  as 
that  would  destroy  the  independence  of  the  observations.  But  we  are 
able  thus  to  get  the  limits  of  the  error  produced. 

During  the  preliminary  experiments  a  water  jacket  was  not  used, 
but  only  a  tin  case,  whose  temperature  was  noted  by  a  thermometer 
above  and  below.  The  radiation  under  these  circumstances  was  larger, 
as  the  case  was  not  entirely  closed  at  the  bottom,  and  so  permitted  more 
circulation  of  air. 

3.    CORRECTIONS  TO  THERMOMETERS,  ETC. 

Among  the  other  corrections  to  the  temperature  as  read  off  from 
the  thermometers,  the  correction  for  the  stem  at  the  temperature  of 
the  air  is  the  greatest.  The  ordinary  formula  for  the  correction  is 
•000156n(£  —  t").  But,  in  applying  this  correction,  it  is  difficult  to 
estimate  n,  the  number  of  degrees  of  thermometer  outside  the  calo- 
rimeter and  at  the  temperature  of  the  air,  seeing  that  part  of  the  stem 
is  heated  by  conduction.  The  uncertainty  vanishes  as  the  thermometer 
becomes  longer  and  longer,  or  rather  as  it  is  more  and  more  sensitive. 
But  even  then  some  of  the  uncertainty  remains.  I  have  sought  to 
avoid  this  uncertainty  by  placing  a  short  tube  filled  with  water  about 
the  lower  part  of  the  thermometer  as  it  comes  out  of  the  calorimeter. 
The  temperature  of  this  was  indicated  by  a  thermometer,  by  aid  of 
which  also  the  heat  lost  to  the  water  by  conduction  through  the  ther- 
mometer stem  could  be  computed;  this,  however,  was  very  minute  com- 
pared with  the  whole  heat  generated,  say  1  in  10,000. 

The  water  being  very  nearly  at  the  temperature  of  the  air,  the  stem 
above  it  could  be  assumed  to  be  at  the  temperature  of  the  air  indicated 
by  a  thermometer  hung  within  an  inch  or  two  of  it.  The  correction  for 
stem  would  thus  have  to  be  divided  into  two  parts,  and  calculated 
separately.  Calculated  in  this  way,  I  suppose  the  correction  is  perfectly 
certain  to  much  less  than  one  hundredth  of  a  degree :  the  total  amount 
was  seldom  over  one-tenth  of  a  degree. 

Among  the  uncertain  errors  to  which  the  measurement  of  tempera- 
ture is  subjected,  I  may  mention  the  following: 

1.  Pressure  on  bulb.  A  pressure  of  60  cm.  of  water  produced  a 
change  of  about  0°-01  in  the  thermometers.  When  the  calorimeter 
was  entirely  closed  there  was  soon  some  pressure  generated.  Hence 
the  introduction  of  the  safety-tube, — a  tube  of  thin  glass  about  10  cm. 


440  HENRY  A.  EOWLAXD 

long,  extending  through  a  cork  in  the  top  of  the  calorimeter.  The  top 
of  the  safety-tube  was  nearly  closed  by  a  cork  to  prevent  evaporation. 
Had  the  tube  been  shorter,  water  would  have  been  forced  out,  as  well 
as  air. 

2.  Conduction  along  stem  from  outside  to  thermometer  bulb.     To 
avoid  this,  not  only  was  the  bulb  immersed,  but  also  quite  a  length  of 
stem.     As  this  portion  of  the  stem,  as  also  the  bulb,  was  surrounded 
by  water  in  violent  motion,  there  could  have  been  no  large  error  from 
this  source.     The  immersed  stem  to  the  top  of  the  bulb  was  generally 
about  5  cm.  or  more,  and  the  stem  only  about  -8  cm.  in  diameter. 

3.  The  thermometer  is  never  at  the  temperature  of  the  water,  be- 
cause the  latter  is  constantly  rising;  but  we  do  not  assume  that  it  is 
so  in  the  experiment.     We  only  assume  that  it  lags  behind  the  water 
to  the  same  amount  at  all  parts  of  the  experiment,  and  this  is  doubt- 
less true. 

To  see  if  the  amount  was  appreciable,  I  suddenly  threw  the  apparatus 
out  of  gear,  thus  stopping  it.  The  temperature  was  observed  to  con- 
tinue rising  about  0°-02  C.  Allowing  0°-01  for  the  rise  due  to  motion 
after  the  word  "Stop"  was  given,  we  have  about  0°-01C.  as  the 
amount  the  thermometer  lagged  behind  the  water. 

4.  Evaporation.     A  possible  source  of  error  exists  in  the  cooling  of 
the  calorimeter  by  evaporation  of  water  leaking  out  from  it. 

The  water  was  always  weighed  before  and  after  the  experiment  in 
a  balance  giving  -i.  gramme  with  accuracy.  The  normal  amount  of 
loss  from  removal  of  thermometer,  wet  corks,  &c.,  was  about  1  gramme. 
The  calorimeter  was  perfectly  tight,  and  had  no  leakage  at  any  point 
in  its  normal  state.  Once  or  twice  the  screws  of  the  stuffing-box 
worked  loose,  but  these  experiments  were  rejected. 

The  evaporation  of  1  gramme  of  water  requires  about  600  heat  units, 
which  is  sufficient  to  depress  the  temperature  of  the  calorimeter  about 
0°-07  C.  As  the  only  point  at  which  evaporation  could  take  place  was 
through  a  hole  less  than  1  mm.  diameter  in  the  safety-tube,  I  think  it 
is  reasonable  to  assume  that  the  error  from  this  source  is  inappreciable. 
But  to  be  doubly  certain,  I  observed  the  time  which  drops  of  water  of 
known  weight  and  area,  placed  on  the  warm  calorimeter,  took  to  dry. 
From  these  experiments  it  was  evident  that  it  would  require  a  consid- 
erable area  of  wet  surface  to  produce  an  appreciable  effect.  This  wet 
surface  never  existed  unless  the  calorimeter  was  wet  by  dew  deposited 
on  the  cool  surface.  To  guard  against  this  error,  the  calorimeter  was 
never  cooled  so  low  that  dew  formed;  it  was  carefully  rubbed  with  a 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  441 

towel,  and  placed  in  the  apparatus  half  an  hour  to  an  hour  before  the 
experiment,  exposed  freely  to  the  air.  The  surface  being  polished,  the 
slightest  deposit  of  dew  was  readily  visible.  The  greatest  care  was 
taken  to  guard  against  this  source  of  error,  and  I  think  the  experiment 
is  free  from  it. 

(d.)  Results 
1.    CONSTANT  DATA 

Joule's  equivalent  in  gravitation  measure  is  of  the  dimensions  of 
length  only,  being  the  height  which  water  would  have  to  fall  to  be 
heated  one  degree.  Or  let  water  flow  downward  with  uniform  velocity 
through  a  capillary  tube  impervious  to  heat;  assuming  the  viscosity 
constant,  the  rate  of  variation  of  height  with  temperature  will  be 
Joule's  equivalent. 

Hence,  besides  the  force  of  gravity  the  only  thing  required  in  abso- 
lute measure  is  some  length.  The  length  that  enters  the  equation 
is  the  diameter  of  the  torsion  wheel.  This  was  determined  under  a 
microscope  comparator  by  comparison  with  a  standard  metre  belong- 
ing to  Professor  Eogers  of  Harvard  Observatory,  which  had  been 
compared  at  Washington  with  the  Coast  Survey  standards,  as  well  as 
by  comparison  with  one  of  our  own  metre  scales  which  had  also  been 
so  compared.  The  result  was  -26908  metre  at  20°  C. 

To  this  must  be  added  the  thickness  of  the  silk  tape  suspending  the 
weights.  This  thickness  was  carefully  determined  by  a  micrometer 
screw  while  the  tape  was  stretched,  the  screw  having  a  flat  end.  The 
result  was  -00031  m. 

So  that,  finally,  D'  ~  -26939  metre  at  20°  C.  Separating  the  con- 
stant from  the  variable  parts,  the  formula  now  becomes 

JL  =  j*6-324^  ^  +  .ooooiS  0"  -  20)  +  ™* 

g  =  9-8005  at  Baltimore. 

It  is  unnecessary  to  have  the  weights  exact  to  standard,  provided  they 
are  relatively  correct,  or  to  make  double  weighings,  provided  the  same 
scale  of  the  balance  is  always  used.  For  both  numerator  and  denomi- 
nator of  the  fraction  contain  a  weight. 

2.     EXPEBIMENTAL  DATA  AND  TABLES  OF  RESULTS 

In  exhibiting  the  results  of  the  experiments,  it  is  much  more  satisfac- 
tory to  compute  at  once  from  the  observations  the  work  necessary  to 
raise  1  kil.  of  the  water  from  the  first  temperature  observed  to  each  sue- 


442  HENRY  A.  EOWLAND 

ceeding  temperature.  By  interpolation  in  such  a  table  we  can  then 
reduce  to  even  degrees.  To  compare  the  different  results  I  have  then 
added  to  each  table  such  a  quantity  as  to  bring  the  result  at  20°  about 
equal  to  10,000  kilogramme-metres. 

The  process  for  each  experiment  may  be  described  as  follows.  The 
calorimeter  was  first  filled  with  distilled  water  a  little  cooler  than  the 
atmosphere,  but  not  so  cool  as  to  cause  a  deposit  of  dew.  It  was  then 
placed  in  the  machine  and  adjusted  to  its  position,  though  the  outer  half 
of  the  jacket  was  left  off  for  some  time,  so  that  the  calorimeter  should 
become  perfectly  dry;  to  aid  which  the  calorimeter  was  polished  with  a 
cloth.  The  thermometer  and  safety-tube  were  also  inserted  at  this 
time. 

After  half  an  hour  or  so,  the  chronograph  was  adjusted,  the  outer  half 
of  the  jacket  put  in  place,  the  wooden  screen  fixed  in  position,  and  all 
was  ready  to  start.  The  engine,  which  had  been  running  quietly  for 
some  time,  was  now  attached,  and  the  experiment  commenced.  First  the 
weights  had  to  be  adjusted  so  as  to  produce  equilibrium  as  nearly  as 
possible. 

The  observers  then  took  their  positions.  One  observer  constantly 
recorded  the  transit  of  the  mercury  over  the  divisions  of  thermometer, 
making  other  suitable  marks,  so  that  the  divisions  could  be  afterwards 
recognized.  He  also  read  the  thermometers  giving  the  temperatures 
of  the  air,  the  bottom  of  the  calorimeter  thermometer,  and  of  the  wheel 
just  above  the  calorimeter;  and  sometimes  another,  giving  that  of  the 
cast-iron  frame  of  the  instrument. 

The  other  observer  read  the  torsion  wheel  once  every  revolution  of 
the  chronograph  cylinder,  recording  the  time  by  his  watch.  He  also 
recorded  on  the  chronograph  every  five  minutes  by  his  watch,  and  like- 
wise stirred  the  water  in  the  jacket  at  intervals,  and  read  its  temper- 
ature. 

The  recording  of  the  time  was  for  the  purpose  of  giving  the  connect- 
ing link  between  the  readings  of  the  torsion  circle  and  of  the  ther- 
mometer. This,  however,  as  the  readings  were  quite  constant,  had 
only  to  be  done  roughly,  say  to  half  a  minute  of  time,  though  the  rec- 
ords of  time  on  the  chronograph  were  true  to  about  a  second. 

The  thermometers  to  read  the  temperature  of  the  water  in  the  jacket 
were  graduated  to  0°-2  C.,  but  were  generally  read  to  0°-1  C.,  and  had 
been  compared  with  the  standards.  There  was  no  object  in  using  more 
delicate  thermometers. 

After  the  experiment  had  continued  long  enough,  the  engine  was 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT  443 

stopped  and  a  radiation  experiment  begun.  The  last  operation  was  to 
weigh  the  calorimeter  again,  after  removing  the  thermometer  and  safety 
tube,  and  also  the  weights  which  had  been  used. 

The  chronograph  sheet,  having  then  been  removed  from  the  cylin- 
der, had  the  time  records  identified  and  marked,  as  well  as  the  ther- 
mometer records.  Each  line  of  the  chronograph  record  was  then  num- 
bered arbitrarily,  and  a  table  made  indicating  the  stand  of  the  ther- 
mometer and  the  number  of  the  revolutions  and  fractions  of  a  revolu- 
tion as  recorded  on  the  chronograph  sheet.  The  times  at  which  these 
temperatures  were  reached  was  also  found  by  interpolation,  and  re- 
corded in  another  column. 

From  the  column  of  times  the  readings  of  the  torsion  circle  could  be 
identified,  and  so  all  the  necessary  data  would  be  at  hand  for  calculating 
the  work  required  to  raise  the  temperature  of  one  kilogramme  of  the 
water  from  the  first  recorded  temperature  to  any  succeeding  tempera- 
ture. 

As  these  temperatures  usually  contained  fractions,  the  amount  of 
work  necessary  to  raise  one  kilogramme  of  the  water  to  the  even  degrees 
could  then  be  found  from  this  table  by  interpolation.  Joule's  equiva- 
lent at  any  point  would  then  be  merely  the  difference  of  any  two  suc- 
ceeding numbers;  or,  better,  one  tenth  the  difference  of  two  numbers 
situated  10°  apart,  or,  in  general,  the  difference  of  the  numbers  divided 
by  the  difference  of  the  temperatures. 

It  would  be  a  perfectly  simple  matter  to  make  the  record  of  the  tor- 
sion circle  entirely  automatic,  and  I  think  I  shall  modify  the  apparatus 
in  that  manner  in  the  future. 

It  would  take  too  much  space  to  give  the  details  of  each  experiment; 
but,  to  show  the  process  of  calculation,  I  will  give  the  experiment  of 
Dec.  17,  1878,  as  a  specimen.  The  chronograph  sheet,  of  course,  I 
cannot  give.  The  computation  is  at  first  in  gravitation  measure,  but 
afterwards  reduced  to  absolute  measure. 

The  calorimeter  before  the  experiment  weighed  12-2733  kil. 
The  calorimeter  after  the  experiment  weighed  12-2716  kil. 

Mean     12-2720  kil. 
Weight  of  calorimeter  alone  3-8721  kil. 


.  •.  Water  alone  weighed  8-3999  kil. 

•3470  kil. 


Total  capacity        8-7469  kil. 


444  HENRY  A.  ROWLAND 

The  correction  for  weighing  in  air  was  -835 /—  -00106. 
The  total  term  containing  the  correction  is  therefore  -99878. 

log  86-324  =1-9361316 

log  -99878  =  1-9994698 

1-9356014 

log  8-7469  =    -9418542 

log  const,  factor  =    -9937472  =  log  9-85706. 

Hence  the  work  per  kilogramme  is  9-85706  S~Wn  in  gravitation 
measure,  the  term  2'Wn  being  used  to  denote  the  sum  of  products 
similar  to  Wn  as  obtained  by  simultaneous  readings  of  torsion  circle 
and  records  on  chronograph  sheet. 

Zero  of  torsion  wheel,  79-3  mm. 

Value  of  1  mm.  on  torsion  wheel  -0118  kil. 

The  following  were  the  records  of  time  on  the  chronograph  sheet : — 

Time  observed.       Revolutions  of  Chronograph.    Time  calculated. 

15  8-74  15-2 

20  25-32  20-1 

25  42-10  25-0 

30  59-05  30-0 

35  76-00  35-0 

40  93-03  40-0 

45  109-97  45-0 

50  126-92  50-0 

55  144.14  55-0 

The  times  were  calculated  by  the  formula 

Time  =  -294  X  Revolutions  +  12-66, 

which  assumes  that  the  engine  moves  with  uniform  velocity.  As  the 
principal  error  in  using  an  incorrect  interpolation  formula  comes  from 
the  calculation  of  the  radiation,  and  as  this  formula  is  correct  within 
a  few  seconds  for  all  the  higher  temperatures,  we  can  use  it  in  the  cal- 
culation of  the  times. 

The  records  of  the  transits  of  the  mercury  over  the  divisions  of  the 
thermometer  were  nearly  always  made  for  each  division,  but  it  is  use- 
less to  calculate  for  each.  I  usually  select  the  even  centimeters,  and 
take  the  mean  of  the  records  for  several  divisions  on  each  side. 

While  the  mercury  was  rising  1  cm.  on  No.  6163,  there  would  be 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  445 

about  seven  revolutions  of  the  chronograph,  and  consequently  seven 
readings  of  the  torsion  circle,  each  one  of  which  was  the  average  for  a 
little  time  as  estimated  by  the  eye. 

I  have  obtained  more  than  thirty  series  of  results,  but  have  thus  far 
reduced  only  fourteen,  five  of  which  are  preliminary,  or  were  made  with 
the  simple  jacket  instead  of  the  water  jacket,  the  radiation  to  which 
was  much  greater,  as  there  was  a  hole  at  the  bottom  which  allowed  more 
circulation  of  the  air.  The  mean  of  the  preliminary  results  agrees  so 
closely  with  the  mean  of  the  final  results,  that  I  have  in  the  end  given 
them  equal  weight. 

On  March  24th,  the  same  thermometer  was  used  for  a  second  experi- 
ment directly  after  the  first,  seeing  that  the  chronograph  failed  to  work 
in  the  first  experiment  until  8°  was  reached.  The  error  from  this  cause 
was  small,  as  the  first  experiment  only  reached  to  26°  C.,  and  hence 
there  could  have  been  no  change  of  zero,  as  this  is  very  nearly  the  tem- 
perature at  which  the  thermometer  was  generally  kept. 

Having  thus  calculated  the  work  in  conjunction  with  the  tempera- 
ture, I  have  next  interpolated  so  as  to  obtain  the  work  at  the  even  de- 
grees. The  tables  so  formed  I  have  combined  in  two  ways :  first,  I  have 
added  to  the  column  of  work  in  each  table  an  arbitrary  number,  such  as 
to  make  the  work  at  20°  about  10,000,  and  have  then  combined  them  as 
seen  in  Table  LI,  and,  secondly,  I  have  subtracted  each  number  from 
the  one  10°  farther  down  the  table,  and  divided  the  numbers  so  found 
by  10,  thus  obtaining  the  mechanical  equivalent  of  heat. 

In  these  tables  four  thermometers  have  been  used,  and  yet  they  were 
so  accurate  that  little  difference  can  be  observed  in  the  experiments 
which  can  be  traced  to  an  error  of  the  thermometer,  although  the  Kew 
standard  has  some  local  irregularities.  The  greatest  difference  between 
any  column  of  Table  LI  and  the  general  mean  is  only  10  kilogramme- 
metres,  or  0-023  degree,  and  this  includes  all  errors  of  calibration  of 
thermometers,  radiation,  &c.  This  seems  to  me  to  be  a  very  remarkable 
result,  and  demonstrates  the  surpassing  accuracy  of  the  method.  In- 
deed, the  limit  of  accuracy  in  thermometry  is  the  only  limit  which  we 
can  at  present  give  to  this  method  of  experiment.  Hence  the  large 
proportional  time  spent  on  that  subject. 

The  accuracy  of  the  radiation  is  demonstrated,  to  some  extent,  by 
the  agreement  of  the  results  obtained  even  with  different  temperatures 
of  the  jacket.  But  on  close  observation  it  seems  apparent  that  the 
coefficients  of  radiation  should  be  further  increased  as  there  is  a  ten- 
dency of  the  end  figures  in  each  series  to  become  too  high.  This  is 


446  HENEY  A.  ROWLAND 

exactly  what  we  should  suppo&e,  as  we  have  seen  that  nearly  all  sources 
of  error  tend  in  the  direction  of  making  the  radiation  too  small.  For 
instance,  an  error  came  from  not  stirring  the  water  during  the  radiation, 
and  there  must  be  a  small  residual  error  from  not  stirring  so  fast 
during  radiation  as  during  the  experiment.  Besides  this,  some  parts 
around  the  calorimeter  were  warm  during  the  radiation  which  were  cool 
during  the  experiment.  And  both  of  these  make  the  correction  for 
radiation  too  small.  However,  the  error  from  this  source  is  small,  and 
cannot  possibly  affect  the  general  conclusions.  In  each  column  of 
Tables  LI  and  LII  a  dash  is  placed  at  the  temperature  of  the  jacket, 
and  for  fifteen  degrees  below  this  point  the  error  in  the  radiation  must 
produce  only  an  inappreciable  error  in  the  equivalent:  taking  the  ob- 
servations within  this  limit  as  the  standards,  and  rejecting  the  others, 
we  should  still  arrive  at  very  nearly  the  same  conclusions  as  if  we  ac- 
cepted the  whole. 

Most  of  the  experiments  are  made  with  a  weight  of  about  7-3  kil.,  as 
everything  seemed  to  work  best  with  this  weight  But  for  the  sake 
of  a  test  I  have  run  the  weight  up  to  8-6  and  down  to  4-4  kil.,  by  which 
the  rate  of  generation  of  the  heat  was  changed  nearly  three  times. 
By  this  the  correction  for  the  radiation  and  the  error  due  to  the  irregu- 
larity of  the  engine  are  changed,  and  yet  scarcely  an  appreciable  differ- 
ence in  the  results  can  be  observed. 

The  tables  explain  themselves  very  well,  but  some  remarks  may  be 
in  order.  Tables  XXXVII  to  L  inclusive  are  the  results  of  fourteen 
experiments  selected  from  the  total  of  about  thirty,  the  others  not  hav- 
ing been  worked  up  yet,  though  I  propose  to  do  so  at  nry  leisure. 

Table  LI  gives  the  collected  results.  At  the  top  of  each  column  the 
date  of  the  experiment  and  number  of  the  thermometer  are  given,  to- 
gether with  the  approximate  torsion  weight  and  the  rate  of  rise  of  tem- 
perature per  hour.  The  dash  in  each  column  gives  approximately  the 
temperature  of  the  jacket,  and  hence  of  the  air.  There  are  four  col- 
umns of  mean  values,  but  the  last,  produced  from  the  combination  of 
the  table  by  parts,  is  the  best. 

Table  LII  gives  the  mechanical  equivalent  of  heat  as  deduced  from 
intervals  of  10°  on  Table  LI.  The  selection  of  intervals  of  10°  tends 
to  screen  the  variation  of  the  specific  heat  of  water  from  view,  but  a 
smaller  interval  gives  too  many  local  irregularities.  In  taking  the 
mean  I  have  given  all  the  observations  equal  weight,  but  as  the  Kew 
standard  was  only  graduated  to  -J°  F.  it  was  impossible  to  calibrate  it 
so  accurately  as  to  avoid  irregularities  of  0°-02C.  which  would  affect 


Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


447 


the  quantities  1  in  500.  Hence,  in  drawing  a  curve  through  the  results, 
as  given  in  the  last  column,  I  have  almost  neglected  the  Kew,  and  have 
otherwise  sought  to  draw  a  regular  curve  without  points  of  inflection. 
The  figures  in  the  last  column  I  consider  the  best. 

Table  LIII  takes  the  mean  values  as  found  in  Tables  LI  and  LII, 
and  exhibits  them  with  respect  to  the  temperatures  on  the  different 
thermometers,  to  the  different  parts  of  the  earth,  and  also  gives  the 
reduction  to  the  absolute  scale.  I  am  inclined  to  favor  the  absolute 
scale,  using  ra=  -00015,  as  given  in  the  Appendix  to  Thermometry, 
rather  than  -00018,  as  used  throughout  the  paper. 

Table  LIV  gives  what  T  consider  the  final  result  of  the  experiment. 
It  is  based  on  the  result  ra=  -00015  for  the  thermometers,  and  is  cor- 
rected for  the  irregularity  of  the  engine  by  adding  1  in  4000. 

The  minor  irregularities  are  also  corrected  so  that  the  results  signify 
a  smooth  curve,  without  irregularity  or  points  of  contrary  flexure. 
But  the  curve  for  the  work  does  not  differ  more  than  three  kilogramme- 
metres  from  the  actual  experiment  at  any  point,  and  generally  coincides 
with  it  to  about  one  kilogramme-metre.  These  differences  signify 
0°-007  C.  and  0°-002  C.,  respectively.  The  mechanical  equivalent  is 
for  single  degrees  rather  than  for  ten  degrees,  as  in  the  other  tables. 

TABLE  XXXVII.— FIRST  SERIES. — Preliminary. 
January  16,  1878.     Jacket  and  Air  about  14°  C. 


h 

£ 

•s* 

jg 

j 

2 

• 

id 

Correction. 

if 

§ 

^§ 

S 

•~  = 
IS 

&£ 

P* 

It 

t  — 

5  8s 
3  C 

15 

A 

§ 

«l 

||1 

-= 

« 
S 
P 

00 

•c 
£ 

8| 

>2 

y 

§ 

S 

*s 

S 

1 

*5 

2 

0 

140 

52-0 

—  •005 

0 

9-185 

5-485 

7  "iflQ 

0 

160 
180 
203 
220 
240 

56-0 
59-2 
63-4 
66-5 
70-2 

—  003 
0 
+  •006 
+  •011 
+  •020 

017 
—  •022 
—  015 
001 
+  •027 

11-412 
13-650 
16-230 
18-137 
20-392 

18-023 
30-652 
45-329 
56-241 
69-153 

7-478 
7-442 
7-394 
7-364 
7.  3^4. 

951 
1906 
3010 
3825 
4786 

io 
11 

12 
13 
14 

348 
775 
1202 
1629 
2056 

5728 
6155 
6582 
7009 
7436 

259 

74-0 

+  •028 

+  •067 

22-538 

81-484 

5702 

15 

2484 

7864 

289 

80-0 

+  •045 

+  •161 

25-943 

101-214 

7156 

16 

2912 

8292 

17 

3340 

8720 

18 

3767 

9147 

19 

4193 

9573 

20 

4619 

9999 

21 

5048 

10428 

22 

5472 

10852 

23 

5899 

11279 

24 

6326 

11706 

25 

6753 

12133 

• 

26 

7180 

12560 

448 


HENRY  A.  ROWLAND 


TABLE  XXXVIII SECOND   SERIES.— Preliminary. 

March  7,  1878.     Jacket  18°.5  to  22°. 5.     Air  about  21°  C. 


Thermometer 
No.  6163. 

« 

e 

R 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight 
W. 

«Work  per  Kilo- 
gramme = 
2  10-060  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  6812 

S 
£ 
• 

i 

f6 

170 
180 
190 
200 
210 
220 
230 
240 
250 
260 
270 
280 
290 
300 
310 
320 
330 
340 
350 
360 
370 
380 
390 

19-9 

—  •016 

0 

12-537 
13-646 
14-755 
15-863 
16-972 
18-085 
19-196 
20-305 
21-419 
22  •  533 
23-642 
24-754 
25-867 
26-990 
28-119 
29-253 
30-393 
31  •  540 
32-689 
33-842 
34-998 
36-158 
37-321 

5-03 
11-12 
17-22 
23-36 
29-55 
35-70 
41-90 
48-09 
54-30 

7-737 
7-710 
7.666 
7-642 
7-641 
7.630 
7.611- 
7.600 
7.596 
7.582 
7.552 
7.547 
7.576 
7-611 
7-604 
7-611 
7-617 
7-602 
7-592 
7-576 
7-550 
7-550 

0 
474 
947 
1421 
1897 
2369 
2845 
3319 
3794 

4740 
5213 
5687 
6164 
6643 
7125 
7608 
8097 
8590 
9081 
9576 
10071 
10567 

°18 

14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 

198 
625 
1052 
1480 
1909 
2333 
2761 
3189 
3615 
4041 
4467 
4892 
5318 
5744 
6168 
6593 
7017 
7441 
7867 
8294 
8722 
9149 
9577 
10004 
10430 

7010 
7437 
7864 
8292 
8721 
9145 
9573 
10001 
10427 
10853 
11279 
11704 
12130 
12556 
12980 
13405 
13829 
14253 
14679 
15106 
15534 
15961 
16389 
16816 
17242 

26-8 

—  •010 

—  .036 

33.8 

+  .003 

—  •036 

66-69 
72-92 
79-16 
85-42 
91-67 
97-98 
104-28 
110-67 
117-12 
123-54 
130-04 
136-56 
143-08 

40-8 

+  0-20 

—  001 

47-8 

+  •044 

+  •073 

51-4 

55-0 

+  •072 

+  •184 

58-7 

+  •588 

+  •261 

TABLE  XXXIX — THIRD  SERIES.—  Preliminary. 
March  12,  1878.     Jacket  13°-2  to  16°-6.     Air  about  15°  C. 


Thermometer 
No.  6166. 

® 
S 
H 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph 
2n. 

4(1  Mean  Weight 
W. 

Work  per 
Kilogramme 
=  2  9-9690  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  7599. 

S 

I 

i 

« 

205 
210 
220 
230 

28-0 
28-6 
29-9 
31-1 

0 
0 

0 
+  -002 

14-368 
14-754 
15-529 
16-307 

3-156 
5-334 

9-770 
14-184 

U-5167 

0 
164 
495 

827 

0 

15 

16 

17 

269 
696 
1122 

7868 
8295 
8721 

+  •003 

+  •010 

45  In  the  calculation  of  this  column,  more  exact  data  were  used  than  given  in  the 
other  two  columns,  seeing  that  the  original  calculation  was  made  every  5  mm.  of  the 
thermometer.     Hence  the  last  figure  may  not  always  agree  with  the  rest  of  the  data. 

46  As  this  table  was  originally  calculated  for  every  5  mm.  on   the  thermometer,  I 
have  given  the  weights  which  were  used  to  check  the  more  exact  calculation. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


449 


TABLE  XXXIX.— Continued. 


Thermometer 
No.  6106. 

i 

EH 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph 
2n. 

Mean  Weight 
W. 

Work  per 
Kilogramme 
=  2  9-690  TFn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  7599. 

1 

• 

I 

240 

250 
260 
270 
280 
290 
300 
310 
320 
330 
340 
350 
360 
370 
380 
390 
400 
410 
420 

32-4 
33-6 
34-9 
36-2 
37-4 
38-7 
39  9 
41-2 
42-5 
43-7 
45-0 
46-3 
47-6 
48-9 
50-1 
51-4 
52-7 
54-0 
55-3 

17-090 
17-875 
18-662 
19-452 
20-242 
21-029 
21-825 
22-619 
23-418 
24-220 
25-023 
28-825 
26-628 
27-438 
28-253 
29-069 
29-884 
30-703 
31-519 

18-642 
23-080 
27-550 
32-014 
36-474 
40-924 
45-424 
49-838 
54-302 
58-844 
63-366 
67.874 
72-403 
76-987 
81-550 
86-100 
90-720 
95-316 
99-920 

(.7-5462 
(.7  -5668 
(.7-5875 
V  7-  5763 
(.7-5872 
(.7-5801 

1160 
1495 
1831 
2167 
2504 
2840 
3179 
3514 
3853 
4194 
4536 
4876 
5219 
5565 
5910 
6255 
6604 
6951 
7299 

o 

18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 

1548 
1975 
2401 
2828 
3253 
3676 
4101 
4526 
4951 
5378 
5803 
6226 
6653 
7078 

9147 
9574 
10000 
10427 
10852 
11275 
11700 
12125 
12550 
12977 
13402 
13825 
14252 
14677 

+  •009 

+  -021 

+  •014 

+  •038 

+  •019 

+  •055 

+  •024 

+  •089 

+  •030 

+  •120 

+  •038 

+  •159 

+  •047 

+  •202 

+  •056 

+  •251 

+  •066 

+  •304 

TABLE  XL.—  FOUBTH  SERIES. — Preliminary." 
March  24,  1878.     Jacket  5°-4  to  8° -2.     Air  about  6°  C. 


Thermometer 
No.  6163. 

I 

B 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph 
In. 

Mean  Weight 
W. 

o.e 

y* 

ft|o 

LJ  03  T—  1 

•*   tHCO 
SH  >s^ 

£.2& 
*|M 

*l 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  4903. 

a 

2 

en 

1 

130 
140 
150 
160 
170 
180 
190 
200 
210 
220 
230 
240 
250 
260 
270 
280 
290 

27;4 
29-2 
31-0 
32-9 
34-7 
36-6 
38-4 
40-3 
42-2 
44-2 
46-1 

+  •002 

0 

8-071 
9-204 
10-340 
11-480 
12-620 
13-763 
14-908 
16-054 
17-202 
18-350 
19-504 

42-364 
48-898 
55-438 
62-066 
68-669 
75-330 
81-973 
88-597 
95-264 
101-941 
108-588 

7-471 
7-446 
7-442 
7-405 
7-390 
7-398 
7-431 
7-429 
7-437 
7-433 

V  7-4617 

7-509 
7-502 

0 
485 
968 
1458 
1944 
2433 
2921 
3410 
3902 
4395 
4886 

6855 
7350 
7844 

O 

8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

-30 

398 
823 
1252 
1680 
2107 
2534 
3960 
3387 
3815 
4245 
4672 
5098 
5524 
5950 
6376 
6802 
7228 
7651 

4872 
5300 
5725 
6154 
6582 
7009 
7436 
8862 
8289 
8717 
9147 
9574 
10000 
10426 
10852 
11278 
11704 
12130 
12553 

+  •010 

+  •019 

+  •017 

+  •050 

+  •025 

+  •093 

+  •034 

+  •150 

+  •046 

+  -222 

.... 







53-6 
55-7 
57-7 

+  •073 

+  •399 

24-124 

25-288 
26-456 

135-158 
141-803 
148-427 

+  •084 

+  •524 

47  The  first  part  of  the  experiments  was   lost,  as  the  pen  of   the  chronograph  did 
not  work. 
29 


450 


HENRY  A.  EOWLAND 


TABLE  XLI. — FIFTH  SERIES. — Preliminary. 
March  24,  1878.     Jacket  5°-4  to  8°-4.     Air  about  6°C. 


Thermometer 
No.  6163. 

1 

H 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph 
2n. 

Mean  Weight 
W. 

Work  per 
Kilogramme 
=  29-8816  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  2250. 

a 

i 

02 

•d 

I 

w 

75 
80 
90 
100 
110 
120 
130 
140 
150 
160 
170 
180 
190 
200 
210 
220 
230 
240 
250 
260 
270 
280 
290 
300 
810 

0-9 
1-7 
3-4 
5-1 
6-8 
8-5 
10-2 
12-0 
13-7 
15-5 
17-2 
19-0 
20-8 
22-6 
24-3 
26-1 
27-9 
29-6 

—  •003 

0 

1-891 
2-451 
3-569 
4-690 
5-810 
6-936 
8-060 
9-190 
10-323 
11-459 
12-600 
13-742 
14-882 
16-025 
17-170 
18-316 
19-467 
20-615 

3-154 
6-118 
12-174 
18-172 
24-212 
30-397 
36-621 
42-854 
49-068 
55  •  398 
61-707 
68-036 
74-358 
80-716 
87-064 
93-402 
99-677 
105-950 

8-1544 
8-0900 
8-0409 
8-0074 
7-9170 
7-8973 
7-8786 
7-8512 
7-8061 
7-7799 
7-7622 
7-7643 
7-7807 
7-8419 
7-8468 
7-8579 
7-8802 

(.7-8980 

7-9038 
7-9091 
7-8979 
7-8974 

0 
239 
723 
1200 
1677 
2161 
2647 
3132 
3614 
4103 
4588 
5073 
5558 
6047 
6539 
7030 
7518 
8006 

9482 
9976 
10474 
10974 
11481 

o 

2 
3 
4 
5 
6 
6 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 

46 

477 
906 
1332 
1759 
2189 
2621 
3050 
3477 
3905 
4333 
4759 
5183 
5608 
6036 
6466 
6895 
7320 
7745 
8170 
8597 
9024 
9451 
9878 
10305 
10733 
11160 

2296 
2727 
3156 
3582 
4009 
4439 
4871 
5300 
5727 
6155 
6583 
7009 
7433 
7858 
8286 
8716 
9145 
9570 
9995 
10420 
10847 
11274 
11701 
11128 
12555 
12983 
13410 

—  •002 

—  •012 

0 

—  •017 

+  •003 

—  012 

+  •007 

+  •005 

+  •015 

+  •032 

+  •024 
+  •028 

+  •068 
+  •092 

+  •039 

+  •150 

+  •050 

+  •270 

34-9 
36-7 
38-5 
40-2 
42-1 

+  •069 

+  •351 

24-072 
25-231 
26-395 
27-565 

28-748 

124-863 
131-181 
137-560 
143-972 
150-467 

+  •087 

+  •450 

+  •109 

+  •583 

TABLE  XLIL— SIXTH  SEEIES. 
May  14,  1878.     Jacket  12°-1  to  12°-4.     Air  about  13°  C. 


Thermometer 
No.  6165. 

I 

p 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight  W 

Work  per 
Kilogramme 
=  2  9.9051  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  5433. 

a 
s 

02 

i 

140 
150 
160 
170 
180 
190 
200 
210 
220 

46-4 
47-9 
49-4 
50-9 
52-5 
54-0 
55-5 
57-0 
58-5 

002 

0 

9-319 
10-178 
11-032 
11-886 
12-740 
13-596 
14-454 
15-314 
16-174 

1-93 
7-07 
12-19 
17-37 
22-52 
27-70 
32-88 
38-07 
43-29 

I  7-  2291 
17-1608 
i  7-  1500 
I  7-1512 

0 
370 
735 
1102 
1467 
1835 
2201 
2568 
2938 

°9 
10 
It 
12 
13 
14 
15 
16 
17 

—  137 
293 
721 
1151 
1579 
2007 
2434 
2863 
3290 

5296 
5726 
6154 

6584 
7012 
7440 
7867 
8296 
8723 

•000 

007 

+  •002 

008 

+  •006 

002 

+  •010 

+  •011 

ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


451 


TABLE  XLII.  —  Continued. 


Thermometer 
No.  6165. 

i 

H 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight  W. 

gtl 

S.B~ 

O  oos 

^5" 
M| 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  5433. 

a 

s 

• 

1 

230 
240 
250 
260 
270 
280 
290 
300 
310 
320 
330 
340 
350 
360 
370 
380 
390 
400 
410 
420 

60-0 
61-6 

17°037 
17-093 

48-50 
53-70 

jl.7-1446 
].  7-1536 
J.  7-1230 
[7-1344 
\.  7-1302 
17-1117 
I  7  -0958 
1^7-1076 
'.  7-1088 
.7-1064 

3306 
3675 

4778 
5148 
5514 
5878 
6240 
6600 
6962 
7319 
7680 
8035 
8396 
8754 
9115 
9475 
9833 
10192 

o 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
83 

3716 
4142 
4567 
4993 
5420 
5846 
6271 
6696 
7121 
7547 
7973 
8400 
8829 
9259 
9678 
10096 

9149 
9575 
10000 
10426 
10853 
11279 
11704 
12129 
12554 
12980 
13406 
13833 
14262 
14692 
15111 
15529 

+  •015 

+  •031 

66-2 
67-7 
69-2 
70-7 
72-2 
73-7 
75-2 
76-2 
78-2 
79-7 
81-2 
82-7 
84-2 
85-7 
87-2 
88-7 

+  •024 

+  •075 

20-500 
21-362 
22-220 
23-076 
23-928 
24-774 
25-624 
26-467 
27-309 
28-147 
28-990 
29-825 
30-663 
31  •  505 
32-377 
33-226 

69-27 
74-50 
79-69 
84-84 
89-97 
95-05 
100-19 
105-27 
110-39 
115-44 
120-57 
125-66 
130-78 
135-90 
140-98 
146-08 

+  •031 

+  •113 

+  •039 

+  •158 

+  •047 

+  •212 

+  •056 

+  •272 

+  •065 

+  -341 

+  •076 

+  •417 

+  •087 

+  •504 

TABLE  XLIII. — SEVENTH  SERIES. 
May  15,  1878.     Jacket  11°.  8  to  12°.     Air  about  12°  C. 


Thermometer 
No.  6163. 

® 

S 

EH 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight  W. 

Work  per 
Kilogramme 
=  2  9.9387  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  5097. 

S 

3 

• 

•d 
* 

130 
140 
150 
160 
170 
180 
190 
200 
210 
220 
230 
240 
250 
260 
270 
280 
290 

30.9 
32.2 
33.6 
35.0 
36.3 
37.6 
38.9 
40.2 
41.5 
42.8 
44.2 
45.5 
46.9 
48.3 
49.6 
50.9 
52.3 

—  .004 

0 

8.538 
9.315 
10.094 
10.875 
11.654 
12.433 
13.209 
13.984 
14.758 
15.536 
16.317 
17.103 
17.891 
18.682 
19.475 
20.269 
21.079 

5.07 
9.73 
14.36 
18.98 
23.56 
28.16 
32.74 
37.31 
41.84 
46.38 
50.99 
55.62 
60.29 

69.63 
74.34 
79.01 

t  7.  2850 
1.7.  3011 
i  7.3165 
i  7.  3460 
17.3094 
|^7.2846 
J^7.2822 
^7.2610 

0 
335 
668 
1003 
1335 
1670 
2003 
2337 
2667 
2998 
3332 
3667 
4005 

4681 
5021 
5358 

0 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

199 
628 
1056 
1484 
1913 
2344 
2770 
3196 
3623 
4052 
4478 
4906 
5324 
5754 
6179 
6603 

5296 
5725 
6153 
6581 
7010 
7441 
7867 
8293 
8720 
9149 
9575 
10003 
10421 
10851 
11276 
11700 

—  .002 

—  .006 

0 

—  .010 

+  .003 

—  .008 

+  .006 

.000 

+  .010 

+  .013 

+  .014 

+  .032 

+  .019 



+  .056 

+  .025 

+  .090 

452 


HENRY  A.  ROWLAND 


TABLE  XLIII.— Continued. 


Thermometer 
No.  6163. 

1 

H 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2». 

Mean  Weight  W. 

Work  per 
Kilogramme 
=  2  9.9387  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 

+5097. 

a 
2 

CD 

•c 

03 

M 

300 
310 
320 
330 
340 
350 
360 
370 
380 
390 
400 
410 
420 

53.6 
55.0 
56.4 
57.8 
59.2 
60.5 
61.9 
63.2 
64.6 
66.0 
67.4 
68.8 
70.1 

21.866 
22.665 
23.471 
24.281 
25.088 
25.896 
26  .  706 
27.523 
28.346 
29.172 
29.996 
30.827 
31.653 

83.71 
88.42 
93.14 
97.88 
102.61 
107.36 
112.14 
116.88 
121.62 
126.34 
131.12 
135.90 
140.66 

)  7.2504 
|  7.2893 
|  7.3047 
)  7.3389 
)  7.4109 

)  7.4356 
'  7.4581 

5697 
6037 
6379 
6722 
7065 
7410 
7759 
8104 
8454 
8801 
9155 
9508 
9861 

2°5 
26 
27 
28 
29 
30 
31 
32 

7028 
7454 
7883 
8307 
8729 
9157 
9582 
10009 

12125 
12551 
12980 
13404 
13826 
14254 
14679 
15106 

+  .032 
+  .039 

+  .127 
+  .172 

+  .046 

+  .222 

+  .055 

+  .279 

+  .065 

+  .345 

+  .075 
+  .080 

+  .419 
+  .456 

TABLE  XLIV EIGHTH  SERIES. 

May  23,  1878.     Jacket  16°.2  to  16°.5.     Air  about  20°  C. 


Thermometer 
No.  6166. 

1 
H 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight  W. 

Work  per 
Kilogramme 
=  2  9.9075  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 

+  8409. 

S 
£ 

GO 

•d 
S 

230 
240 
250 
260 
270 
280 
290 
300 
310 
320 
330 
340 
350 
360 
370 
380 
390 
400 
410 
420 

23.9 

25.4 
26.8 
28.3 
29.7 
31.2 
32.7 
34.2 
35.6 
37.1 
38.6 
40.1 
41.6 
43.1 
44.6 
46.0 
47.5 
49.0 
50.6 
52.1 

—  .007 

0 

16?287 
17.063 

39.120 
43.982 

6.9137 
L  6.  9358 

6.9007 
6.9125 

6.8878 
6.8866 
6.8594 
6.8358 
6.8748 
6.9184 
6.9444 
6.9291 
6.9338 
6.9385 
6.9444 
6.9467 
6.9314 

0 
333 

1338 
1673 
2010 
2346 
2682 
3020 
3363 
3702 
4044 
4385 
4727 
5074 
5418 
5766 
6115 
6464 

o 

17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 

306 
735 
1163 
1592 
2019 
2446 
2871 
3298 
3722 
4150 
4574 
4999 
5423 
5851 
6275 

8715 
9144 
9572 
10001 
10428 
10855 
11280 
11707 
12131 
12559 
12983 
13408 
13832 
14260 
14684 

.000 

+  .005 

19.405 
20.190 
20.978 
21.765 
22.554 
23.350 
24.151 
24.952 
25.751 
26.552 
27.361 
28.175 
28.989 
29.800 
30.624 
31.445 

58.602 
63.503 
68.428 
73.351 
78.283 
83.245 
88.314 
93.294 
98.275 
103.232 
108.216 
113.269 
118.281 
123.329 
128.399 
133.480 

+  !008 

+  .040 

+  .017 

+  .028 

+  .085 
+  .144 

+  .039 

+  .217 

+  .047 

+  .281 

Ox  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


453 


TABLE  XLV.— NINTH  SERIES. 
May  27,  1878.  Jacket  19°.6  to  20°.     Air  about  23°  C. 


Thermometer 
No.  6163. 

1 

B 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2w. 

Mean  Weight.  W. 

Work  per 
Kilogramme 
=  2  9.9077  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  8246. 

S 
5 

• 

1 

200 
210 
220 
230 
240 
250 
260 
270 
280 
290 
300 
310 
320 
330 
340 
350 
360 
370 
380 
390 
400 
410 
420 

38.0 
39.4 
40.9 
42.3 
43.8 
45.3 

—  .015 

0 

15.890 
17.000 
18.106 
19.219 
.20.329 
21.442 
22.552 
23.659 
24.771 
25.885 
27.006 
28.133 
29.264 
30.404 
31.552 
32.702 
33.853 
35.011 
36.170 
37.331 
38.497 
39.664 
40.833 

6.33 
11.74 
17.17 
22.62 
28.13 
33.68 

1  8.  8108 

1  8.  7341 
8.6030 

)  8.4800 

•^8.4399 

J 

^8.4765 

\  8.4552 
-I  8.4015 
1  8.4222 
•I  8.4706 
•»  8.4316 

0 
473 
946 
1419 
1895 
2368 

3785 
4263 
4737 
5215 
5697 
6182 
6669 
7159 
7652 
8143 
8638 
9128 
9626 
10126 
10620 

16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 

47 
473 
901 
1326 
1754 
2180 
2606 
3031 
3457 
3883 
4312 
4734 
5159 
5584 
6010 
6435 
6860 
7286 
7714 
8138 
8565 
8988 
9414 
9842 
10268 
10691 

8293 
8719 
9147 
9572 
10000 
10426 
10852 
11277 
11703 
12129 
12558 
12980 
13405 
13830 
14256 
14681 
15106 
15532 
15960 
16384 
16811 
17234 
17660 
18088 
18514 
18937 

—  Oil 

—  .010 

-.005 

—  .011 

+  .002 

—  .004 

49.8 
51.3 
52.9 
54.4 
56.0 
57.5 
59.1 
60.6 
62.2 
63.8 
65.4 
67.0 
68.6 
70.2 
71.8 

+  .009 

+  .012 

50.55 
56.25 
61.93 
67.63 
73.36 
79.15 
84.97 
90.85 
96.78 
102.66 
108.59 
114.45 
120.36 
126.33 
132.26 

+  .019 

+  .037 

+  .029 

+  .072 

+  .042 

+  .118 

+  .056 

+  .173 

+  .071 

+  .242 

+  .088 

+  .322 

+  .105 

+  .419 

454 


HENRY  A.  KOWLAND 


TABLE  XLVL— TENTH  SERIES. 
June  3,  1878.     Jacket  18°. 1  to  18°. 4.     Air  about  20°  C. 


Thermometer 
No.  6166. 

6 
S 

B 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight  W. 

Work  per 
Kilogramme 
=  2  9.8878  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  9076. 

S 
• 

as 

1 

250 
260 
270 
280 
290 
300 
310 
320 
330 
340 
350 
360 
370 
380 
390 
400 
410 

4.1 
7.0 
9.9 
12.8 
15.7 
18.7 
21.6 
24.5 
27.5 
30.5 
33.6 
36.6 
39.6 
42.7 
45.8 
48.9 
52.0 

-.007 
—  !6o3 

0 
+  .004 

17.838 
18.617 
19.401 
20.188 
20.978 
21.763 
22.551 
23.354 
24.  162 
24.970 
25.780 
26.593 
27.415 
28.246 
29.079 
29.911 
30.754 

7.82 

23.19 
30.95 
38.70 
46.41 
54.21 
62.04 
69.92 
77.92 
85.89 
93.94 
102.05 
110.34 
118.49 
126.66 
134.89 

|  4.  3899 
1  4.  3919 
J4.3912 
1  4.  3907 
|  4.  3624 
J4.3542 
1  4.  3362 
i  4.  3978 

0 

667 
1005 
1341 
1676 
2014 
2354 
2696 
3041 
3385 
3731 
4081 
4437 
4786 
5141 
5499 

18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 

69 
496 
925 
1350 
1778 
2204 
2627 
3054 
3479 
3904 
4332 
4852 
5179 
5604 

9145 
9572 
10001 
10426 
10854 
11280 
11703 
12130 
12555 
12980 
13408 
13828 
14255 
14680 

+  .003 

+  .020 

+  .008 

+  0.037 

+  .014 

+  .078 

+  .020 

+  .132 

+  .028 

+  .198 

+  .036 

+  .281 

+  .044 

+  .377 

.  .   I   

TABLE  XLVIL— ELEVENTH  SERIES. 
June  19,  1878.     Jacket  19°. 6  to  20°.     Air  about  23°  C. 


Thermometer 
No.  6163. 

6 
S 

B 

Correction. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight  W. 

Work  per 
Kilogramme 
=  2  9.8404  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  10620. 

S 
5 

-t-> 

02 

i 

W 

250 

260 
270 
280 
290 
300 
310 
320 
330 
340 
350 
360 
370 
380 
390 
400 
410 
420 

.... 

—  .002 
+  .002 

0 
+  .006 

21?450 
22.562 

8.933 
16.087 

6.7572 

I  6.  7678 

0 
476 

o 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 

-192 
235 

662 
1087 
1511 
1939 
2365 
2789 
3214 
3638 
4063 
4488 
4913 
5337 
5760 
6187 
6614 
7040 
7465 
7891 
8317 

10428 
10855 
11282 
11707 
12131 
12559 
12985 
13409 
13834 
14258 
14683 
15108 
15533 
15957 
16380 
16807 
17234 
17660 
18085 
18511 
18937 

.... 

+  .010 

+  .029 

24.789 
25.907 
27.032 
28.168 
29.307 
30.456 
31.612 
32.774 
33.939 
35.110 
36.280 
37.456 
38.637 
39.821 
41.010 

30  281 
37.439 
44.655 
51.848 
59.098 
66.390 
73  .  724 
81.153 
88.462 
95.734 
103.093 
110-560 
118.121 
125.693 
133.250 

i  6  .  7749 
i  6.  7896 
j.  6.  7973 
i  6.  8188 
I  6.  9165 
j.  6.  7876 
I  6.  7808 

1421 
1899 
2379 
2860 
3344 
3832 
4323 
4817 
5311 
5807 
6307 
6808 
7311 
7815 
8321 

+  .019 

+  .063 

.... 

+  .031 

+  .113 

— 

+  .043 

+  .177 

+  .058 

+  .257 

+  .072 

+  .351 

+  .087 

+  .463 

+  .106 

+  .595 

ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


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HENRY  A.  EOWLAND 


TABLE  XLIX.—  THIRTEENTH  SERIES. 
Dec.   19,  1878.     Jacket  3°.2  to  3°.5.     Air  4°. 2  to  5.2 


C. 


Thermometer 
No.  6163. 

Corrections. 

Corrected 
Temperature. 

Revolutions  of 
Chronograph  2n. 

Mean  Weight  W. 

Work  per 
Kilogramme 
9.8938  X  Wn. 

2  9.8938  Wn. 

Temperature. 

Work  per 
Kilogramme. 

Work  +  1964. 

a 
5 

00 

1 

70 
80 
90 
100 
110 
120 
130 
140 
150 
160 
170 
180 
190 
200 
210 
220 
230 
240 
250 
260 
270 
280 

0 

0 

1?248 
2.378 
3.500 
4.626 
5.751 
6.881 
8.013 
9.148 
10.284 
11.424 
12.569 
13.713 
14.859 
16.005 
17.154 
18.300 
19.452 
20.604 
21.760 
22.912 
24.065 
25.221 

1.72 
7.38 
13.11 
18.89 
24.70 
30.55 
36.38 
42.27 
48.10 
53.92 
59.81 
65.72 
71.57 
77.50 
83.40 
89.30 
95.23 
101.17 

8.6610 
8.5571 
8.4325 
8.3688 
8.4155 
8.4189 
8.3953 
8.4366 
8.4484 
8.4189 
8.3988 
8.4153 
8.3811 
8.3835 
8.3976 
8.4035 

8.4460 

1 

5*8.4555 

8.4602 
8.4779 

485.0 
485.1 
482.2 
481.1 
487.1 
485.6 
489.2 
486.6 
486.5 
490.6 
491.1 
487.1 
491.7 
489.4 
490.2 
493.0 
496.4 

981.3 

494.7 
494.0 

0 
485.0 
970.1 
1452.3 
1933.4 
2420.5 
2906.1 
3395  .  3 
3881.9 
4368.4 
4859.0 
5350.1 
5837.2 
6328.9 
6818.3 
7308.5 
7801.5 
8297.9 

°1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

—  106 
+  323 
754 
1184 
1612 
2041 
2472 
2901 
3331 
3760 
4187 
4615 
5045 
5472 
5898 
6327 
6753 
7180 
7608 
8038 
8465 
8891 
9317 
9746 
10173 

1858 
2287 
2718 
3148 
3576 
4005 
4436 
4865 
5295 
5724 
6151 
6579 
7009 
7436 
7862 
8291 
8717 
9144 
9572 
10002 
10429 
10855 
11281 
11710 
12137 

0 

—  .003 

+  .001 

+  .003 

+  .005 

+  .019 

+  .009 

+  .044 

+  .016 

+  .080 

+  .023 

+  .126 

+  .033 

+  .183 

+  .044 

+  .251 

+  .056 

+  .332 

112.90 
118.81 
124.70 

9279.2 
9773.9 
10267.9 

+  .069 

+  .424 

ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT 


457 


TABLE  L. — FOURTEENTH   SERIES. 
December  20,  1878.     Jacket  1°.5  to  1°.9.     Air  about  3°.4  C. 


Temperature 
by  Kew 
Standard. 

4 

a 

H 

Corrections. 

Corrected  Tem- 
perature Abso- 
lute Scale. 

Revolution  of 
Chronograph 
2n. 

Mean  Weight 
W. 

®ke 

11^ 
Sfi 

0  0  2 

*s« 

Temperature. 

Work  per 
Kilogramme. 

Work  per 
Kilogramme 
+  2210. 

Reduction 
to  Absolute 
Scale. 

1 

i 

36.0 
38.5 
41.0 
43.5 
46.0 
48.5 
51.0 
53.5 
56.0 
58.5 
61.0 
63.5 
66.0 
68.5 
71.0 
73.5 
76.0 
78.5 

56.0 
58.4 
.9 
3.3 
5.8 
8.2 
10.7 
13.2 
15.6 
18.2 
20.7 
23.3 
25.9 
28.5 
31.2 
33.8 
36.5 
39.2 

.00 

0 

0 

1°82 
3.23 
4.62 
6.02 
7.43 
8.84 
10.26 
11.68 
13.12 
14.56 
16.01 
17.46 
18.92 
20.39 
21.86 
23.34 
24.84 
26.33 

8.03 
16.37 
24.78 
33.19 
41.48 
49.81 
58.18 
66.56 
74.95 
83.56 
92.27 
100.99 
109.95 
118.84 
127.83 
136.75 
145.78 
154.80 

7.3682 
7.3458 
7.3705 
7.4012 
7.4142 
7.4177 
7.4390 
7.4107 
7.3493 
7.3269 
7.2335 
7.1603 
7.2075 
7.1839 
7.2122 
7.2252 
7.2134 

0 
601 

1206 
1812 
2412 
3016 
3624 
4234 
4842 
5461 
6085 
6703 
7330 
7957 
8589 
9218 
9857 
10493 

O 

2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

77 
503 
936 
1370 
1803 
2226 
2656 
3084 
3513 
3942 
4369 
4790 
5220 
5650 
6081 
6507 
6935 
7364 
7791 
8219 
8648 
9074 
9499 
9925 
10352 

2287 
2713 
3146 
3580 
4013 
4436 
4866 
5294 
5723 
6152 
6579 
7000 
7430 
7860 
8291 
8717 
9145 
9574 
10001 
10429 
10858 
11284 
11709 
12135 
12562 

-.01 

.00 

+  .01 

-.02 

+  .01 

+  .04 

-.03 

+  .02 

+  .09 

-.04 

+  .03 

+  .16 

-.04 

+  .05 

+  .25 

-.05 

+  .06 

+  .38 

-.05 

+  .08 

+  .52 

-.05 

+  .10 

+  .69 

458 


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HEXEY  A.  EOWLAND 


Mechanical  Equivalent  of  Heat.  10°  Series  on  the 

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Per  Kilogr.  of  Water. 

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CXJl~'-llCOTjHCCCOl-THlCOTtHOO<Mt- 
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Temperature. 

Approximate,  Mercurial  Thermom. 

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co-*iC5Ocoo5Oi-iffjeo-*ic«ot>aso 

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(MCO-*»C«Ot-OOOSOT-liNCO-*iC®I> 

Absolute  Scalel 

•QIOOO-  =  i« 

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'81000'  =  ™  Smsn 

0<MC0^1CCOI-OOOSO^<MCO^>C501- 

Ox  THE  MECHANICAL  EQUIVALENT  or  HEAT 


463 


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COt-COlC-*OlO1r-(OOOOSOOOrHO1O1CO 

»CIC1^'C1CIC1C1C1C1C1C'<<1C1C1C1C1C1C1C          "          *          * 
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464 


HENEY  A.  KOWLAND 


TABLE  LIV. — FINAL  MOST  PROBABLE  RESULTS. 


CD 

Work. 

Mechanical 
Equivalent. 

2 

Work. 

Mechanical 
Equivalent. 

O  o  *® 

®-P  • 

a 

i 

,io$ 

(BOOO 

i      . 

a 

i 

,io5 

pi 

22 

§32 

<!~   . 

S"5  £ 

2-2 

lug 

^G3  ' 

a»§ 

2£ 

a»g 

•  .  S 

-u"S 

S  OD  9 

;3  t»> 

a  <*>  s 

.  .  S 

8  "8 

sga 

OCQ 

S  2 

a>S->-U 

8*3 

s  25 

•302 

s  2  a 

aJu2 

&gs 

11  5 

00     . 

bc+^'-S 

Jv83 

ll« 

SS  g 

ttf)'*J  4^* 

o  ®  p~~( 

|o6 

l"|l 

|||" 

H 

2  K 

q 

S  m 

hi 

ID 
g 

2  = 

0 

5  w 

£i 

00000. 

0000. 

o 

00000. 

0000. 

2 

2289 

2443 

22 

10852 

10835 

426.1 

4176 

3 

2720 

2865 

23 

11278 

11253 

426.0 

4175 

4 

3150 

3286 

24 

11704 

11670 

425.9 

4174 

5 

3580 

3708 

429.8 

4212 

25 

12130 

12088 

425.8 

4173 

6 

4009 

4129 

429.5 

4209 

26 

12556 

12505 

425.7 

4172 

7 

4439 

4550 

429.3 

4207 

27 

12982 

12922 

425.6 

4171 

8 

4868 

4970 

429.0 

4204 

28 

13407 

13339 

425.6 

4171 

9 

5297 

5390 

428.8 

4202 

29 

13833 

13756 

425.5 

4170 

10 

5726 

5811 

428.5 

4200 

30 

14258 

14173 

425.6 

4171 

11 

6154 

6230 

428.3 

4198 

31 

14684 

14950 

425.6 

4171 

12 

6582 

6650 

428.1 

4196 

32 

15110 

15008 

425.6 

4171 

13 

7010 

7070 

427.9 

4194 

33 

15535 

15425 

425.7 

4172 

14 

7438 

7489 

427.7 

4192 

34 

15961 

15842 

425.7 

4172 

15 

7865 

7908 

427.4 

4189 

35 

16387 

16259 

425.8 

4173 

16 

8293 

8327 

427.2 

4187 

36 

16812 

16676 

425.8 

4173 

17 

8720 

8745 

427.0 

4185 

37 

17238 

17094 

18 

9147 

9164 

426.8 

4183 

38 

17664 

17511 

19 

9574 

9582 

426.6 

4181 

39 

18091 

17930 

20 

10000 

10000 

426.4 

4179 

40 

18517 

18347 

21 

10426 

10418 

426.2 

4177 

41 

18943 

18765 

TABLE    LV.— QUANTITY   TO   ADD   TO    THE   EQUIVALENT    AT    BALTIMORE    TO 
REDUCE  TO  ANT  LATITUDE. 


Latitude. 

Addition  in 
Kilogramme-Metres. 

0 

0 

+  0.89 

10 

+  0.82 

20 

+  0.63 

30 

+  0.34 

40 

+  0.08 

50 

—0.41 

60 

—0.77 

70 

-1.06 

80 

—1.26 

90 

-1.33 

Manchester— 0.5  ;  Paris  — 0.4  ;  Berlin  — 0.5. 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  465 

V.     CONCLUDING  REMARKS,  AND  CRITICISM  OF  RESULTS  AND 

METHODS 

On  looking  over  the  last  four  columns  of  Table  LIII,  which  gives 
the  results  of  the  experiments  as  expressed  in  terms  of  the  different 
mercurial  thermometers,  we  cannot  but  be  impressed  with  the  unsatis- 
factory state  of  the  science  of  thermometry  at  the  present  day,  when 
nearly  all  physicists  accept  the  mercurial  thermometer  as  the  standard 
between  0°  and  100°.  The  wide  discrepancy  in  the  results  of  calori- 
metric  experiments  requires  no  further  explanation,  especially  when 
physicists  have  taken  no  precaution  with  respect  to  the  change  of  zero 
after  the  heating  of  the  thermometer.  They  show  that  thermometry 
is  an  immensely  difficult  subject,  and  that  the  results  of  all  physicists 
who  have  not  made  a  special  study  of  their  thermometers,  and  a  com- 
parison with  the  air  thermometer,  must  be  greatly  in  error,  and  should 
be  rejected  in  many  cases.  And  this  is  specially  the  case  where  Geissler 
thermometers  have  been  used. 

The  comparison  of  my  own  thermometers  with  the  air  thermometer  is 
undoubtedly  by  far  the  best  so  far  made,  and  I  have  no  improvements  to 
offer  beyond  those  I  have  already  mentioned  in  the  '  Appendix  to  Ther- 
mometry/ And  I  now  believe  that,  with  the  improvement  to  the  air 
thermometer  of  an  artificial  atmosphere  of  constant  pressure,  we  could 
be  reasonably  certain  of  obtaining  the  temperature  at  any  point  up  to 
50°  C.  within  0°-01  C.  from  the  mean  of  two  or  three  observations. 
I  believe  that  my  own  thermometers  scarcely  differ  much  more  than 
that  from  the  absolute  scale  at  any  point  up  to  40  °C.,  but  they  represent 
the  mean  of  eight  observations.  However,  there  is  an  uncertainty  of 
0°-01  C.  at  the  20°  point,  owing  to  the  uncertainty  of  the  value  of  m. 
But  taking  m=  -00015,  I  hardly  think  that  the  point  is  uncertain  to 
more  than  that  amount  for  the  thermometers  Nos.  6163,  6165,  and  6166. 

As  to  the  comparison  of  the  other  thermometers,  it  is  evidently  un- 
satisfactory, as  they  do  not  read  accurately  enough.  However,  the  fig- 
ures given  in  Table  LIII  are  probably  very  nearly  correct. 

The  study  of  the  thermometers  from  the  different  makers  introduces 
the  question  whether  there  are  any  thermometers  which  stand  below  the 
air  thermometer  between  0°  and  100°.  As  far  as  I  can  find,  nobody  has 
ever  published  a  table  showing  such  a  result,  although  Bosscha  infers  that 
thermometers  of  "  Cristal  de  Choisy-le-Eoi "  should  stand  below,  and 
his  inference  has  been  accepted  by  Eegnault.  But  it  does  not  seem 
to  have  been  proved  by  direct  experiment.  My  Baudin  thermometers 
seem  to  contain  lead  as  far  as  one  can  tell  from  the  blackening  in  a  gas 
30 


466  HENRY  A.  ROWLAND 

flame,  but  they  stand  very  much  above  the  air  thermometer  at  40°.  I 
have  since  tried  some  of  the  Baudin  thermometers  up  to  300°,  and  find 
that  they  stand  Mow  the  air  thermometer  between  100°  and  240° ;  they 
coincide  at  about  240°,  and  stand  above  between  240°  and  300°.  This 
is  very  nearly  what  Eegnault  found  for  "  Verre  Ordinaire."  It  is  to  be 
noted  that  the  formula  obtained  from  experiments  below  100°  makes 
them  coincide  at  233°,  which  is  remarkably  close  to  the  result  of  actual 
experiment,  especially  as  it  would  require  a  long  series  of  experiments 
to  determine  the  point  within  10°. 

The  comparison  of  thermometers  also  shows  that  all  thermometers 
in  accurate  investigations  should  be  used  as  thermometers  with  arbi- 
trary scales,  neither  the  position  of  the  zero  point  nor  the  interval  be- 
tween the  0°  and  100°  points  being  assumed  correct.  The  text  books 
only  give  the  correction  for  the  zero  point,  but  my  observations  show 
that  the  interval  between  the  0°  and  100°  points  is  also  subject  to  a  sec- 
ular change  as  well  as  to  the  temporary  change  due  to  heating.  Of 
all  the  thermometers  used,  the  Geissler  is  the  worst  in  this  as  in  other 
respects,  except  accuracy  of  calibration,  in  which  it  is  equal  to  most  of 
the  others. 

The  experiments  on  the  specific  heat  of  water  show  an  undoubted 
decrease  as  the  temperature  rises,  a  fact  which  will  undoubtedly  sur- 
prise most  physicists  as  much  as  it  surprised  me.  Indeed,  the  dis- 
covery of  this  fact  put  back  the  completion  of  this  paper  many  months, 
as  I  wished  to  make  certain  of  it.  There  is  now  no  doubt  in  my  mind, 
and  I  put  the  fact  forth  as  proved.  The  only  way  in  which  an  error 
accounting  for  this  decrease  could  have  been  made  appears  to  me  to  be 
in  the  determination  of  ra  in  "  Thermometry."  The  determination  of 
m  rests  upon  the  determination  of  a  difference  of  only  0°-05  C.  between 
the  air  thermometer  and  the  mercurial,  the  0°  and  40°  points  coincid- 
ing, and  also  upon  the  comparison  of  the  thermometers  with  others 
whose  value  of  m  was  known,  as  in  the  Appendix.  Although  the  quan- 
tity to  be  measured  is  small,  yet  there  can  be  no  doubt  at  least  that  m 
is  larger  than  zero;  and  if  so,  the  specific  heat  of  water  certainly  has  a 
minimum  at  about  30°. 

One  point  that  might  be  made  against  the  fact  is  that  the  Kew  stand- 
ard, Table  L,  gives  less  change  than  the  others.  But  the  calibra- 
tion of  the  Kew  standard,  although  excellent,  could  hardly  be  trusted  to 
0°-02  or  0°-03  C.,  as  the  graduation  was  only  to  £°  F.  In  drawing  the 
curve  for  the  difference  between  the  Kew  standard  and  the  air  ther- 
mometers, I  ignored  small  irregularities  and  drew  a  regular  curve.  On 


ON  THE  MECHANICAL  EQUIVALENT  OF  HEAT  467 

looking  over  the  observations  again,  I  see  that,  had  I  taken  account  of 
the  small  irregularities,  it  would  have  made  the  observations  agree  more 
nearly  with  the  other  thermometers.  Hence  the  objection  vanishes. 
However,  I  intend  working  up  some  observations  which  I  have  with  the 
Kew  standard  at  a  higher  temperature,  and  shall  publish  them  at  a 
future  time. 

There  is  one  other  error  that  might  produce  an  apparent  decrease  in 
the  specific  heat,  and  that  is  the  slight  decrease  in  the  torsion  weight 
from  the  beginning  to  the  end  of  most  of  the  experiments,  probably  due 
to  the  slowing  of  the  engine.  By  this  means  the  torsion  circle  might 
lag  behind.  I  made  quite  an  investigation  to  see  if  this  source  of  error 
existed,  and  came  to  the  conclusion  that  it  produced  no  perceptible 
effect.  An  examination  of  the  different  experiments  shows  this  also, 
for  in  some  of  them  the  weight  increases  instead  of  decreasing.  See 
Tables  XXXVII  to  L. 

The  error  from  the  formation  of  dew  might  also  cause  an  apparent 
decrease;  but  I  have  convinced  myself  by  experiment,  and  others  can 
convince  themselves  from  the  tables,  that  this  error  is  also  inappre- 
ciable. 

The  observations  seem  to  settle  the  point  with  regard  to  the  specific 
heat  at  the  4°  point  within  reasonable  limits.  There  does  not  seem 
to  be  a  change  to  any  great  extent  at  that  point,  but  the  specific  heat 
decreases  continuously  through  that  point.  It  would  hardly  be  possible 
to  arrive  at  this  so  accurately  as  I  have  done  by  any  method  of  mixture, 
for  Pfaundler  and  Platter,  who  examined  this  point,  could  not  obtain 
results  within  one  per  cent,  while  mine  show  the  fact  within  a  fraction 
of  one  per  cent. 

The  point  of  minimum  cannot  be  said  to  be  known,  though  I  have 
placed  it  provisionally  between  30°  and  35°  C.,  but  it  may  vary  much 
from  that. 

The  method  of  obtaining  the  specific  heat  of  the  calorimeter  seems 
to  be  good.  The  use  of  solder  introduces  an  uncertainty,  but  it  is  too 
small  to  affect  the  result  appreciably.  The  different  determinations  of 
the  specific  heat  of  the  calorimeter  do  not  agree  so  well  as  they  might, 
but  the  error  in  the  equivalent  resulting  from  this  error  is  very  small, 
and,  besides,  the  mean  result  agrees  well  with  the  calculated  result.  It 
may  be  regarded  as  satisfactory. 

The  apparatus  for  determining  the  equivalent  could  scarcely  be  im- 
proved much,  although  perhaps  the  record  of  the  torsion  might  be  made 
automatic  and  continuous.  The  experiment,  however,  might  be  im- 


HENRY  A.  ROWLAND 

proved  in  two  ways;  first,  by  the  use  of  a  motive  power  more  regular  in 
its  action;  and,  second,  by  a  more  exact  determination  of  the  loss  due  to 
radiation.  The  effect  of  the  irregularity  of  the  engine  has  been  calcu- 
lated as  about  1  in  4000,  and  I  suppose  that  the  error  due  to  it  cannot 
be  as  much  as  that  after  applying  the  correction.  The  error  due  to 
radiation  is  nearly  neutralized,  at  least  between  0°  and  30°,  by  using 
the  jacket  at  different  temperatures.  There  may  be  an  error  of  a  small 
amount  at  that  point  (30°)  in  the  direction  of  making  the  mechanical 
equivalent  too  great,  and  the  specific  heat  may  keep  on  decreasing  to 
even  40°. 

Between  the  limits  of  15°  and  25°  I  feel  almost  certain  that  no  sub- 
sequent experiments  will  change  my  values  of  the  equivalent  so  much 
as  two  parts  in  one  thousand,  and  even  outside  those  limits,  say  be- 
tween 10°  and  30°,  I  doubt  whether  the  figures  will  ever  be  changed 
much  more  than  that  amount. 

It  is  my  intention  to  continue  the  experiments,  as  well  as  work  up 
the  remainder  of  the  old  ones.  I  shall  also  use  some  liquids  in  the 
calorimeter  other  than  water,  and  so  have  the  equivalent  in  terms  of 
more  than  one  fluid. 

Baltimore,  1878-79.     FinisTied  May  27,  1879. 


21 


APPENDIX  TO  PAPEE  ON  THE  MECHANICAL  EQUIVALENT 
OF  HEAT,  CONTAINING  THE  COMPARISON  WITH  DR. 
JOULE'S  THERMOMETER 

[Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  XVI,  38-45,  1881] 
Presented,    March,  1880 

In  the  body  of  this  paper  I  have  given  an  estimate  of  the  departure  of 
Dr.  Joule's  thermometer  from  the  air  thermometer,  based  on  the  com- 
parison of  thermometers  of  similar  glass.  But  as  it  seemed  important 
that  the  classical  determinations  of  this  physicist  should  be  reduced  to 
some  exact  standard,  I  took  to  England  with  me  last  summer  one  of 
my  standards, — Baudin,  No.  6166, — and  sent  it  to  Dr.  Joule  with  a 
statement  of  the  circumstances.  He  very  kindly  consented  to  make 
the  comparison,  and  I  now  have  the  results  before  me.  These  confirm 
the  estimate  that  I  had  previously  made,  and  cause  our  values  for  the 
equivalent  to  agree  with  great  accuracy.  The  following  is  the  table  of 
the  comparison : — 


Readings. 

Temperatures. 

By  perfect  Air 

Baudin,  No.  6166. 

Joule. 

Thermometer 
according  to 

By  Joule's 
Thermometer. 

Difference. 

No.  6166. 

21.88 

22.62 

8 

8 

o 
0 

41.930 

59.410 

1  .  590 

1.578 

—  .012 

48.782 

72.200 

2.126 

2.127 

+  .001 

53.705 

81.340 

2.511 

2.519 

.008 

58.916 

90.877 

2.918 

2.928 

.010 

64.914 

101.777 

3.382 

3.396 

.014 

73.374 

117.291 

4.039 

4.061 

.022 

80.176 

129.990 

4.567 

4.606 

.039 

85.268 

139.255 

4.961 

5.003 

.042 

90.564 

148.834 

5.370 

5.414 

.044 

94.243 

155.460 

5.654 

5.698 

.044 

99.168 

164.400 

6.036 

6.082 

.046 

104.030 

173.140 

6.413 

6.457 

.044 

108.863 

182.040 

6.789 

6.839 

.050 

113.706 

190.885 

7.165 

7.218 

.053 

114.000 

191.382 

7.188 

7.239 

.051 

'121.507 

'219.497 

'7.772 

'8.445 

1  Evidently  a  mistake  in  the  readings. 


470 


HENBY  A.  ROWLAND 


Continued. 


Readings. 

Temperatures. 

Baudin,  No.  6166. 

Joule. 

By  perfect  Air 
Thermometer 
according  to 
No.  6166. 

By  Joule's 
Thermometer. 

Difference. 

o 

o 

o 

135.858 

231.115 

8.890 

8.944 

.054 

140.467 

239.939 

9.249 

9  .  309 

.060 

143.405 

245.006 

9.479 

9.540 

.061 

146.445 

250.566 

9.717 

9.778 

.061 

152.360 

261.481 

10.180 

10.246 

.066 

158.770 

273.239 

10.681 

10.751 

070 

164.635 

283.957 

11.138 

11.211 

.073 

170.485 

294  .  739 

11  .  595 

11.670 

.075 

175.436 

303.682 

11.979 

12.057 

.078 

182.795 

316.968 

12.550 

12.627 

.077 

188.705 

327.746 

13.008 

13.089 

.081 

193.954 

337.220 

13.412 

13.495 

.083 

199.558 

347.294 

13.844 

13.928 

.084 

206.054 

259.060 

14.343 

14.432 

.089 

211.528 

368.953 

14.764 

14.857 

.093 

216.440 

377.826 

15.142 

15.237 

.095 

221.858 

387.562 

15.560 

15.655 

.095 

229.601 

401.419 

16.158 

16.249 

.091 

235.598 

412.367 

16.623 

16  .  719 

.096 

241.028 

422.258 

17.045 

17.143 

.098 

247.436 

433.800 

17.541 

17.638 

.097 

253.704 

445.267 

18.028 

18.130 

.102 

259".  786 

456.286 

18.500 

18.603 

.103 

266.086 

467.817 

19  .  991 

19.097 

.106 

273  .  143 

480.643 

19.539 

19.648 

.109 

280.176 

493.442 

20.086 

20.197 

.111 

287.634 

506.906 

20.666 

20.774 

.108 

294.927 

520.052 

21.232 

21.338 

.106 

304.148 

536.832 

21.947 

22.058 

.111 

310.397 

548.152 

22.432 

22.544 

.112 

316.596 

559.336 

22.916 

23.023 

.107 

321.271 

568.051 

23.282 

23.397 

.115 

327.148 

578.528 

23.742 

23.846 

.104 

333.661 

590.661 

24.251 

24.367 

.116 

339.664 

601.596 

24.719 

24.836 

.117 

346.557 

614.004 

25.254 

25.369 

.115 

352.878 

625.510 

25.746 

25.862 

.116 

359.986 

638.526 

26.299 

26.421 

.122 

365.080 

647  .  833 

26.697 

26.820 

.123 

371.811 

660.071 

27.225 

27.345 

.120 

382.770 

680.149 

28.087 

28.206 

.119 

We  can  discuss  the  comparison  of  these  thermometers  in  two  ways; 
either  by  direct  comparison  at  the  points  we  desire,  or  by  the  repre- 
sentation of  the  differences  by  a  formula. 

Joule's  result  in  1850  was  referred  to  water  at  about  14°  C.,  and  in 
1878  to  water  at  16° -5  C.  Taking  intervals  in  the  above  table  of  from 


APPENDIX  TO  THE  MECHANICAL  EQUIVALENT  OF  HEAT       471 

6°  to  12°,  so  that  the  mean  shall  be  nearly  14°  and  16° -5,  I  find  the 
following  for  the  ratios : — 

1-0044  1-0042 

1-0042  1-0042 

1-0049  1-0040 

1-0047  1-0030 

1-0047  1-0035 

1-0052  1-0035 


Mean,  1-0047  1-0037 

So  that  we  have  the  following  for  Joule's  old  and  new  values : — 

Old.  New. 

423-9  423-9 

Correction  for  thermometer                                2-0  1-6 

Correction  for  latitude                                          -5  -5 
Correction  for  sp.  ht.  of  copper                              -7 


427-1  426-0 

My  value  427-7  427-1 


Difference  -6  1-1 

or  1  in  700  and  1  in  390,  respectively. 

But  the  correction  found  in  this  way  is  subject  to  local  irregulari- 
ties, and  it  is  perhaps  better  in  many  respects  to  get  the  equation  giving 
the  temperature  of  Joule's  thermometer  on  the  air  thermometer.  Let 
T  be  the  temperature  by  Joule's  thermometer,  and  t  that  by  the  air 
thermometer.  Then  I  have  found 

t  =  0-002  +  1-00125  T  —  -00013  \  100  —  T\  \  1  —  -003  (100  -f  T) \ 

The  factor  1-00125  enters  in  the  formula,  probably  because  the  ther- 
mometer which  Joule  used  to  get  the  value  of  the  divisions  of  his  ther- 
mometer was  not  of  the  same  kind  of  glass  as  his  standard.  The  rela- 
tive error  at  any  point  due  to  using  the  mercurial  rather  than  the  air 
thermometer  will  then  be 

E  =  1  — $**  =  —00125  +  -00000039  \  23300  —  666  t  +  3  f\ 
dT  * 


472 


HENRY  A.  ROWLAND 


From  this  I  have  constructed  the  following  table : — 


Approximate  Addition  to  Equivalent 
as  measured  on  Joule's  Thermometer. 

Temperature. 

Metric  System. 

English  System. 

0 

.0078 

3.3 

6.0 

5 

.0066 

2.8 

5.1 

10 

.0054 

2.3 

4.2 

15 

.0042 

1.8 

3.2 

20 

.0031 

1.8 

2.4 

25 

.0021 

.9 

1.6 

30 

.0011 

.5 

.8 

Corrected  in  this  way  we  have, — 

Joule's  value 

Eeduction  to  air  thermometer 
Reduction  to  latitude  of  Baltimore 
Correction  for  sp.  ht.  of  copper 

My  value 
Difference 


Old. 

423-9 
1-9 

•5 

•7 

427-0 

427-7 


New. 

423-9 

1-7 
•5 

426-1 
427-1 

1-0 


or  1  in  600  and  1  in  426,  respectively. 

But  it  is  evident  that  all  the  other  temperatures  used  in  the  experi- 
ment must  also  be  corrected,  and  I  have  done  this  in  the  following  man- 
ner. The  principal  other  correction  required  is  in  the  capacity  of  the 
calorimeter,  and  this  amounts  to  considerable  in  the  experiments  on 
mercury  and  cast-iron,  where  no  water  is  used.  Dr.  Joule  informs  me 
that  the  thermometer  with  which  he  compared  mine  was  made  in  1844, 
but  does  not  give  any  mark  by  which  to  designate  it,  although  it  is  evi- 
dently the  thermometer  called  "A"  by  him.  I  shall  commence  with  the 
experiments  of  1847.  The  calorimeter  was  composed  of  the  following 
substances,  whose  capacities  I  recompute  according  to  what  in  my  paper 
I  have  considered  the  most  probable  specific  heats. 

wai-o-ht          Capacity  accord-  Most  probable     Most  probable 
ing  to  Joule.     Specific  Heat.  Capacity. 

Water  77617  grains  77617  1-000  77617 

Brass  24800  grains  2319  -0900  2232 

Copper  11237  grains  1056  -0922  1036 

Tin  (?)  363                 363 


Total  capacity 


81355 


81248 


APPENDIX  TO  THE  MECHANICAL  EQUIVALENT  OF  HEAT       473 

Equivalent  found  781-5  at  about  59°  F. 

Correction  for  thermometer  3-3 

Correction  for  capacity  1-3 

Correction  for  latitude  -9 


Corrected  value  787-0 

or  442-8  at  15°  C.  on  the  air  thermometer. 

The  other  experiment,  on  sperm  oil,  made  at  this  time,  is  probably 
hardly  worth  reducing.  The  experiments  of  1850  are  of  the  highest 
importance  and  should  be  accurately  reduced. 

In  the  experiments  with  water  the  capacity  of  the  calorimeter  is  cor- 
rected as  follows : — 


Weight. 

Capacity  used    > 
by  Joule.        S 

[ost  probable 
peciflc  Heat. 

Most  probable 
Capacity. 

Water 

93229-7 

93229-7 

1-000 

93229-7  ^ 

Copper 

25541- 

2430-2 

•092 

2349-8  * 

Brass 

18901- 

1800-0 

•091 

1720-0 

Brass  stopper 

10-3 

10-3 

Total  capacity  97470-2  97309-8 

Therefore  correction  is  -0016. 

Hence  the  result  with  water  requires  the  following  corrections : — 

Joule's  value  772-7  at  14°  C. 
Correction  for  thermometer  3-2 

Correction  for  latitude  -9 

Correction  for  capacity  1-2 

778-0 

or  426-8  on  the  air  thermometer  in  the  latitude  of  Baltimore  at  the 
temperature  of  14°  C.,  nearly. 

In  the  next  experiment,  with  mercury,  Joule  determined  the  capacity 
of  the  apparatus  by  experiment.  The  mean  of  the  experiments  was  that 
the  apparatus  lost  20° -33155  F.  in  heating  143430  grains  of  water 
3° •  13305  F.  To  reduce  these  to  the  air  thermometer  we  must  divide 
respectively  by  1-0042  and  1-0056.  Therefore  the  capacity  must  be 
divided  by  1-0014.  Therefore  the  corrected  values  are: — 

772-8  at  9°  C.     775-4  at  11°  C. 
Correction  for  thermometer          4-4  4-0 

Correction  for  capacity  1-1  1-1 

Correction  for  latitude  -9  -9 

779-2  781-4 


474  HENEY  A.  ROWLAND 

The  reduction  to  the  air  thermometer  was  made  for  the  temperatures 
of  9°  C.  and  11°  C.  respectively,  but  they  both  refer  to  the  temperature 
of  the  water  used  when  the  capacity  was  determined;  this  was  about 
9°  C.  Hence  these  experiments  gave  427-5  and  428-7  on  the  air  ther- 
mometer, with  the  water  at  about  9°  C. 

The  next  experiments,  with  cast-iron,  can  be  corrected  in  the  same 
manner,  and  thus  become 

776-0  773-9 

Correction  for  thermometer                             4-2  4-3 

Correction  for  capacity                                      1*1  !•! 

Correction  for  latitude                                         -9  -9 


782-2  780-2 

and  these  are  as  before  for  water  at  9°. 

The  determination  by  the  heating  of  a  wire,  whose  resistance  was 
measured  in  ohms,  can  be  thus  reduced.  The  value  found  by  Joule 
was  429-9  in  the  latitude  of  Baltimore  at  18° -6  C. 

Using  the  capacity  of  the  copper  -0922,  as  I  have  done  in  my  paper, 
this  quantity  will  be  increased  to  430-3.  But  I  have  given  reasons  in 
my  paper  on  the  "  Absolute  Unit  of  Electrical  Resistance  "  to  show  that 
there  should  be  a  correction  to  the  B.  A.  Committee's  experiments, 
which  would  make  the  ohm  -993  earth  quadrant  -f-  second,  instead  of 
1-000  as  it  was  meant  to  be,  which  nearly  agrees  with  the  quantity 
which  I  found,  namely,  -991.  Taking  my  value  -9911,  Joule's  result 
will  reduce  as  follows : — 

429.9  at  18° -6  C. 

Correction  for  thermometer  -|-  1-5 

Correction  for  capacity  -|-    -4 

Corrected  for  ohm  —  3-8 


Corrected  value  428-0  at  18° -6  C. 

The  last  determinations  in  the  '  Philosophical  Transactions '  of  1878 
can  be  reduced  as  follows : 

The  capacity  of  the  calorimeter  was  determined  by  experiment,  in- 
stead of  calculated  from  the  specific  heat  of  copper  given  by  Regnault, 
as  in  the  older  experiments.  The  value  used,  4842-4  grains,  corre- 
sponded to  a  specific  heat  of  brass  of  about  -090,  which  is  almost  exactly 
what  I  have  considered  right.  The  reduction  to  the  air  thermometer 
will  decrease  it  somewhat,  and  the  correction  for  the  increase  of  the 


APPENDIX  TO  THE  MECHANICAL  EQUIVALENT  OF  HEAT       475 


specific  heat  of  brass  and  the  decrease  of  the  specific  heat  of  water  will 
also  change  it  somewhat.  In  all,  the  amount  will  be  about  1  in  200. 
Hence  the  reduction  becomes  as  follows : 


Joule's  values 

Correction  for  thermometer 
Correction  for  capacity 
Correction  for  latitude 
Correction  to  vacuum 

Corrected  values 


772-7  774-6 

3-2  3-7 

•2  -2 

•9  -9 


773-1 

3-1 

•2 

•9 


767-0  774-0 

3-3  2-8 

•2  -2 

•9  -9 

—  •9  —-9 


776-1     778-5     776-4     770-5     777-0 
at  14°-7  atl2°-7  at!2°-5  at  14°-5  at  17°-3 

To  reduce  the  values  in  English  measure  to  metres  and  the  Centi- 
grade scale,  I  have  simply  taken  the  reducing  factor  1-8  X  -304794, 
although  the  barometer  on  the  two  systems  is  not  exactly  the  same: 
for  this  is  taken  into  account  in  the  comparison  of  the  thermometers. 
However,  a  barometer  at  30  in.  and  60°  F.  is  equivalent  to  759-86  mm. 
at  0°  C.  which  hardly  makes  a  difference  of  0°-01  C.  in  the  temperature 
of  the  hundred-degree  point. 


Joule's  Value  re- 

duced to  Air  Ther- 

<a 

•o  . 

No. 

Date. 

Method. 

Tern, 
of 

Joule's 
Value. 

mometer  and  Lati- 
tude of  Baltimore. 

q  ® 

J.-R. 

11 

o^ 

to  ^ 

English 

Metric 

H 

measure. 

system. 

o 

1 

1847 

Friction  of  water 

15 

781.5 

787.0 

442.8 

427.4 

+  15.4 

0 

2 

1850 

water 

14 

772.7 

778.0 

426.8 

427.7 

—      .9 

10 

3 

«' 

mercury 

9         772.8 

779.2 

427.5 

428.8 

—   1.3 

2 

4 

ii 

mercury 

9       !  775.4 

781.4 

428.7 

428.8 

—      .1 

2 

5 

ii 

iron 

9 

776.0 

782.2 

429.1 

428.8 

+      .3 

1 

6 

u 

iron 

9 

773.9 

780.2 

428.0 

428.8 

-      .8 

1 

7 

1867 

Elec  ric  heating 

18.6 

428.0 

426.7 

+    1.3 

3 

8 

1878 

Friction  of  water 

14.7 

772.7 

776.1 

425.8 

427.6 

-    1.8 

2 

9 

u 

u 

12.7 

774.6 

778.5 

427.1 

428  .  0 

—      .9 

3 

10 

u 

11 

15.5 

773.1 

776.4 

426.0 

427.3 

-   1.3 

5 

11 

ii 

u 

14.5 

767.0 

770.5 

422.7 

427.5 

-   4.8 

1 

12 

" 

ii 

17.3 

774.0 

777.0 

426.3 

426.9 

—      .6 

1 

In  combining  these  so  as  to  get  at  the  true  difference  of  Joule's  and 
my  result,  we  must  give  these  different  determinations  weights  accord- 
ing to  their  respective  accuracy,  especially  as  some  of  the  results,  as 
No.  11,  have  very  little  weight.  Joule  rejected  quite  a  number  of  his 
results,  but  I  have  thought  it  best  to  include  them,  giving  them  small 
weights,  however.  In  this  way  we  obtain  a  value  for  Joule's  experiment 


476  HENEY  A.  ROWLAND 

of  426-75  at  14° -6,  my  value  at  this  point  being  427-52.  The  difference 
amounts  to  1  in  550  only.  Giving  the  observations  equal  weight,  this 
would  have  been  1  in  430  nearly.  The  quantity  426-75  is  what  I  find 
at  18°  C.  So  that  my  result  at  this  particular  temperature  differs  from 
that  of  Joule  only  the  amount  that  water  changes  in  specific  heat  in 
3°-4C. 

Joule's  value  is  less  than  my  value  to  the  amount  given,  but  the  value 
from  the  properties  of  air,  430-7  at  14°  C.  is  greater,  although  the 
method  can  have  little  weight. 

It  might  be  well  to  diminish  my  values  by  1  part  in  1000  so  as  to  make 
them  represent  the  mean  of  Joule's  and  my  own  experiments.  It  is 
seen  that  the  experiment  by  the  method  of  electric  heating  agrees  very 
exactly  with  the  other  experiments,  because  I  have  reduced  it  to  my  value 
of  the  ohm.  Hence  I  regard  it  as  a  very  excellent  confirmation  of  my 
value  of  that  unit. 
Baltimore,  February  16,  1880. 


20 

PHYSICAL   LABORATOKY:    COMPARISONS    OF   STANDARDS 

[Johns  Hopkins  University  Circulars,  N~o.  3,  p.  31,  1880] 

In  order  to  secure  uniformity  throughout  the  country  in  certain 
physical  standards,  and  to  facilitate  the  use  of  the  absolute  system  of 
heat  measurement,  it  has  been  thought  advisable  to  organize  in  the 
physical  department  of  this  University  a  sub-department,  where  com- 
parisons of  standards  can  be  made. 

Comparison  of  Thermometers. — At  present  we  are  only  able  to  make 
comparisons  of  thermometers,  and  so  to  reduce  their  degrees  to  the  abso- 
lute scale  of  the  perfect  gas  thermometer. 

As  the  work  is  very  laborious,  it  is  proposed  to  make  this  sub-depart- 
ment self-supporting,  by  a  system  of  fees  sufficient  to  cover  the  bare  cost 
of  the  labor,  so  that  all  may  avail  themselves  of  the  facilities  here 
offered. 

In  a  recent  study  of  standard  thermometers  by  Geissler,  Baudin, 
Fastre,  Casella  and  from  Kew,  and  the  comparison  of  the  same  with 
the  air  thermometer,  the  differences  due  to  the  variety  of  the  glass 
amounted  to  0°-2  or  0°-3  C.,  and  the  differences  from  the  air  thermom- 
eter were  as  high  sometimes  as  0°-3  C.  at  the  40°  point. 

The  error  from  using  uncompared  mercurial  thermometers  in  calori- 
metric  investigations  may  amount  to  one  or  two  per  cent.  For  this 
reason  the  air  thermometer  has  been  taken  as  the  standard,  and  all  com- 
parisons will  be  reduced  to  the  final  absolute  standard  of  the  perfect 
gas  thermometer. 

Very  complete  studies  of  thermometers  have  been  made  between 
0°  and  40°  C.,  and  a  less  complete  study  between  0°  and  100°,  and  be- 
tween 100°  and  250°.  Up  to  100°  our  thermometers  have  not  only  been 
compared  with  the  air  thermometer,  but  also  with  standards  by  Fastre, 
Geissler,  Casella,  Baudin  and  from  Kew. 

The  study  from  0°  to  40°  has  been  published  by  the  American  Acad- 
emy of  Sciences,  at  Boston,  in  a  memoir  on  the  Mechanical  Equivalent 
of  Heat.  One  of  our  thermometers  is  also  now  in  the  hands  of  Dr. 
Joule,  who  has  compared  it  with  the  original  thermometers  used  by  him 
in  the  determination  of  the  Mechanical  Equivalent  of  Heat. 


478  HENKY  A.  EOWLAND 

The  apparatus  for  the  comparison  up  to  100°  C.  is  described  in  the 
paper  above  referred  to.  The  thermometers  are  totally  immersed  in 
the  water  with  their  stems  very  near  the  bulbs  of  the  air  thermometers. 
From  100°  up  to  250°  an  oil  bath  is  used,  the  bulbs  only  being  in  the 
oil,  but  the  stems  are  heated  to  the  same  degree  by  being  in  contact  with 
a  heavy  copper  bar,  whose  temperature  is  noted  by  separate  thermome- 
ters. 

The  ordinary  comparison  is  made  with  the  stems  of  the  thermometers 
in  a  vertical  position.  Where  they  are  used  in  a  horizontal  position  a 
correction  will  have  to  be  made,  and  this  correction  will  be  determined 
when  it  is  so  desired.  When  the  comparison  is  made  only  to  40°,  we 
can  compare  them  in  a  horizontal  position,  but  we  cannot  then  insure 
the  same  accuracy  as  when  they  are  vertical,  and  it  is  never  advisable  to 
use  them  in  that  position. 

Where  desired,  a  study  will  be  made  of  the  changes  of  the  zero  point 
as  a  function  of  the  temperature  to  which  it  has  been  heated,  and  of  the 
time,  but  this  study  is  not  advised,  as  it  does  not  lead  to  very  valuable 
results. 

Thermometers  with  metal,  wooden  or  paper  scales  are  generally  too 
poor  to  be  worth  comparison,  and  would  often  be  spoiled  by  the  immer- 
sion in  the  water.  Thermometers  with  metal  caps  of  Geissler's  form 
are  often  injured,  especially  when  heated  to  250°  C.  Therefore,  com- 
parisons of  thermometers  of  these  classes  will  not  be  undertaken,  ex- 
cept in  the  case  of  standards  long  used  for  some  particular  purpose,  or 
in  that  of  fine  G-eissler  thermometers. 

Three  intervals  for  the  comparison  have  been  selected. 

A.  Between  0°   and  40°  for  thermometers  used  for  meteorological 
observations,  determination  of  the  temperature  of  standards  of  length, 
calorimetric  determinations,  and  all  purposes  where  extreme  accuracy  is 
desired  within  that  limit.     To  obtain  the  full  value  of  such  a  compari- 
son, thermometers  should  be  graduated  at  least  as  fine  as  0°-1  C.  or 
0°-2F. 

B.  Between  0°  and  100°  C.     It  is  advised  that  the  thermometers  gent 
be  graduated  at  least  as  fine  as  0°-2  C.  or  0°-5  F. 

C.  Between  100°  and  250°  for  thermometers  used  by  chemists  in  the 
determination  of  melting  or  boiling  points.     Thermometers  should  be 
graduated  to  1°  C.  or  1°  F. 

Three  kinds  of  comparison  will  be  made  for  each  of  the  intervals 
0°  to  40°,  0°  to  100°,  and  100°  to  250°,  as  follows: 

1st.  Direct  comparison  with  the  air  thermometer,  and  also  a  primary 


PHYSICAL  LABORATORY:  COMPARISONS  OF  STANDARDS        479 

standard.  This  comparison  is  very  laborious,  and  is  not  recommended 
except  in  very  exceptional  cases,  as  more  than  one  comparison  should 
be  made  to  insure  good  results. 

2nd.  Comparison  with  primary  standards  which  have  been  compared 
many  times  with  the  air  thermometer.  This  is  recommended  where  an 
error  of  y^0  is  of  some  importance. 

3rd.  Comparison  with  secondary  standards  which  have  been  com- 
pared many  times  with  the  primary  standards,  and  not  very  often 
directly  with  the  air  thermometer.  This  is  recommended  in  all  ordi- 
nary cases,  where  an  error  of  yf^0  can  be  tolerated. 

When  several  comparisons  are  made,  the  following  intervals  will  be 
allowed  between  the  experiments,  so  that  the  zero  reading  may  be 
allowed  to  return  to  its  primitive  value. 

Thermometers  heated  to     40°  C.  about  1  week. 
Thermometers  heated  to  100°  C.  about  6  weeks. 
Thermometers  heated  to  250°  C.  about  4  months. 

The  latter  interval  is  too  small  for  an  accurate  return. 

For  the  exact  details  of  the  method  of  comparison,  I  must  refer  to  the 
above  mentioned  paper  on  the  Mechanical  Equivalent  of  Heat. 

It  is  advisable  in  all  cases  where  great  accuracy  is  desired,  that  a 
numbers  of  comparisons  be  made,  seeing  that  delicate  thermometers  are 
constantly  varying  through  slight  limits,  and  the  average  state  can  only 
be  determined  by  repeated  experiments. 

Reports. — In  the  report  of  the  comparison,  the  original  readings  will 
be  given  together  with  the  reduced  ones,  and  the  plot  of  the  curve  of 
errors  of  the  thermometer  at  every  point.  From  this  curve,  the  error 
of  the  thermometer  at  any  reading  can  be  found. 

It  is  proposed  to  publish  at  the  end  of  the  year  a  complete  report  of 
all  the  comparisons  made  during  the  year,  together  with  all  new  deter- 
minations of  the  errors  of  the  standards,  and  to  send  it  to  any  address 
at  a  price  which  we  will  hereafter  announce. 

Fees. — The  comparators  allow  five  thermometers  only  to  be  placed  in 
them,  of  which  two  are  our  own  standards  in  ordinary  comparisons, 
and  one  in  direct  comparisons  with  the  air  thermometer.  Therefore, 
three  thermometers  can  be  compared  as  easily  as  one  in  ordinary  cases, 
and  four  in  direct  comparisons.  Hence  the  following  system  of  fees 
has  been  made  out. 


480  HENEY  A.  EOWLAND 

A.  When  a  number  of  Thermometers  are  sent 
Comparison  between  0°  and  40°  C.  for  3  or  4  thermometers. 

Direct,  probable  error  at  each  point =TOT°     $20  °° 

Primary  Standards,  probable  error  at  each  point  C^T^T°       11  00 
Secondary  Standards,  probable  error  at  each  point  =  Tf -g-0         8  00 

0°  and  100°  for  3  or  4  thermometers. 

Direct,  probable  error  at  each  point =T^°     $25  00 

Primary  Standards,  probable  error  at  each  point  =  ^-3-°       12  00 
Secondary  Standards,  probable  error  at  each  point  =  T^¥°         9  00 

100°  to  250°  for  3  or  4  thermometers. 

Direct,  probable  error  at  each  point —    y1^0     $20  00 

Primary  Standards,  probable  error  at  each  point  =   y1^0       12  00 
Secondary  Standards,  probable  error  at  each  point  =      -^°         9  00 

B.  For  Single  Thermometers 

For  single  thermometers,  the  fees  for  the  direct  comparisons  should 
be  reduced  to  one-third,  and'  for  the  ordinary  ones  to  one-half  the 
above  figures.  But  in  this  case  the  thermometer  will  have  to  remain 
here  until  enough  accumulate  to  fill  the  comparators. 

Directions  for  Sending. — With  each  thermometer,  send  the  name  of 
maker,  the  date  when  made,  purpose  for  which  it  is  used,  and  the 
highest  temperature  to  which  it  has  lately  been  heated,  and  the  date 
of  such  heating,  together  with  the  kind  of  comparison  desired,  and 
whether  the  thermometer  is  generally  used  in  the  horizontal  or  the 
vertical  position. 

In  packing,  the  thermometer  should  be  placed  in  a  small  box,  which 
should  again  be  packed  with  straw  in  a  larger  box. 

The  thermometers,  both  during  transit  and  while  here,  must  be  at 
the  owners'  risk.  Only  sufficient  fees  have  been  charged  to  cover  the 
bare  cost  of  the  comparison,  and  we  bear  the  risk  of  our  own  standards, 
which  are  probably  more  valuable  than  any  of  those  which  will  be  sent 
to  us.  But  every  care  will  be  taken,  and  the  probability  of  an  accident 
is  very  small. 

We  expect  soon  to  be  able  to  make  other  comparisons,  and  notice  will 
then  be  given  of  the  fact  by  the  issue  of  another  circular. 


26 

ON  GEISSLEK  THERMOMETERS:  REMARKS  BY  PROFESSOR 
ROWLAND  ON  THE  PRECEDING  LETTER,1  IN  A  COMMU- 
NICATION DATED  JOHNS  HOPKINS  UNIVERSITY,  APRIL 
29,  1881 

[American  Journal  of  Science  [3],  XXI,  451-453,  1881] 

Through  the  kindness  of  Dr.  Waldo,  I  have  been  allowed  to  see  the 
above  and  would  like  to  give  a  few  words  of  explanation. 

In  reading  what  I  had  to  say  with  respect  to  the  Geissler  thermom- 
eter, the  reader  should  remember  that  I  was  not  writing  on  general 
thermometry,  but  only  on  that  part  which  should  be  useful  to  me  in 
measuring  differences  of  temperature  within  the  limits  of  0°  and  45°  C. 
And  so  I  merely  made  a  study  of  thermometers,  their  change  of  zero 
and  other  points,  as  it  affected  the  problem  which  I  had  before  me.  I 
am  well  aware  that  there  are  formulae  for  giving  the  changed  readings 
of  thermometers  due  to  previous  heating,  but,  according  to  well  known 
principles  in  such  cases,  I  preferred  to  eliminate  such  error  by  the 
proper  use  of  the  thermometer  rather  than  trust  to  an  uncertain  theory. 

In  the  course  of  my  investigation  I  discovered  the  fact  that  the 
Geissler  thermometers,  especially  the  one  I  then  used,  departed  more 
from  the  air  thermometer  than  any  other.  Now  the  Geissler  ther- 
mometer has  been  used  for  many  years  by  physicists,  principally  Ger- 
man, without  any  reduction  to  the  air  thermometer.  And  this  correc- 
tion was  so  great,  amounting  to  over  0°-3  C.,  for  the  specimen  I  used,  at 
the  45°  point,  that  I  thought  it  right  to  call  attention  to  the  point. 
And  I  acknowledge  that  the  picture  was  present  in  my  mind  of  a  physi- 
cist reading  a  thermometer  from  a  distance  by  a  telescope  to  avoid  the 
heat  of  the  body  and  parallax,  and  recording  his  results  to  thousandth 
of  a  degree,  and  all  this  on  a  thermometer  having  an  error  of  0°-3  C. ! 
As  Dr.  Thiesen  remarks:  If  one  is  to  compare  his  thermometer  with 
the  air  thermometer,  the  amount  of  correction  is  of  little  importance: 
but  departure  from  the  air  thermometer  is  certainly  not  a  recommenda- 
tion and,  indeed,  must  introduce  slight  errors.  The  most  accurate 

1  [By  Dr.  M.  Thiesen,  replying  to  Rowland's  criticisms  of  the  Geissler  thermometers, 
as  expressed  in  his  memoir  'On  the  Mechanical  Equivalent  of  Heat.'] 
31 


482  HENRY  A.  ROWLAND 

readings  which  one  can  make  on  an  air  thermometer  will  vary  several 
hundredths  of  a  degree. 

Hence  we  can  never  use  with  accuracy  the  direct  comparison  with  the 
air  thermometer  but  must  express  the  difference  of  the  two  instruments 
by  some  formula  of  the  form: 

J  =  a  +  bt  +  ci1  +  &c. 

Should  we  take  an  infinite  number  of  terms  this  formula  would  ex- 
press all  the  irregularities  of  our  observations.  But  by  limiting  the 
number  of  terms  the  curve  of  differences  becomes  smoother  and 
smoother  and  the  formula  expresses  less  and  less  the  irregularities  of 
the  experiment.  The  number  of  terms  to  be  used  is  a  matter  of  judg- 
ment, and  this  point  I  sought  to  determine  by  the  use  of  the  observa- 
tions of  Eegnault  and  others.  The  rejection  of  the  higher  powers  of  t 
is  more  or  less  of  an  assumption  founded  on  the  fact  that  we  are 
reasonably  certain  that  the  curve  of  differences  between  the  mercurial 
and  the  air  thermometer  is  a  smooth  curve.  It  is  evident  that  the 
less  the  correction  to  be  introduced  the  less  the  rejection  of  the  higher 
powers  of  t  will  affect  our  results. 

We  now  come  to  my  criticism  of  the  Geissler  thermometer  for  not 
having  a  reservoir  at  the  top.  Dr.  Thiesen  has  in  some  way  misunder- 
stood my  principal  reason  for  its  presence.  My  reason  was  not  that 
"  es  vermindert  die  Schadlichkeit  der  im  Quecksilber  zuriickgebliebenen 
Spuren  von  Luft "  but  that  only  by  its  use  can  the  mercury  in  the  bulb 
be  entirely  free  from  air.  Take  a  thermometer  and  turn  it  with  the 
bulb  on  top.  If  the  thermometer  is  large,  in  nine  cases  out  of  ten  the 
mercury  will  separate  and  fall  down:  allow  it  to  remain  and  observe  the 
bubble-like  vacuum  in  the  bulb.  Turn  the  bulb  in  various  directions  so 
as  to  wash  the  whole  interior  of  the  bulb,  as  it  were,  and  then  bring 
the  thermometer  into  a  vertical  position,  keeping  the  bubble  in  sight. 
As  the  mercury  flows  back,  the  bubble  diminishes  and  finally,  in  a  good 
thermometer,  almost  disappears:  but  in  most  thermometers  a  good 
sized  bubble  of  air,  in  some  cases  as  large  as  the  wire  of  a  pin,  remains. 
It  is  the  most  important  function  of  a  reservoir  at  the  top  to  permit 
such  manipulations  as  to  drive  all  such  air  into  the  top  reservoir  and  to 
make  the  mercury  and  the  glass  assume  such  perfect  contact  that  the 
bulb  can  be  turned  uppermost  without  the  mercury  separating,  even  in 
thermometers  of  large  size  and  with  good  generous  bulbs.  In  many 
Geissler  thermometers  such  a  test  might  succeed,  not  on  account  of  the 
freedom  from  air,  but  because  the  capillary  tube  and  bulb  are  so  small 


Ox  THE  GEISSLER  THERMOMETEKS  483 

and  the  column  so  short  that  the  capillary  action  is  sufficient  to  prevent 
the  fall.  Now  I  think  that  a  thermometer  in  which  there  is  this  layer 
of  air  around  the  mercury  in  the  bulb  must  be  uncertain  in  its  action; 
hence  my  opinion  is  unaltered  that  all  thermometers  in  which  we  can- 
not remove  this  layer  or  at  least  make  certain  of  its  absence  should  be 
rejected. 

Furthermore,  with  respect  to  calibration,  the  reservoir  is  not  essen- 
tial to  the  calibration  of  thermometers  whose  range  is  0°  and  100°  C. 
But  my  remarks  apply  better  to  those  whose  range  is  between  0°  and 
30°  C.  or  40°  C.  Here  calibration  is  impossible  with  a  short  column 
at  ordinary  temperatures  unless  some  of  the  mercury  can  be  stored  up 
in  the  reservoir  so  as  to  allow  the  column  to  move  over  the  whole  scale. 
And  it  is  within  this  limit  that  thermometers  are  of  the  greatest  value 
in  the  physical  laboratory. 

The  other  defects  of  the  Geissler  thermometer,  the  scale  which  was 
always  coming  loose,  the  metal  cap  which  was  never  tight  and  always 
allowe'd  water  to  enter,  the  small  capillary  tube  which  wandered  with 
perfect  irregularity  from  side  to  side  over  the  scale,  all  these  were  so 
obvious  that  I  confined  my  remarks  to  the  more  obscure  errors. 

Furthermore,  I  believe  there  is  some  error  in  most  Geissler  ther- 
mometers from  the  small  size  of  the  bulb  and  the  capillary  tube,  and 
this  I  have  mentioned  on  p.  124 '  of  the  paper  referred  to.  Pfaundler 
and  Platter,  in  a  paper  on  the  specific  heat  of  water,  in  Poggendorff's 
Annalen  for  1870,  found  an  immense  variation  within  small  limits.  In 
a  subsequent  paper2  the  authors  traced  this'error  to  the  lagging  of  the 
thermometer  behind  its  true  reading. 

The  authors  used  Geissler  thermometers  graduated  to  ^j-  °  C. !  in  a 
series  of  experiments  made  by  plunging  the  thermometer  into  water 
after  slightly  heating  or  cooling  the  thermometer  so  that  in  one  case 
the  mercury  fell  and  the  other  rose  to  the  required  point.  When  the 
thermometer  fell  about  6°  or  8°  C.  it  lagged  behind  0°-0654  and  when 
it  rose  3°  or  4°  it  lagged  0°-022,  making  a  difference  of  0°-087  C.!  Now 
my  thermometers  made  by  Baudin  show  no  effect  of  this  kind.  They 
indicate  accurately  the  temperature  whether  they  rise  or  fall  to  the 
given  point,  provided  the  interval  is  not  too  great.  The  fact  then 
remains  that  a  Geissler  thermometer  graduated  to  7V°  C.  may  be  uncer- 
tain to  0°-087C.,  while  a  Baudin  graduated  to  mm.,  one  mm.  being 
from  TV°  to  TV°  C.  is  not  uncertain  to  0°-01  or  0°-02  C.  May  not  the 

1  [p.  393  this  volume.!  *  Poggendorff's  Annalen,  cxli,  p.  537. 


484  HENEY  A.  KOWLAND 

cause  be  found  in  the  layer  of  air  around  the  mercury  of  the  bulb 
which  cannot  be  removed  without  a  reservoir  at  the  top?  Or  may  we 
not  also  look  for  such  an  effect  from  the  minute  size  of  the  bore  of  the 
capillary  tube  which  creates  a  different  pressure  in  the  bulb  from  a 
rising  or  falling  meniscus  ?  Possibly  the  two  may  be  combined. 


PART  IV 

LIGHT 


29 

PRELIMINARY  NOTICE  OF  THE  RESULTS  ACCOMPLISHED 
IN  THE  MANUFACTURE  AND  THEORY  OF  GRATINGS  FOR 
OPTICAL  PURPOSES 

[Johns  Hopkins  University  Circulars,  No.  17,  pp.  248,  249,  1882 ;  Philosophical  Magazine 
[4],  XIII,  469-474,  1882;  Nature,  26,  211-213,  1882;  Journal  de  Physique, 
II,  5-11,  1883] 

It  is  not  many  years  since  physicists  considered  that  a  spectroscope 
constructed  of  a  large  number  of  prisms  was  the  best  and  only  instru- 
ment for  viewing  the  spectrum,  where  great  power  was  required.  These 
instruments  were  large  and  expensive,  so  that  few  physicists  could  pos- 
sess them.  Professor  Young  was  the  first  to  discover  that  some  of  the 
gratings  of  Mr.  Rutherfurd  showed  more  than  any  prism  spectroscope 
which  had  then  been  constructed.  But  all  the  gratings  which  had  been 
made  up  to  that  time  were  quite  small,  say  one  inch  square,  whereas 
the  power  of  a  grating  in  resolving  the  lines  of  the  spectrum  increases 
with  the  size.  Mr.  Rutherfurd  then  attempted  to  make  as  large  grat- 
ings as  his  machine  would  allow,  and  produced  some  which  were  nearly 
two  inches  square,  though  he  was  rarely  successful  above  an  inch  and 
three-quarters,  having  about  thirty  thousand  lines.  These  gratings 
were  on  speculum  metal  and  showed  more  of  the  spectrum  than  had 
ever  before  been  seen,  and  have,  in  the  hands  of  Young,  Rutherfurd, 
Lockyer  and  others,  done  much  good  work  for  science.  Many  mechanics 
in  this  country  and  in  France  and  Germany,  have  sought  to  equal 
Mr.  Rutherfurd' s  gratings,  but  without  success. 

Under  these  circumstances,  I  have  taken  up  the  subject  with  the 
resources  at  command  in  the  physical  laboratory  of  the  Johns  Hopkins 
University. 

One  of  the  problems  to  be  solved  in  making  a  machine  is  to  make  a 
perfect  screw,  and  this,  mechanics  of  all  countries  have  sought  to  do 
for  over  a  hundred  years  and  have  failed.  On  thinking  over  the  matter, 
I  devised  a  plan  whose  details  I  shall  soon  publish,  by  which  I  hope  to 
make  a  practically  perfect  screw,  and  so  important  did  the  problem  seem 
that  I  immediately  set  Mr.  Schneider,  the  instrument  maker  of  the 
university,  at  work  at  one.  The  operation  seemed  so  successful  that  I 


488  HENRY  A.  ROWLAND 

immediately  designed  the  remainder  of  the  machine,  and  have  now  had 
the  pleasure  since  Christmas  of  trying  it.  The  screw  is  practically  per- 
fect, not  by  accident,  but  because  of  the  new  process  for  making  it,  and 
I  have  not  yet  been  able  to  detect  an  error  so  great  as  one  one-hundred- 
thousandth  part  of  an  inch  at  any  part.  Neither  has  it  any  appreciable 
periodic  error.  By  means  of  this  machine  I  have  been  able  to  make 
gratings  with  43,000  lines  to  the  inch,  and  have  made  a  ruled  surface 
with  160,000  lines  on  it,  having  about  29,000  lines  to  the  inch.  The 
capacity  of  the  machine  is  to  rule  a  surface  6^  x  4|  inches  with  any 
required  number  of  lines  to  the  inch,  the  number  only  being  limited  by 
the  wear  of  the  diamond.  The  machine  can  be  set  to  almost  any  num- 
ber of  lines  to  the  inch,  but  I  have  not  hitherto  attempted  more  than 
43,000  lines  to  the  inch.  It  ruled  so  perfectly  at  this  figure  that  I  see 
no  reason  to  doubt  that  at  least  two  or  three  times  that  number  might 
be  ruled  in  one  inch,  though  it  would  be  useless  for  making  gratings. 

*A11  gratings  hitherto  made  have  been  ruled  on  flat  surfaces.  Such 
gratings  require  a  pair  of  telescopes  for  viewing  the  spectrum;  these 
telescopes  interfere  with  many  experiments,  absorbing  the  extremities 
of  the  spectrum  strongly;  besides,  two  telescopes  of  sufficient  size  to 
use  with  six  inch  gratings  would  be  very  expensive  and  clumsy  affairs. 
In  thinking  over  what  would  happen  were  the  grating  ruled  on  a  sur- 
face not  flat,  I  thought  of  a  new  method  of  attacking  the  problem,  and 
soon  found  that  if  the  lines  were  ruled  on  a  spherical  surface  the 
spectrum  would  be  brought  to  a  focus  without  any  telescope.  This 
discovery  of  concave  gratings  is  important  for  many  physical  investiga- 
tions, such  as  the  photographing  of  the  spectrum  both  in  the  ultra- 
violet and  the  ultra-red,  the  determination  of  the  heating  effect  of  the 
different  rays,  and  the  determination  of  the  relative  wave  lengths  of 
the  lines  of  the  spectrum.  Furthermore  it  reduces  the  spectroscope  to 
its  simplest  proportions,  so  that  spectroscopes  of  the  highest  power  may 
be  made  at  a  cost  which  can  place  them  in  the  hands  of  all  observers. 
With  one  of  my  new  concave  gratings  I  have  been  able  to  detect  double 
lines  in  the  spectrum  which  were  never  before  seen. 

The  laws  of  the  concave  grating  are  very  beautiful  on  account  of  their 
simplicity,  especially  in  the  case  where  it  will  be  used  most.  Draw  the 
radius  of  curvature  of  the  mirror  to  the  centre  of  the  mirror,  and  from 
its  central  point  with  a  radius  equal  to  half  the  radius  of  curvature 
draw  a  circle;  this  circle  thus  passes  through  the  centre  of  curvature 
of  the  mirror  and  touches  the  mirror  at  its  centre.  Now  if  the  source 
of  light  is  anywhere  in  this  circle,  the  image  of  this  source  and  the 


GRATINGS  FOR  OPTICAL  PURPOSES  489 

different  orders  of  the  spectra  are  all  brought  to  focus  on  this  circle. 
The  word  focus  is  hardly  applicable  to  the  case,  however,  for  if  the 
source  of  light  is  a  point  the  light  is  not  brought  to  a  single  point  on 
the  circle  but  is  drawn  out  into  a  straight  line  with  its  length  parallel 
to  the  axis  of  the  circle.  As  the  object  is  to  see  lines  in  the  spectrum 
only,  this  fact  is  of  little  consequence  provided  the  slit  which  is  the 
source  of  light  is  parallel  to  the  axis  of  the  circle.  Indeed  it  adds  to 
the  beauty  of  the  spectra,  as  the  horizontal  lines  due  to  dust  in  the  slit 
are  never  present,  as  the  dust  has  a  different  focal  length  from  the  lines 
of  the  spectrum.  This  action  of  the  concave  grating,  however,  some- 
what impairs  the  light,  especially  of  the  higher  orders,  but  the  intro- 
duction of  a  cylindrical  lens  greatly  obviates  this  inconvenience. 

The  beautiful  simplicity  of  the  fact  that  the  line  of  foci  of  the  dif- 
ferent orders  of  the  spectra  are  on  the  circle  described  above  leads 
immediately  to  a  mechanical  contrivance  by  which  we  can  move  from 
one  spectrum  to  the  next  and  yet  have  the  apparatus  always  in  focus; 
for  we  only  have  to  attach  the  slit,  the  eye-piece  and  the  grating  to  three 
arms  of  equal  length,  which  are  pivoted  together  at  their  other  ends 
and  the  conditions  are  satisfied.  However  we  move  the  three  arms  the 
spectra  are  always  in  focus.  The  most  interesting  case  of  this  contriv- 
ance is  when  the  bars  carrying  the  eye-piece  and  grating  are  attached 
end  to  end,  thus  forming  a  diameter  of  the  circle  with  the  eye-piece  at 
the  centre  of  curvature  of  the  mirror,  and  the  rod  carrying  the  slit 
alone  movable.  In  this  case  the  spectrum  as  viewed  by  the  eye-piece 
is  normal,  and  when  a  micrometer  is  used  the  value  of  a  division  of  its 
head  in  wave-lengths  does  not  depend  on  the  position  of  the  slit,  but 
is  simply  proportional  to  the  order  of  the  spectrum,  so  that  it  need  be 
determined  once  only.  Furthermore,  if  the  eye-piece  is  replaced  by  a 
photographic  camera  the  photographic  spectrum  is  a  normal  one.  The 
mechanical  means  of  keeping  the  focus*  is  especially  important  when 
investigating  the  ultra-violet  and  ultra-red  portions  of  the  solar 
spectrum. 

Another  important  property  of  the  concave  grating  is  that  all  the 
superimposed  spectra  are  in  exactly  the  same  focus.  When  viewing 
such  superimposed  spectra  it  is  a  most  beautiful  sight  to  see  the  lines 
appear  colored  on  a  nearly  white  ground.  By  micrometric  measurement 
of  such  superimposed  spectra  we  have  a  most  beautiful  method  of 
determining  the  relative  wave  lengths  of  the  different  portions  of  the 
spectrum,  which  far  exceeds  in  accuracy  any  other  method  yet  devised. 
In  working  in  the  ultra-violet  or  ultra-red  portions  of  the  spectrum  we 


490  HENRY  A.  EOWLAND 

can  also  focus  on  the  superimposed  spectrum  and  so  get  the  focus  for 
the  portion  experimented  on. 

The  fact  that  the  light  has  to  pass  through  no  glass  in  the  concave 
grating  makes  it  important  in  the  examination  of  the  extremities  of 
the  spectrum  where  the  glass  might  absorb  very  much. 

There  is  one  important  research  in  which  the  concave  grating  in  its 
present  form  does  not  seem  to  be  of  much  use,  and  that  is  in  the  exami- 
nation of  the  solar  protuberances;  an  instrument  can  only  be  used  for 
this  purpose  in  which  the  dust  in  the  slit  and  the  lines  of  the  spectrum 
are  in  focus  at  once.  It  might  be  possible  to  introduce  a  cylindrical 
lens  in  such  a  way  as  to  obviate  this  difficulty.  But  for  other  work  on 
the  sun  the  concave  grating  will  be  found  very  useful.  But  its  principal 
use  will  be  to  get  the  relative  wave  lengths  of  the  lines  of  the  spectrum, 
and  so  to  map  the  spectrum;  to  divide  lines  of  the  spectrum  which  are 
very  near  together,  and  so  to  see  as  much  as  possible  of  the  spectrum; 
to  photograph  the  spectrum  so  that  it  shall  be  normal;  to  investigate 
the  portions  of  the  spectrum  beyond  the  range  of  vision;  and  lastly  to 
put  in  the  hands  of  any  physicist  at  a  moderate  cost  such  a  powerful 
instrument  as  could  only  hitherto  be  purchased  by  wealthy  individuals 
or  institutions. 

To  give  further  information  of  what  can  be  done  in  the  way  of  grat- 
ings I  will  state  the  following  particulars : 

The  dividing  engine  can  rule  a  space  6|  inches  long  and  4£  inches 
wide.  The  lines,  which  can  be  4^  inches  long,  do  not  depart  from  a 
straight  line  so  much  as  nnnnnr  inch,  and  the  carriage  moves  forward  in 
an  equally  straight  line.  The  screw  is  practically  perfect  and  has  been 
tested  to  nnmnj"  inch  without  showing  error.  Neither  does  it  have  any 
appreciable  periodic  error,  and  the  periodic  error  due  to  the  mounting 
and  graduated  head  can  be  entirely  eliminated  by  a  suitable  attachment. 
For  showing  the  production  of  ghosts  by  a  periodic  error,  such  an  error 
can  be  introduced  to  any  reasonable  amount.  Every  grating  made  by 
the  machine  is  a  good  one,  dividing  the  1474  line  with  ease,  but  some 
are  better  than  others.  Eutherfurd's  machine  only  made  one  in  every 
four  good,  and  only  one  in  a  long  time  which  might  be  called  first-class. 
One  division  of  the  head  of  the  screw  makes  14,438  lines  to  the  inch. 
Any  fraction  of  this  number  in  which  the  numerator  is  not  greater 
than  say  20  or  30  can  be  ruled.  Some  exact  numbers  to  the  millimetre, 
such  as  400,  800,  1200,  etc.,  can  also  be  ruled.  For  the  finest  definition 
either  14,438  or  28,876  lines  to  the  inch  are  recommended,  the  first  for 
ordinary  use  and  the  second  for  examining  the  extremities  of  the 


GRATINGS  FOR  OPTICAL  PURPOSES  491 

spectrum.  Extremely  brilliant  gratings  have  been  made  with  43,314 
lines  to  the  inch,  and  there  is  little  difficulty  in  ruling  more  if  desired. 
The  following  show  some  results  obtained: 

Flat  grating,  1  inch  square,  43,000  lines  to  the  inch.  Divides  the 
1474  line  in  the  first  spectrum. 

Flat  grating,  2X3  inches,  14,438  lines  to  the  inch,  total  43,314. 
Divides  1474  in  the  first  spectrum,  the  E  line  (Angstrom  5269-4)  in 
the  second  and  is  good  in  the  fourth  and  even  fifth  spectrum. 

Flat  grating,  2X3  inches,  1200  lines  to  one  millimetre.  Shows  very 
many  more  lines  in  the  B  and  A  groups  than  were  ever  before  seen. 

Flat  grating,  2  X  3£  inches,  14,438  lines  to  the  inch.  This  has  most 
wonderful  brilliancy  in  one  of  the  first  spectra,  so  that  I  have  seen 
the  Z  line,  wave-length  8240  (see  Abney^s  map  of  the  ultra-red  region), 
and  determined  its  wave-length  roughly,  and  have  seen  much  further 
below  the  A  line  than  the  B  line  is  above  the  A  line.  The  same  may 
be  said  of  the  violet  end  of  the  spectrum.  But  such  gratings  are  only 
obtained  by  accident. 

Concave  grating,  2X3  inches,  7  feet  radius  of  curvature,  4818  lines 
to  the  inch.  The  coincidences  of  the  spectra  can  be  observed  to  the 
tenth  or  twelfth  spectrum. 

Concave  grating,  2X3  inches,  14,438  lines  to  the  inch,  radius  of  cur- 
vature 8  feet.  Divides  the  1474  line  in  the  first  spectrum,  the  E  line 
in  the  second,  and  is  good  in  the  third  or  fourth. 

Concave  grating,  3  X  5£  inches,  17  feet  radius  of  curvature,  28,876 
lines  to  the  inch,  and  thus  nearly  160,000  lines  in  all.  This  shows 
more  in  the  first  spectrum  than  was  ever  seen  before.  Divides  1474 
and  E  very  widely  and  shows  the  stronger  component  of  Angstrom  5275 
double.  Second  spectrum  not  tried. 

Concave  grating,  4  X  5f  inches,  3610  lines  to  the  inch,  radius  of  cur- 
vature 5  feet  4  inches.  This  grating  was  made  for  Professor  Langley's 
experiments  on  the  ultra-red  portion  of  the  spectrum,  and  was  thus 
made  very  bright  in  the  first  spectrum.  The  definition  seems  to  be 
very  fine  notwithstanding  the  short  focus  and  divides  the  1474  line  with 
ease.  But  it  is  difficult  to  rule  so  concave  a  grating  as  the  diamond 
marks  differently  on  the  different  parts  of  the  plate. 

These  give  illustrations  of  the  results  accomplished,  but  of  course 
many  other  experiments  have  been  made.  I  have  not  yet  been  able  to 
decide  whether  the  definition  of  the  concave  grating  fully  comes  up  to 
that  of  a  flat  grating,  but  it  evidently  does  so  very  nearly. 


30 
ON  CONCAVE  GEATINGS  FOE  OPTICAL  PUEPOSES * 

[American  Journal  of  Science  [3],  XXVI,  87-98,  1883  ;  Philosophical  Magazine 
[5],  XVI,  197-210,  1883] 

GENERAL  THEORY 

Having  recently  completed  a  very  successful  machine  for  ruling 
gratings,  my  attention  was  naturally  called  to  the  effect  of  irregularity 
in  the  form  and  position  of  the  lines  and  the  form  of  the  surface  on 
the  definition  of  the  grating.  Mr.  C.  S.  Peirce  has  recently  shown,  in 
the  American  Journal  of  Mathematics,  that  a  periodic  error  in  the 
ruling  produces  what  have  been  called  ghosts  in  the  spectrum.  At  first 
I  attempted  to  calculate  the  effect  of  other  irregularities  by  the  ordi- 
nary method  of  integration,  but  the  results  obtained  were  not  commen- 
surate with  the  labor.  I  then  sought  for  a  simpler  method.  Guided  by 
the  fact  that  inverse  methods  in  electrical  distribution  are  simpler 
than  direct  methods,  I  soon  found  an  inverse  method  for  use  in  this 
problem. 

In  the  use  of  the  grating  in  most  ordinary  spectroscopes,  the  tele- 
scopes are  fixed  together  as  nearly  parallel  as  possible,  and  the  grating 
turned  around  a  vertical  axis  to  bring  the  different  spectra  into  the 
field  of  view.  The  rays  striking  on  the  grating  are  nearly  parallel, 
but  for  the  sake  of  generality  I  shall  assume  that  they  radiate  from  a 
point  in  space  and  shall  investigate  the  proper  ruling  of  the  grating 
to  bring  the  rays  back  to  the  point  from  which  they  started.  The  wave 
fronts  will  be  a  series  of  spherical  shells  at  equal  distances  apart.  If 

JAn  abstract  of  this  paper  with  some  other  matter  was  given  at  the  Physical 
Society  of  London  in  November  last,  the  paper  being  in  my  hand  in  its  present  shape 
at  that  time.  As  I  wished  to  make  some  additions,  for  which  I  have  not  yet  had 
time,  I  did  not  then  publish  it.  I  was  much  surprised  soon  after  to  see  an  article 
on  this  subject  which  had  been  presented  to  the  Physical  Society  and  was  published 
in  the  Philosophical  Magazine.  The  article  contains  nothing  more  than  an  exten- 
sion of  my  remarks  at  the  Physical  Society  and  formula;  similar  to  those  in  this 
paper.  As  I  have  not  before  Ihis  published  anything  except  a  preliminary  notice  of 
the  concave  gratings,  I  expected  a  little  time  to  work  up  the  subject,  seeing  that  the 
practical  work  of  photographing  the  spectrum  has  recently  absorbed  all  my  time. 
But  probably  I  have  waited  too  long. 


ON  CONCAVE  GRATINGS  FOR  OPTICAL  PURPOSES  493 

these  waves  strike  on  a  reflecting  surface,  they  will  be  reflected  back 
provided  they  can  do  so  all  in  the  same  phase.  A  sphere  around  the 
radiant  point  satisfies  the  condition  for  waves  of  all  lengths  and  thus 
gives  the  case  of  ordinary  reflection.  Let  any  surface  cut  the  wave 
surfaces  in  any  manner  and  let  us  remove  those  portions  of  the  surface 
which  are  cut  by  the  wave  surfaces;  the  light  of  that  particular  wave- 
length can  then  be  reflected  back  along  the  same  path  in  the  same 
phase  and  thus,  by  the  above  principle,  a  portion  will  be  sent  back. 
But  the  solution  holds  for  only  one  wave-length  and  so  white  light  will 
be  drawn  out  into  a  spectrum.  Hence  we  have  the  important  conclu- 
sion that  a  theoretically  perfect  grating  for  one  position  of  the  slit  and 
eye-piece  can  be  ruled  on  any  surface,  flat  or  otherwise.  This  is  an 
extremely  important  practical  conclusion  and  explains  many  facts  which 
have  been  observed  in  the  use  of  gratings.  For  we  see  that  errors  of 
the  dividing  engine  can  be  counterbalanced  by  errors  in  the  flatness  of 
the  plate,  so  that  a  bad  dividing  engine  may  now  and  then  make  a 
grating  which  is  good  in  one  spectrum  but  not  in  all.  And  so  we  often 
find  that  one  spectrum  is  better  than  another.  Furthermore  Professor 
Young  has  observed  that  he  could  often  improve  the  definition  of  a 
grating  by  slightly  bending  the  plate  on  which  it  was  ruled. 

From  the  above  theorem  we  see  that  if  a  plate  is  ruled  in  circles 
whose  radius  is  r  sin  [JL  and  whose  distance  apart  is  dr  /  sin  //,  where  Ar 
is  constant,  then  the  ruling  will  be  appropriate  to  bring  the  spectrum 
to  a  focus  at  a  distance,  r,  and  angle  of  incidence,  //.  Thus  we  should 
need  no  telescopes  to  view  the  spectrum  in  that  particular  position  of 
the  grating.  Had  the  wave  surfaces  been  cylindrical  instead  of  spher- 
ical the  lines  would  have  been  straight  instead  of  circular,  but  at  the 
above  distances  apart.  In  this  case  the  spectrum  would  have  been 
brought  to  a  focus,  but  would  have  been  diffused  in  the  direction  of 
the  lines.  In  the  same  way  we  can  conclude  that  in  flat  gratings  any 
departure  from  a  straight  line  has  the  effect  of  causing  the  dust  in  the 
slit  and  the  spectrum  to  have  different  foci,  a  fact  sometimes  observed. 

We  also  see  that,  if  the  departure  from  equal  spaces  is  small,  or,  in 
other  words,  the  distance  r  is  great,  the  lines  must  be  ruled  at  distances 
apart  represented  by 


r  sin  n 

in  order  to  bring  the  light  to  a  focus  at  the  angle  p.  and  distance  r,  c 
being  a  constant  and  x  the  distance  from  some  point  on  the  plate.  If 
f*  changes  sign,  then  r  must  change  in  sign.  Hence  we  see  that  the 


494  HENKY  A.  ROWLAND 

effect  of  a  linear  error  in  the  spacing  is  to  make  the  focus  on  one  side 
shorter  and  the  other  side  longer  than  the  normal  amount.  Professor 
Peirce  has  measured  some  of  Mr.  Eutherfurd's  gratings  and  found  that 
the  spaces  increased  in  passing  along  the  grating,  and  he  also  found 
that  the  foci  of  symmetrical  spectra  were  different.  But  this  is  the 
first  attempt  to  connect  the  two.  The  definition  of  a  grating  may 
thus  be  very  good  even  when  the  error  of  run  of  the  screw  is  consider- 
able, provided  it  is  linear. 

CONCAVE  G-KATINGR 

Let  us  now  take  the  special  case  of  lines  ruled  on  a  spherical  surface; 
and  let  us  not  confine  ourselves  to  light  coming  back  to  the  same  point, 
but  let  the  light  return  to  another  point.  Let  the  co-ordinates  of  the 
radiant  point  and  focal  point  be  y<=0,  x  =  —  a  and  y  =  0,  x*+-  a,  and 
let  the  centre  of  the  sphere  whose  radius  is  p  be  at  xr,  y'.  Let  r  be  the 
distance  from  the  radiant  point  to  the  point  x,  y,  and  let  R  be  that  from 
the  focal  point  to  x,  y.  Let  us  then  write 

2b  =  R  -f  re, 

where  c  is  equal  to  ±  1  according  as  the  reflected  or  transmitted  ray  is 
used.  Should  we  increase  b  by  equal  quantities  and  draw  the  ellip- 
soids or  hyperboloids  so  indicated,  we  could  use  these  surfaces  in  the 
same  way  as  the  wave  surfaces  above.  The  intersections  of  these 
surfaces  with  any  other  surface  form  what  are  known  as  Huyghens' 
zones.  By  actually  drawing  these  zones  on  the  surface,  we  form  a 
grating  which  will  diffract  the  light  of  a  certain  wave-length  to  the 
given  focal  point.  For  the  particular  problem  in  hand,  we  need  only 
work  in  the  plane  x,  y  for  the  present. 

Let  s  be  an  element  of  the  curve  of  intersection  of  the  given  surface 
with  the  plane  x,  y.  Then  our  present  problem  is  to  find  the  width  of 
Huyghens'  zones  on  the  surface,  that  is  ds  in  terms  of  db. 

The  equation  of  the  circle  is 

(x-xy  +  (y-y'?  =  f>* 
and  of  the  ellipse  or  hyperbola 

R  +  re  =  2* 

or  (i2  —  a2)  x3  +  fry2  =  tf(V  —  a'i) 

in  which  c  has  disappeared. 

dx  y  —  y' 

-        --- 


ON  CONCAVE  GRATINGS  FOR  OPTICAL  PURPOSES  495 


dzl  (bz  —  a2)  x—Py  ^^  }  =  b\W  — 


-  (a? 

x      x 


.  -  •  ,b 
" 


—  (V  +  y*  +  a2) 


This  equation  gives  us  the  proper  distance  of  the  rulings  on  the  sur- 
face, and  if  we  could  get  a  dividing  engine  to  rule  according  to  this 
formula  the  problem  of  bringing  the  spectrum  to  a  focus  without  tele- 
scopes would  be  solved.  But  an  ordinary  dividing  engine  rules  equal 
spaces  and  so  we  shall  further  investigate  the  question  whether  there 
is  any  part  of  the  circle  where  the  spaces  are  equal.  We  can  then  write 

ds  __  n 
db~ 

And  the  differential  of  this  with  regard  to  an  arc  of  the  circle  must 
be  zero.  Differentiating  and  reducing  by  the  equations 

dx  _     _y  —  y'  .     db        _         p 
~dy  ~        x=2'    ~dy  ~         G  (x  —  a/)' 
we  have 

P  {  2xb  (y  —  y'}  -  2yb  (x  —  x'}-  -£  [6ia  -  (a?  +  y1  +  a1)]  } 


It  is  more  simple  to  express  this  result  in  terms  of  E,  r,  p  and  the 
angles  between  them. 

Let  fi.  be  the  angle  between  p  and  r,  and  v  that  between  p  and  R.     Let 
us  also  put 


Let  /?,  f  and  3  also  represent  the  angles  made  by  r,  R  and  p  respec- 
tively with  the  line  joining  the  source  of  light  and  focus,  and  let 


Then  we  have 

_  R  cos  f  +  r  cos  ,5  _  R  sin  f  +  r  sin  p          _r  cos  /3  —  R  cos  y 

-I       2/  —  9  9.  "   » 


496  HENKY  A.  ROWLAND 

(b*  -  a^(y  -y'T  +  P  (x  -  x'J  =  f  (£2  -  «8  sin2  3)  , 
I1  —  a*  =  Rr  cos2  a  , 

R  -\-  r  ir  _  R 

simj  =      ^        sin  a;     cos  -n  =  —  -  —  cos  a, 
2a  2a 


=     --,        =        -, 

0  0 

T  cos  7]  sin  r  sin  ft       Rr    . 

x=b  -  r  ;      v  =  a  -.  —  '-  -  -  =  —r-  sm  in  cos  a  , 

COS  a  Sin  a  COS  a  0 


Vy  (y  -y'}+x  (I*  -  a2)  (a;  -  aT)  =  (cos  ,,.  +  cos 

262  —  (V  +  */2  +  O  =  #r, 

-  x')=  (sin  n  +  sin  v) 


sin  /jt  +  sin  v      cos  a  sin  e 
2a  cos  5  =  r  cos  /j.  —  R  cos  y  , 
2a  sin  5  =  r  sin  /*  —  R  sin  v  .  . 
On  substituting  these  values  and  reducing,  we  find 

2  2Rr  cos  a  cos  e 

~  r  cos2  y  +  R  cos2  n  ' 

ds 

2  A  more  simple  solution  is  the  following:  —  _  mnst  be  constant  in  the  direction 

do 

in  which  the  dividing  engine  rules.  If  the  dividing  engine  rules  in  the  direction  of 
the  axis  y,  the  differential  of  this  with  respect  to  y  must  be  zero.  But  we  can  also 
take  the  reciprocal  of  this  quantity  and  so  we  can  write  for  the  equation  of  condi- 
tion 

d       d(R+  r)  _  0 

dy  ds 

Taking  a  circle  as  our  curve  we  can  write 

(Z_X')2+  (y  —  yf)*  =  p* 

and  (x  —  x")*  +  (y  —  y"V  =  -R2, 

(X  -  2///)2  +    (y  -  y'")1  =  r2, 


+  r)_  i  (         ,j*-x"      x-x>»\_  {^_^ly-y"  +  y-v"'\) 

~~i\(l/       y\—2t—         —  -  J  \~~W~         ~r  -  j} 

(R  +  r)  _    1    rx  —  x"x  —  x'"  ,    \~  x  —  x")(y  —  y"} 

dT~      ~yj~  R-         ~T~  ~^~~ 

\  _<r 


Making  x  =  0,     y  =  0,     y'  =  0,     x'  —  p, 

we  have  x"        xf"  I  x//2       x///~i\ 

~         '    ~  P     ~        +  ~  =  °' 


_n          cos  p  +  cos  v      _     2Rr  cos  a  cose 

r  cos"  v  +  R  cos2  u      r  cos2  v  +  R  cos2  u  ' 


Ox  CONCAVE  GRATINGS  FOR  OPTICAL  PURPOSES 


497 


Whence  the  focal  length  is 


pR  cos' 


COS  a  COS  £  —  p  COb  v 

For  the  transmitted  beam,  change  the  sign  of  R.  Supposing  p,  R  and  v 
to  remain  constant  and  r  and  //  to  vary,  this  equation  will  then  give  the 
line  on  which  all  the  spectra  and  the  central  image  are  brought  to  a 
focus. 

By  far  the  most  interesting  case  is  obtained  by  making 


since  these  values  satisfy  the  equation.     The  line  of  foci  is  then  a 
circle  with  a  radius  equal  to  one-half  p.     Hence  if  a  source  of  light 


FIG.  i. 


exists  on  this  circle,  the  reflected  image  and  all  the  spectra  will  be 
brought  to  a  focus  on  the  same  circle.  Thus  if  we  attach  the  slit,  the 
eye-piece  and  the  grating  to  the  three  radii  of  the  circle,  however  we 
move  them,  we  shall  always  have  some  spectrum  in  the  focus  of  the 
eye-piece.  But  in  some  positions  the  line  of  foci  is  so  oblique  to  the 
direction  of  the  light  that  only  one  line  of  the  spectrum  can  be  seen 
well  at  any  one  time.  The  best  position  of  the  eye-piece  as  far  as  we 
consider  this  fact  is  thus  the  one  opposite  to  the  grating  and  at  its 
centre  of  curvature.  In  this  position  the  line  of  foci  is  perpendicular 
to  the  direction  of  the  light,  and  we  shall  show  presently  that  the 
spectrum  is  normal  at  this  point  whatever  the  position  of  the  slit,  pro- 
vided it  is  on  the  circle. 

Fig.  1  represents  this  case;  A  is  the  slit,  C  is  the  eye-piece,  and  B  is 
the  grating  with  its  centre  of  curvature  at  C.     In  this  case  all  the  con- 
ditions are  satisfied  by  fixing  the  grating  and  eye-piece  to  the  bar  BC 
32 


498  HENRY  A.  ROWLAND 

whose  ends  rest  on  carriages  moving  on  the  rails  AB  and  AC  at  right 
angles  to  each  other;  when  desired,  the  radius  AD  may  be  put  in  to  hold 
everything  steady,  but  this  has  been  found  practically  unnecessary. 

The  proper  formula?  for  this  case  are  as  follows:  If  ^  is  the  wave- 
length and  w  the  distance  apart  of  the  lines  of  the  grating  from  centre 
to  centre,  then  we  have 

1     _  IN  _  sin  v 

~~d~  %w~  ~T~ 

where  N  is  the  order  of  the  spectrum. 

w  sin  v 


/  = 


Now  in  the  given  case  p  is  constant  and  so  NX  is  proportional  to  the 
line  AC.  Or,  for  any  given  spectrum,  the  wave-length  is  proportional 
to  that  line. 

If  a  micrometer  is  fixed  at  C  we  can  consider  the  case  as  follows  : 

1        )N 
-tf  ^^(sin^  +  sinv), 

d).         w 

7i~  =  ~W  cos  /•*• 
a/i          N 

If  D  is  the  distance  the  cross-hairs  of  the  micrometer  move  forward 
for  one  division  of  the  head,  we  can  write  for  the  point  C 

A.,  =  I- 

!' 

and  for  the  same  point  ft  is  zero.     Hence 


But  this  is  independent  of  v  and  we  thus  arrive  at  the  important  fact 
that  the  value  of  a  division  of  the  micrometer  is  always  the  same  for 
the  same  spectrum  and  can  always  be  determined  with  sufficient  accu- 
racy from  the  dimensions  of  the  apparatus  and  number  of  lines  on  the 
grating,  as  well  as  by  observation  of  the  spectrum. 

Furthermore,  this  proves  that  the  spectrum  is  normal  at  this  point 
and  to  the  same  scale  in  the  same  spectrum.  Hence  we  have  only  to 
photograph  the  spectrum  to  obtain  the  normal  spectrum  and  a  centi- 
meter for  any  of  the  photographs  always  represents  the  same  increase 
of  wave-length. 

It  is  to  be  specially  noted  that  this  theorem  is  rigidly  true  whether 
the  adjustments  are  correct  or  not,  provided  only  that  the  micrometer 
is  on  the  line  drawn  perpendicularly  from  the  centre  of  the  grating,  even 
if  it  is  not  the  centre  of  curvature. 


Ox  CONCAVE  GRATINGS  FOE  OPTICAL  PURPOSES  499 

As  the  radius  of  curvature  of  concave  gratings  is  usually  great,  the 
distance  through  which  the  spectrum  remains  practically  normal  is  very 
great.  In  the  instrument  which  I  principally  use,  the  radius  of  curva- 
ture p,  is  about  21  feet  4  inches,  the  width  of  the  ruling  "being  about  5-5 
inches.  In  such  an  instrument  the  spectrum  thrown  on  a  flat  plate  is 
normal  within  about  1  part  in  1,000,000,  for  6  inches  and  less  than  1  in 
35,000,  for  18  inches.  In  photographing  the  spectrum  on  a  flat  plate, 
the  definition  is  excellent  for  12  inches,  and  by  use  of  a  plate  bent  to  11 
feet  radius,  a  plate  of  20  inches  in  length  is  in  perfect  focus  and  the 
spectrum  still  so  nearly  normal  as  to  have  its  error  neglected  for  most 
purposes. 

Another  important  property  of  the  concave  grating  is  that  all  the 
superimposed  spectra  are  in  focus  at  the  same  point,  and  so  by  micro- 
metric  measurements  the  relative  wave-lengths  are  readily  determined. 
Hence,  knowing  the  absolute  wave-length  of  one  line,  the  whole  spec- 
trum can  be  measured.  Professor  Peirce  has  determined  the  absolute 
wave-length  of  one  line  with  great  care  and  I  am  now  measuring  the 
coincidences.  This  method  is  greatly  more  accurate  than  any  hitherto 
known,  as  by  a  mere  eye  inspection,  the  relative  wave-length  can  often 
be  judged  to  1  part  in  20,000  and  with  a  micrometer  to  1  in  1,000,000. 
Again,  in  dealing  with  the  invisible  portion  of  the  spectrum,  the  focus 
can  be  obtained  by  examining  the  superimposed  spectrum.  Captain 
Abney,  by  using  a  concave  mirror  in  the  place  of  telescopes,  has  been 
enabled  to  use  this  method  f or^  obtaining  the  focus  in  photographing  the 
ultra  red  rays  of  the  spectrum.  It  is  also  to  be  noted  that  this  theorem 
of  the  normal  spectrum  applies  also  to  the  flat  grating  used  with  tele- 
scopes and  to  either  reflecting  or  transmitting  gratings;  but  in  these 
cases  only  a  small  portion  of  the  spectrum  can  be  used,  as  no  lens  can 
be  made  perfectly  achromatic.  And  so,  as  the  distance  of  the  microme- 
ter has  constantly  to  be  changed  when  one  passes  along  the  spectrum, 
its  constant  does  not  remain  constant  but  varies  in  an  irregular  man- 
ner. But  it  would  be  possible  to  fix  the  grating,  one  objective  and  the 
camera  rigidly  on  a  bar,  and  then  focus  by  moving  the  slit  or  the  other 
objective.  In  this  case  the  spectrum  would  be  rigidly  normal,  but 
would  probably  be  in  focus  for  only  a  small  length  and  the  adjustment 
of  the  focus  would  not  be  automatic. 

But  nothing  can  exceed  the  beauty  and  simplicity  of  the  concave  graj- 
ing  when  mounted  on  a  movable  bar  such  as  I  have  described  and  illus- 
trated in  Fig.  1.  Having  selected  the  grating  which  we  wish  to  use, 
we  mount  it  in  its  plate-holder  and  put  the  proper  collimating  eye-piece 


500  HENRY  A.  EOWLAND 

in  place.  We  then  carefully  adjust  the  focus  by  altering  the  length  of 
D  until  the  cross-hairs  are  at  the  exact  centre  of  curvature  of  the  grat- 
ing. On  moving  the  bar  the  whole  series  of  spectra  are  then  in  exact 
focus,  and  the  value  of  a  division  of  the  micrometer  is  a  known  quan- 
tity for  that  particular  grating.  The  wooden  way  AC,  on  which  the 
carriage  moves,  is  graduated  to  equal  divisions  representing  wave- 
lengths, since  the  wave-length  is  proportional  to  the  distance  AC.  Wo 
can  thus  set  the  instrument  to  any  particular  wave-length  we  may  wish 
to  study,  or  even  determine  the  wave-length  to  at  least  one  part  in  five 
thousand  by  a  simple  reading.  By  having  a  variety  of  scales,  one  for 
each  spectrum,  we  can  immediately  see  what  lines  are  superimposed  on 
each  other  and  identify  them  accordingly  when  we  are  measuring  their 
relative  wave-length.  On  now  replacing  the  eye-piece  by  a  camera,  we 
are  in  a  position  to  photograph  the  spectrum  with  the  greatest  ease. 
We  put  in  the  sensitive  plate,  either  wet  or  dry,  and  move  to  the  part 
we  wish  to  photograph;  having  exposed  for  that  part,  we  move  to 
another  part,  raise  the  plate  to  another  position  and  expose  once  more. 
We  have  no  thought  for  the  focus,  for  that  remains  perfect,  but  simply 
refer  to  the  table  giving  the  proper  exposure  for  that  portion  of  the 
spectrum  and  so  have  a  perfect  plate.  Thus  we  can  photograph  the 
whole  spectrum  on  one  plate  in  a  few  minutes,  from  the  F  line  to  the 
extreme  violet  in  several  strips,  each  20  inches  long.  Or  we  may  photo- 
graph to  the  red  rays  by  prolonged  exposure.  Thus  the  work  of  days 
with  any  other  apparatus  becomes  the  work  of  hours  with  this.  Fur- 
thermore, each  plate  is  to  scale,  an  inch  on  any  one  of  the  strips  repre- 
senting exactly  so  much  difference  of  wave-length.  The  scale  of  the 
different  orders  of  spectra  are  exactly  proportional  to  the  order.  Of 
course  the  superposition  of  the  spectra  gives  the  relative  wave-length. 
To  get  the  superposition,  of  course,  photography  is  the  best  method. 

Having  so  far  obtained  only  the  first  approximation  to  the  theory  of 
the  concave  grating,  let  us  now  proceed  to  a  second  one.  The  dividing 
engine  rules  equal  spaces  along  the  chord  of  the  circular  arc  of  the  grat- 
ing: the  question  is  whether  any  other  kind  of  ruling  would  be  better, 
for  the  dividing  engine  is  so  constructed  that  one  might  readily  change 
it  to  rule  slightly  different  from  equal  spaces. 

The  condition  for  theoretical  perfection  is  that  C  shall  remain  con- 
stant for  all  portions  of  the  mirror.  I  shall  therefore  investigate  how 
nearly  this  is  true. 

Let  p  be  the  radius  of  curvature  and  let  R  and  r  be  the  true  dis- 
tances to  any  point  of  the  grating,  R0  and  r0  being  the  distances  to  the 


ON  CONCAVE  GRATINGS  FOR  OPTICAL  PURPOSES  501 

centre.  Let  fi  and  v  be  the  general  values  of  the  angles  and  //<,  and  VQ 
the  angles  referred  to  the  centre  of  the  mirror.  The  condition  is  that 

o 

-^  =  sin  //  +  sin  v 
L/ 

shall  be  a  constant  for  all  parts  of  the  surface  of  the  grating.  Let  us 
then  develope  sin  //  and  sin  v  in  terms  of  /*0,  v0  and  the  angle  d  between 
the  radii  drawn  to  the  centre  of  the  grating  and  to  the  point  under  con- 
sideration. Let  d'  be  the  angle  between  R  and  R0.  Then  we  can  write 
immediately 

/>  sin  fi  =  p  sin  /./„  cos  8'  +  R0  sin  d'  —  p  cos  //„  sin  8', 

sin  /j.  =  sin  //0  cos  d'  \  1  +  —  rJl  —  A  tan  8f  i  , 

iOsmjH,  y 

where  *  _  -.  _  p  cos  ,u0 

Developing  the  value  of  cos  d'  in  terms  of  d,  we  have 
cos  »"  =  cos  S  {  1  +  A  [l  +  ''™8"'"|  «' 


As  the  cases  we  are  to  consider  are  those  where  A  is  small,  it  will  be 
sufficient  to  write 

tan  *:= 

Whence  we  have 

sin  <,.  =  sin  //„  cos  d 


» 

+  ,53+  &c. 


\       - 
We  can  write  the  value  of  sin  v  from  symmetry.     But  we  have 

2  -7-  =  sin  fj.  +  sin  v  . 
as 

In  this  formula,  db  can  be  considered  as  a  constant  depending  on 
wave-length  of  light,  etc.,  and  ds  as  the  width  apart  of  the  lines  on  the 
grating.  The  dividing  engine  rules  lines  on  the  curved  surface  accord- 
ing to  the  formula 

2  -7-  =  cos  8  (sin  //,+  sin  v0). 

CL8 

But  this  is  the  second  approximation  to  the  true  theoretical  ruling. 
And  this  ruling  will  not  only  be  approximately  correct,  but  exact  when 


502  HENRY  A.  ROWLAND 

all  the  terms  of  the  series  except  the  first  vanish.  In  the  case  where  the 
slit  and  focus  are  on  the  circle  of  radius  %p,  as  in  the  automatic  arrange- 
ment described  above,  we  have  A  =  0  and  the  second  and  third  terms  of 
the  series  disappear,  and  we  can  write  since  we  have 

TO  r 

— t  =  cos  fJL0    and    — -   —  cos  v0 , 
P  P 

n  db  » /  .  •        \/i       i  sin  >j.0  tan  //„  +  sin  v0  tan  *„    3      „     \ 

2  —  =  cos  d  (sin  ,u0+  sin  >0 )  1—  J  - r+  &c.  . 

ds  \  sm  fj0  +  sm  >0  / 

But  in  the  automatic  arrangement  we  also  have  v0  =  0,  and  so  the 
formula  becomes 

2  -j-  =  cos  d  (sin  /;„  +  sin  KO)  { 1  —  J  tan  ^0^!  +  &c. }. 

6t5 

To  find  the  greatest  departure  from  theoretical  perfection,  d  must 
refer  to  the  edge  of  the  grating.  In  the  gratings  which  I  am  now  mak- 
ing, p  is  about  260  inches  and  the  width  of  the  grating  about  5-4  inches. 

Hence  d  =  —-  approximately  and  the  series  becomes 


Hence  the  greatest  departure  from  the  theoretical  ruling,  even  when 
ta.nfji(f=2,  is  1  in  1,000,000.  Now  the  distance  apart  of  the  compon- 
ents of  the  1474  line  is  somewhat  nearly  one  forty-thousandth  of  the 
wave-length  and  I  scarcely  suppose  that  any  line  has  been  divided  by 
the  best  spectroscope  in  the  world  whose  components  are  less  than  one- 
third  of  this  distance  apart.  Hence  we  see  that  the  departure  of  the 
ruling  from  theoretical  perfection  is  of  little  consequence  until  we  are 
able  to  divide  lines  twenty  times  as  fine  as  the  1474  line.  Even  in  that 
case,  since  the  error  of  ruling  varies  as  3s,  the  greater  portion  of  the 
grating  would  be  ruled  correctly. 

The  question  now  comes  up  as  to  whether  there  is  any  limit  to  the 
resolving  power  of  a  spectroscope.  This  evidently  depends  upon  the 
magnifying  power  and  the  apparent  width  of  the  lines.  The  magnify- 
ing power  can  be  varied  at  pleasure  and  so  we  have  only  to  consider  the 
width  of  the  lines  of  the  spectrum.  The  width  of  the  lines  evidently 
depends,  in  a  perfect  grating,  upon  three  circumstances,  the  width  of 
the  slit,  the  number  of  lines  in  the  grating  and  the  true  physical  width 
of  the  line.  The  width  of  the  slit  can  be  varied  at  pleasure,  the  number 
of  lines  on  the  grating  can  be  made  very  great  (160,000  in  one  of  mine), 
and  hence  we  are  only  limited  by  the  true  physical  width  of  the  lines. 


Ox  COXCAVE  GRATINGS  FOR  OPTICAL  PURPOSES  503 

We  have  numerous  cases  of  wide  lines,  such  as  the  C  line,  the  compon- 
ents of  the  D3  and  H  lines  and  numerous  others  which  are  perfectly 
familiar  to  every  spectroscopist.  Hence  we  are  free  to  suppose  that  all 
lines  have  some  physical  width,  and  we  are  limited  by  that  width  in  the 
resolving  power  of  our  spectroscope.  Indeed,  from  a  theoretical  stand- 
point, we  should  suppose  this  to  be  true :  for  the  molecules  only  vibrate 
freely  while  swinging  through  their  free  path  and  in  order  to  have  the 
physical  width  one  one-hundred-thousandth  of  the  wave-length,  the 
molecule  must  make  somewhat  nearly  one  hundred  thousand  vibrations 
in  its  free  path:  but  this  would  require  a  free  path  of  about  sooVoo 
inch !  Hence  it  would  be  only  the  outermost  solar  atmosphere  that  could 
produce  such  fine  lines  and  we  could  hardly  expect  to  see  much  finer 
ones  in  the  solar  spectrum.  Again  *  it  is  found  impossible  to  obtain 
interference  between  two  rays  whose  paths  differ  by  much  more  than 
50,000  wave-lengths. 

All  the  methods  of  determining  the  limits  seem  to  point  to  about  the 
150,000th  of  the  wave-length  as  the  smallest  distance  at  which  the  two 
lines  can  be  separated  in  the  solar  spectrum  by  even  a  spectroscope  of 
infinite  power.  As  we  can  now  nearly  approach  this  limit  I  am  strongly 
of  the  opinion  that  we  have  nearly  reached  the  limit  of  resolving  power, 
and  that  we  can  never  hope  to  see  very  many  more  lines  in  the  spectrum 
than  can  be  seen  at  present,  either  by  means  of  prisms  or  gratings. 

It  is  not  to  be  supposed,  however,  that  the  average  wave-length  of  the 
line  is  not  more  definite  than  this,  for  we  can  easily  point  the  cross- 
hairs to  the  centre  of  the  line  to  perhaps  1  in  1,000,000  of  the  wave- 
length. The  most  exact  method  of  detecting  the  coincidences  of  a  line 
of  metal  with  one  in  the  solar  spectrum  would  thus  be  to  take  micro- 
metric  measurements  first  on  one  and  then  on  the  other;  but  I  suppose 
it  would  take  several  readings  to  make  the  determination  to  1  in 
1,000,000. 

Since  writing  the  above  I  have  greatly  improved  my  apparatus  and 
can  now  photograph  150  lines  between  the  H  and  K  lines,  including 
many  whose  wave-length  does  not  differ  more  than  1  in  about  80,000. 
I  have  also  photographed  the  1474  and  b3  and  &4,  widely  double,  and  also 
E  just  perceptibly  double.  With  the  eye  much  more  can  be  seen,  but 
I  must  say  that  I  have  not  yet  seen  many  signs  of  reaching  a  limit.  The 

3 1  have  recently  discovered  that  each  component  of  the  D  line  is  double  probably 
from  the  partial  reversal  of  the  line  as  we  nearly  always  see  it  in  the  flame  spectrum. 

*This  method  of  determining  the  limit  has  been  suggested  to  me  by  Prof.  C.  8. 
Hastings,  of  this  University. 


504  HE^RY  A.  EOWLAND 

lines  yet  appear  as  fine  and  sharp  as  with  a  lower  power.  If  my  grat- 
ing is  assumed  to  be  perfect,  in  the  third  spectrum  I  should  be  able  to 
divide  lines  whose  wave-lengths  differed,  in  about  150,000,  though  not 
to  photograph  them. 

The  E  line  has  components,  about  ^uwfrth  of  the  wave-length  apart. 
I  believe  I  can  resolve  lines  much  closer  than  this,  say  1  in  100,000  at 
least.  Hence  the  idea  of  a  limit  has  not  yet  been  proved. 

However,  as  some  of  the  lines  of  the  spectrum  are  much  wider  than 
others  we  should  not  expect  any  definite  limit,  but  a  gradual  falling  off 
as  we  increase  our  power.  At  first,  in  the  short  wave-lengths  at  least, 
the  number  of  lines  is  nearly  proportional  to  the  resolving  power,  but 
this  law  should  fail  as  we  approach  the  limit. 


31 

ON  MR.   GLAZEBROOK'S   PAPER  ON   THE   ABERRATION   OF 
CONCAVE  GRATINGS 

[American  Journal  of  Science  [3],  XXVI,  214,  1883  ;  Philosophical  Magazine  [5], 

XVI,  210,  1883] 

In  the  June  number  of  the  Philosophical  Magazine.,  Mr.  R.  T.  Glaze- 
brook  has  considered  the  aberration  of  the  concave  grating  and  arrives 
at  the  conclusion  that  the  ones  which  I  have  hitherto  made  are  too 
wide  for  their  radius  of  curvature.  As  I  had  published  nothing  but  a 
preliminary  notice  of  the  grating  at  that  time,  Mr.  Glazebrook  had  not 
then  seen  my  paper  on  the  subject,  of  which  I  gave  an  abstract  at  the 
London  Physical  Society  in  November  last.  In  this  paper  I  arrive  at 
the  conclusion  that  there  is  practically  no  aberration  and  that  in  this 
respect  there  is  nothing  further  to  be  desired. 

The  reason  of  this  discrepancy  is  not  far  to  seek.  Mr.  Glazebrook 
assumes  that  the  spaces  are  equal  on  the  arc  of  the  circle.  But  I  do 
not  rule  them  in  this  manner;  but  the  equal  spaces  are  equal  along 
the  chord  of  the  arc.  Again,  the  surface  is  not  cylindrical,  but  spherical. 

These  two  errors  entirely  destroy  the  value  of  the  paper  as  far  as  my 
gratings  are  concerned,  for  it  only  applies  to  a  theoretical  grating,  ruled 
in  an  entirely  different  manner  from  my  own,  and  on  a  different  form 
of  surface. 

I  am  very  much  surprised  to  see  the  method  given  near  the  end  of 
the  paper  for  constructing  aplanatic  gratings  on  any  surface,  for  this 
is  the  method  by  which  I  discovered  the  concave  grating  originally,  and 
the  figure  is  the  same  as  I  put  on  the  blackboard  at  the  meeting  of  the 
Physical  Society  in  November  last.  I  say  I  am  surprised,  for  Mr.  Glaze- 
brook's  paper  was  read  at  the  Physical  Society,  where  I  had  given  the 
same  method  a  few  months  before,  and  yet  it  passed  without  comment. 
Indeed,  I  have  given  the  same  method  many  times  at  various  scientific 
societies  of  my  own  country.  However,  as  Mr.  Glazebrook  was  not 
present  at  the  meeting  referred  to,  he  is  entirely  without  blame  in  the 
matter. 


33 

SCEEW 

[Encyclopedia  Britannica,  Ninth  Edition,   Volume  XXI  \ 

The  screw  is  the  simplest  instrument  for  converting  a  uniform  motion 
of  rotation  into  a  uniform  motion  of  translation  (see  '  Mechanics/  vol. 
xv,  p.  754).  Metal  screws  requiring  no  special  accuracy  are  generally  cut 
by  taps  and  dies.  A  tap  is  a  cylindrical  piece  of  steel  having  a  screw 
on  its  exterior  with  sharp  cutting  edges;  by  forcing  this  with  a  revolv- 
ing motion  into  a  hole  of  the  proper  size,  a  screw  is  cut  on  its  interior 
forming  what  is  known  as  a  nut  or  female  screw.  The  die  is  a  nut  with 
sharp  cutting  edges  used  to  screw  upon  the  outside  of  round  pieces  of 
metal  and  thus  produce  male  screws.  More  accurate  screws  are  cut  in 
a  lathe  by  causing  the  carriage  carrying  the  tool  to  move  uniformly  for- 
ward, thus  a  continuous  spiral  line  is  cut  on  the  uniformly  revolving 
cylinder  fixed  between  the  lathe  centres.  The  cutting  tool  may  be  an 
ordinary  form  of  lathe  tool  or  a  revolving  saw-like  disk  (see  '  Machine 
Tools/  vol.  xv,  p.  153). 

Errors  of  Screws. — For  scientific  purposes  the  screw  must  be  so  regu- 
lar that  it  moves  forward  in  its  nut  exactly  the  same  distance  for  each 
given  angular  rotation  around  its  axis.  As  the  mountings  of  a  screw 
introduce  many  errors,  the  final  and  exact  test  of  its  accuracy  can  only 
be  made  when  it  is  finished  and  set  up  for  use.  A  large  screw  can,  how- 
ever, be  roughly  examined  in  the  following  manner:  (1)  See  whether 
the  surface  of  the  threads  has  a  perfect  polish.  The  more  it  departs 
from  this,  and  approaches  the  rough,  torn  surface  as  cut  by  the  lathe 
tool,  the  worse  it  is.  A  perfect  screw  has  a  perfect  polish.  (2)  Mount 
upon  it  between  the  centres  of  a  lathe  and  the  slip  a  short  nut  which 
fits  perfectly.  If  the  nut  moves  from  end  to  end  with  equal  friction, 
the  screw  is  uniform  in  diameter.  If  the  nut  is  long,  unequal  resist- 
ance may  be  due  to  either  an  error  of  run  or  a  bend  in  the  screw. 
(3)  Fix  a  microscope  on  the  lathe  carriage  and  focus  its  single  cross- 
hair on  the  edge  of  the  screw  and  parallel  to  its  axis.  If  the  screw  runs 
true  at  every  point,  its  axis  is  straight.  (4)  Observe  whether  the  short 
nut  runs  from  end  to  end  of  the  screw  without  a  wabbling  motion  when 
the  screw  is  turned  and  the  nut  kept  from  revolving.  If  it  wabbles  the 


SCREW  507 

screw  is  said  to  be  drunk.  One  can  see  this  error  better  by  fixing  a 
long  pointer  to  the  nut,  or  by  attaching  to  it  a  mirror  and  observing  an 
image  in  it  with  a  telescope.  The  following  experiment  will  also  detect 
this  error:  (5)  Put  upon  the  screw  two  well-fitting  and  rather  short 
nuts,  which  are  kept  from  revolving  by  arms  bearing  against  a  straight 
edge  parallel  to  the  axis  of  the  screw.  Let  one  nut  carry  an  arm  which 
supports  a  microscope  focused  on  a  line  ruled  on  the  other  nut.  Screw 
this  combination  to  different  parts  of  the  screw.  If  during  one  revolu- 
tion the  microscope  remains  in  focus,  the  screw  is  not  drunk;  and  if 
the  cross-hairs  bisect  the  lines  in  every  position,  there  is  no  error  of 
run. 

Making  Accurate  Screws. — To  .produce  a  screw  of  a  foot  or  even  a 
yard  long  with  errors  not  exceeding  -nnn^h  of  an  inch  is  not  difficult. 
Prof.  Wm.  A.  Eogers,  of  Harvard  Observatory,  has  invented  a  process 
in  which  the  tool  of  the  lathe  while  cutting  the  screw  is  moved  so  as  to 
counteract  the  errors  of  the  lathe  screw.  The  screw  is  then  partly 
ground  to  get  rid  of  local  errors.  But,  where  the  highest  accuracy  is 
needed,  we  must  resort  in  the  case  of  screws,  as  in  all  other  cases,  to 
grinding.  A  long,  solid  nut,  tightly  fitting  the  screw  in  one  position, 
cannot  be  moved  freely  to  another  position  unless  the  screw  is  very  accu- 
rate. If  grinding  material  is  applied  and  the  nut  is  constantly  tight- 
ened, it  will  grind  out  all  errors  of  run,  drunkenness,  crookedness,  and 
irregularity  of  size.  The  condition  is  that  the  nut  must  be  long,  rigid 
and  capable  of  being  tightened  as  the  grinding  proceeds ;  also  the  screw 
must  be  ground  longer  than  it  will  finally  be  needed  so  that  the  imper- 
fect ends  may  be  removed. 

The  following  process  will  produce  a  screw  suitable  for  ruling  grat- 
ings for  optical  purposes.  Suppose  it  is  our  purpose  to  produce  a  screw 
which  is  finally  to  be  9  inches  long,  not  including  bearings,  and  1-|  in. 
in  diameter.  Select  a  bar  of  soft  Bessemer  steel,  which  has  not  the 
hard  spots  usually  found  in  cast  steel,  and  about  If  inches  in  diameter 
and  30  long.  Put  it  between  lathe  centres  and  turn  it  down  to  one 
inch  diameter  everywhere,  except  about  12  inches  in  the  centre,  where 
it  is  left  a  little  over  1£  inches  in  diameter  for  cutting  the  screw.  Now 
cut  the  screw  with  a  triangular  thread  a  little  sharper  than  60°.  Above 
all,  avoid  a  fine  screw,  using  about  20  threads  to  the  inch. 

The  grinding  nut,  about  11  inches  long,  has  now  to  be  made.  Fig.  1 
represents  a  section  of  the  nut,  which  is  made  of  brass,  or  better,  of 
Bessemer  steel.  It  consists  of  four  segments, — a,  a,  which  can  be  drawn 
about  the  screw  by  two  collars,  &,  &,  and  the  screw  c.  Wedges  between 


508 


HENEY  A.  ROWLAND 


the  segments  prevent  too  great  pressure  on  the  screw.  The  final  clamp- 
ing is  effected  by  the  rings  and  screws,  d,  d,  which  enclose  the  flanges,  e, 
of  the  segments.  The  screw  is  now  placed  in  a  lathe  and  surrounded 
by  water  whose  temperature  can  be  kept  constant  to  1°  C.,  and  the  nut 
placed  on  it.  In  order  that  the  weight  of  the  nut  may  not  make  the 
ends  too  small,  it  must  either  be  counterbalanced  by  weights  hung  from 
a  rope  passing  over  pulleys  in  the  ceiling,  or  the  screw  must  be  vertical 
during  the  whole  process.  Emery  and  oil  seem  to  be  the  only  available 
grinding  materials,  though  a  softer  silica  powder  might  be  used  towards 
the  end  of  the  operation  to  clean  off  the  emery  and  prevent  future  wear. 
Now  grind  the  screw  in  the  nut,  making  the  nut  pass  backwards  and 
forwards  over  the  screw,  its  whole  range  being  nearly  20  inches  at  first. 


FIG.  1. — Section  of  Grinding  Nut. 

Turn  the  nut  end  for  end  every  ten  minutes  and  continue  for  two  weeks, 
finally  making  the  range  of  the  nut  only  about  10  inches,  using  finer 
washed  emery  and  moving  the  lathe  slower  to  avoid  heating.  Finish 
with  a  fine  silica  powder  or  rouge.  During  the  process,  if  the  thread 
becomes  too  blunt,  recut  the  nut  by  a  short  tap  so  as  not  to  change  the 
pitch  at  any  point.  This  must,  of  course,  not  be  done  less  than  five 
days  before  the  finish.  Now  cut  to  the  proper  length;  centre  again  in 
the  lathe  under  a  microscope,  and  turn  the  bearings.  A  screw  so  ground 
has  less  errors  than  from  any  other  system  of  mounting.  The  periodic 
error  especially  will  be  too  small  to  be  discoverefl,  though  the  mountings 
and  graduation  and  centering  of  the  head  will  introduce  it;  it  must 
therefore  finally  be  corrected. 

Mounting  of  Screws. — The  mounting  must  be  devised  most  carefully, 
and  is,  indeed,  more  difficult  to  make  without  error  than  the  screw  itself. 
The  principle  which  should  be  adopted  is  that  no  workmanship  is  per- 
fect; the  design  must  make  up  for  its  imperfections.  Thus  the  screw 


SCREW  509 

can  never  be  made  to  run  true  on  its  bearings,  and  hence  the  device  of 
resting  one  end  of  the  carriage  on  the  nut  must  be  rejected.  Also  all 
rigid  connection  between  the  nut  and  the  carriage  must  be  avoided,  as 
the  screw  can  never  be  adjusted  parallel  to  the  ways  on  which  the  car- 
riage rests.  For  many  purposes,  such  as  ruling  optical  gratings,  the 
carriage  must  move  accurately  forward  in  a  straight  line  as  far  as  the 
horizontal  plane  is  concerned,  while  a  little  curvature  in  the  vertical 
plane  produces  very  little  effect.  These  conditions  can  be  satisfied 
by  making  the  ways  Y-shaped  and  grinding  with  a  grinder  some- 
what shorter  than  the  ways.  By  constant  reversals  and  by  lengthen- 
ing or  shortening  the  stroke,  they,  will  finally  become  nearly  per- 
fect. The  vertical  curvature  can  be  sufficiently  tested  by  a  short  car- 
riage carrying  a  delicate  spirit  level.  Another  and  very  efficient  form 
of  ways  is  V-shaped  with  a  flat  top  and  nearly  vertical  sides.  The 
carriage  rests  on  the  flat  top  and  is  held  by  springs  against  one  of  the 
nearly  vertical  sides.  To  determine  with  accuracy  whether  the  ways 
are  straight,  fix  a  flat  piece  of  glass  on  the  carriage  and  rule  a  line  on 
it  by  moving  it  under  a  diamond ;  reverse  and  rule  another  line  near  the 
first,  and  measure  the  distance  apart  at  the  centre  and  at  the  two  ends 
by  a  micrometer.  If  the  centre  measurement  is  equal  to  the  mean  of  the 
two  end  ones,  the  line  is  straight.  This  is  better  than  the  method  with 
a  mirror  mounted  on  the  carriage  and  a  telescope.  The  screw  itself 
must  rest  in  bearings,  and  the  end  motion  be  prevented  by  a  point  bear- 
ing against  its  flat  end,  which  is  protected  by  hardened  steel  or  a  flat 
diamond.  Collar  bearings  introduce  periodic  errors.  The  secret  of 
success  is  so  to  design-  the  nut  and  its  connections  as  to  eliminate  all 
adjustments  of  the  screw  and  indeed  all  imperfect  workmanship.  The 
connection  must  also  be  such  as  to  give  means  of  correcting  any  residual 
periodic  errors  or  errors  of  run  which  may  be  introduced  in  the  mount- 
ings or  by  the  wear  of  the  machine. 

The  nut  is  shown  in  Fig  2.  It  is  made  in  two  halves,  of  wrought  iron 
filled  with  boxwood  or  lignum  vitae  plugs,  on  which  the  screw  is  cut. 
To  each  half  a  long  piece  of  sheet  steel  is  fixed  which  bears  against  a 
guiding  edge,  to  be  described  presently.  The  two  halves  are  held  to  the 
screw  by  springs,  so  that  each  moves  forward  almost  independently  of 
the  other.  To  join  the  nut  to  the  carriage,  a  ring  is  attached  to  the 
latter,  whose  plane  is  vertical  and  which  can  turn  round  a  vertical  axis. 
The  bars  fixed  midway  on  the  two  halves  of  the  nut  bear  against  this 
ring  at  points  90°  distant  from  its  axis.  Hence  each  half  does  its  share 
independently  of  the  other  in  moving  the  carriage  forward.  Any  want 


510 


HENRY  A.  ROWLAND 


of  parallelism  between  the  screws  and  the  ways  or  eccentricity  in  the 
screw  mountings  thus  scarcely  affects  the  forward  motion  of  the  car- 
riage. The  guide  against  which  the  steel  pieces  of  the  nut  rest  can  be 
made  of  such  form  as  to  correct  any  small  error  of  run  due  to  wear  of 
the  screw.  Also,  by  causing  it  to  move  backwards  and  forwards  peri- 
odically, the  periodic  error  of  the  head  and  mountings  can  be  corrected. 
In  making  gratings  for  optical  purposes  the  periodic  error  must  be 
very  perfectly  eliminated,  since  the  periodic  displacement  of  the  lines 
only  one-millionth  of  an  inch  from  their  mean  position  will  produce 


m 


FIG.  2. 

"  ghosts  "  in  the  spectrum.1  Indeed,  this  is  the  most  sensitive  method  of 
detecting  the  existence  of  this  error,  and  it  is  practically  impossible  to 
mount  the  most  perfect  of  screws  without  introducing  it.  A  very  prac- 
tical method  of  determining  this  error  is  to  rule  a  short  grating  with 
very  long  lines  on  a  piece  of  common  thin  plate  glass ;  cut  it  in  two  with 
a  diamond  and  superimpose  the  two  halves  with  the  rulings  together 
and  displaced  sideways  over  each  other  one-half  the  pitch  of  the  screw. 
On  now  looking  at  the  plates  in  a  proper  light  so  as  to  have  the  spec- 

1  In  a  machine  made  by  the  present  writer  for  ruling  gratings  the  periodic  error  is 
entirely  due  to  the  graduation  and  centering  of  the  head.  The  uncorrected  periodic 
error  from  this  cause  displaces  the  lines  ^^fa^ih  of  an  inch,  which  is  sufficient  to 
entirely  ruin  all  gratings  made  without  correcting  it. 


SCREW  511 

tral  colors  show  through  it,  dark  lines  will  appear,  which  are  wavy  if 
there  is  a  periodic  error  and  straight  if  there  is  none.  By  measuring 
the  comparative  amplitude  of  the  waves  and  the  distance  apart  of  the 
two  lines,  the  amount  of  the  periodic  error  can  be  determined.  The 
phase  of  the  periodic  error  is  best  found  by  a  series  of  trials  after  set- 
ting the  corrector  at  the  proper  amplitude  as  determined  above. 

A  machine  properly  made  as  above  and  kept  at  a  constant  tempera- 
ture should  be  able  to  make  a  scale  of  6  inches  in  length,  with  errors  at 
no  point  exceeding  nnnnnrth  of  an  inch.  When,  however,  a  grating  of 
that  length  is  attempted  at  the  rate  of  14,000  lines  to  the  inch,  four  days 
and  nights  are  required,  and  the  result  is  seldom  perfect,  possibly  on 
account  of  the  wear  of  the  machine  or  changes  of  temperature.  Grat- 
ings, however,  less  than  3  inches  long  are  easy  to  make. 


39 

ON"  THE  RELATIVE  WAVE-LENGTH  OF  THE  LINES  OF  THE 

SOLAE  SPECTRUM 

[American  Journal  of  Science  [3J,  XXXIII,  182-190,  1887  ;  Philosophical  Magazine 
[5],  XXIII,  257-265,  1887] 

For  several  years  past  I  have  been  engaged  in  making  a  photographic 
map  of  the  solar  spectrum  to  replace  the  ordinary  engraved  maps  and 
I  have  now  finished  the  map  from  the  extreme  ultra  violet,  wave-length 
3200,  down  to  wave-length  5790.  In  order  to  place  the  scale  correctly 
on  this  map,  I  have  found  it  necessary  to  measure  the  relative  wave- 
lengths of  the  spectrum  and  to  reduce  it  to  absolute  wave-lengths  by 
some  more  modern  determination.  I  have  not  yet  entirely  finished  the 
work,  but  as  my  map  of  the  spectrum  is  now  being  published  and  as 

O 

all  observers  so  far  seem  to  accept  the  measures  of  Angstrom,  I  have 
decided  that  a  table  of  my  results  would  be  of  value.  For  as  they  stand 
now  they  have  at  least  ten  times  the  accuracy  of  any  other  determina- 
tion. This  great  accuracy  arises  from  the  use  of  the  concave  grating 
which  reduces  the  problem  of  relative  wave-lengths  to  the  measure  of 
the  coincidences  of  the  lines  in  the  different  spectra  by  a  micrometer. 

The  instrument  which  I  have  employed  has  concave  gratings  5  or  6  in. 
diameter,  having  either  7200  or  14,400  lines  to  the  inch  and  a  radius  of 
21  ft.  6  in.  By  my  method  of  mounting,  the  spectrum  is  normal  where 
measured,  and  thus  it  is  possible  to  use  a  micrometer  with  a  range  of 
5  inches.  The  spectrum  keeps  in  focus  everywhere  and  the  constant 
of  the  micrometer  remains  unchanged  except  for  slight  variations  due 
to  imperfections  in  the  workmanship.  The  micrometer  has  no  errors 
of  run  or  period  exceeding  the  -J^TTF  inch.  The  probable  error  of  a 
single  setting  on  a  good  clear  line  is  about  ^nrVur  °^  the  wave-length. 
1"  of  arc  is  about  -0012  inch.  The  D  line  in  the  second  spectrum  is  -17 
inch  or  4-4  mm.  wide.  Determinations  of  relative  wave-length  of  good 
lines  seldom  differ  1  in  500,000  from  each  other  and  never  exceed  1  in 
100,000,  even  with  different  gratings.  This  is,  of  course,  for  the  prin- 
cipal standard  lines,  and  the  chance  of  error  is  greater  at  the  extremities 
of  the  spectrum.  The  interpolation  of  lines  was  made  by  running  the 
micrometer  over  the  whole  spectrum,  5  inches  at  a  time,  and  adding  the 


KELATIVE  WAVE-LENGTH  OF  LINES  OF  SOLAS  SPECTEUM       513 

readings  together  so  as  to  include  any  distance,  even  the  whole  spec- 
trum. The  wave-length  is  calculated  for  a  fixed  micrometer  constant 
and  then  corrected  so  as  to  coincide  everywhere  very  nearly  with  the 
standards.  I  suppose  the  probable  error  of  the  relative  determinations 
with  the  weight  1  in  my  table  to  be  not  far  from  1  in  500,000.  Ang- 
strom thinks  his  standard  lines  have  an  accuracy  of  about  1  in  50,000 
and  ordinary  lines  much  less. 

As  to  the  absolute  measure,  it  is  now  well  determined  that  Angstrom's 
figures  are  too  small  by  about  1  part  in  6000.  This  rests:  1st,  on  the 
determination  of  Peirce  made  for  the  U.  S.  Coast  Survey  with  Ruther- 
furd's  gratings  and  not  yet  completely  published;  2d,  on  an  error  made 
by  Tresca  in  the  length  of  the  standard  metre  used  by  Angstrom 1  which 
increases  his  value  by  about  1  in  7700;  3d,  on  a  result  obtained  in  my 
laboratory  with  two  of  my  gratings  by  Mr.  Bell,  which  is  published  with 
this  paper.  Mr.  C.  S.  Peirce  has  kindly  placed  his  grating  at  our  dis- 
posal and  we  have  detected  an  error  of  ruling  which  affects  his  result 
and  makes  it  nearly  coincide  with  our  own.  The  wave-length  of  the 
mean  of  the  two  E  lines  is 

Angstrom  (atlas)  5269-12   ±  -5 

Angstrom  (Corrected  by  Thalen)  5269-80  l 

Peirce     5270-16 

Peirce  (Corrected  by  Rowland  and  Bell) 5270-00 * 

Bell     5270-04 

These  results  are  for  air  at  ordinary  pressures  and  temperatures.  The 
last  is  reduced  to  20°  C.  and  760  mm.  pressure.  To  reduce  to  a  vacuum 
multiply  by  the  following : 

Fraunhofer  line  A  C  E  G  H 

Correction   factor.  .1-000291    1-000292    1-000294    1-000297    1-000298 

o 

The  relation  between  my  wave-lengths  and  those  of  Angstrom  are 

O 

given  by  the  following,   Angstrom's  value  being  from  p.   31   of  his 

memoir: 

A  (edge)          B  (edge)  C 

Angstrom    7597-5       6867-10     6717-16     6562-10     6264-31 

Rowland  .  .   7593-97     6867-38     6717-83     6562-96     6265-27 


Difference    —3-5  -28  -67  -86  -96 

1  Thal6n,   Sur   Spectre   du    Fer,    Societe  Royale  des  Sciences  d'Upsal,  September, 
1884,  p.  25.  2From  one  grating  only. 


514  HENRY  A.  ROWLAND 

0  Da                   A  Peirce's  line 

Angstrom    5895-13     5889-12     5708-45  5623-36     5454-84 

Eowland  .   5896-08     5890-12     5709-56  5624-70     5455-68 


Difference -95  1-00  1-11  1-34  -84 

0                                                              E  E  bi  F 

Angstrom    5269-59  5268-67  5183-10  5138-78  4860-74 

Rowland    ,                    .   5270-43  5269-65  5183-73  5139-47  4861-43 


Difference   -84  -98  -63  -69  -69 

o  ° 

Angstrom    4702-44  4307-25 

Rowland    ,  .  4703-11  4307-96 


Difference  -67  -71      * 

The  greatest  variation  in  these  differences  is  evidently  due  to  the 
poor  definition  of  Angstrom's  grating  by  which  the  numbers  refer  to 
groups  of  lines  rather  than  to  single  ones.  Selecting  the  best  figures, 
we  find  that  Angstrom's  wave-lengths  must  be  multiplied  by  1-00016  to 
agree  with  Bell,  while  the  correction  for  Angstrom's  error  of  scale 
would  be  1-000110. 

It  is  impossible  for  me  to  give  at  present  all  the  data  on  which  my 
determinations  rest,  but  I  have  given  in  Table  I  many  of  the  coinci- 
dences as  observed  with  several  gratings,  the  number  of  single  readings 
being  given  in  the  parenthesis  over  each  set. 

Table  II  gives  the  wave-lengths  as  interpolated  by  the  micrometer. 
It  is  scarcely  possible  that  any  error  will  be  found  (except  accidental 
errors)  of  more  than  -02,  and  from  the  agreement  of  the  observations 
I  scarcely  expect  to  make  any  changes  in  the  final  table  of  more  than 
•01,  except  in  the  extremities  of  the  spectrum,  where  it  may  amount 
to  -03  in  the  region  of  A  and  H  lines.  The  wave-lengths  of  weight 
greater  than  1  will  probably  be  found  more  exact  than  this.  The  lines 
can  be  identified  on  my  new  photograph  of  the  spectrum  down  to  5790. 
Below  this  there  is  little  trouble  in  finding  the  right  ones.  All  maps 
of  the  spectrum,  especially  above  F,  are  so  imperfect  that  it  is  almost 
impossible  to  identify  my  lines  upon  them.  The  lines  can  only  be  prop- 
erly identified  by  a  power  sufficient  to  clearly  divide  &3  and  &4.  Some  of 
them  are  double  and  most  of  these  have  been  marked,  but  as  the  table 
has  been  made  for  my  own  use,  I  have  not  been  very  careful  to  examine 
each  line.  This  will,  however,  be  finally  done.  Micrometric  measures 


KELATIVE  WAVE-LENGTH  OF  LINES  OF  SOLAK  SPECTRUM      515 

have  now  been  made  of  nearly  all  the  lines  below  &  with  a  view  of  mak- 
ing a  map  of  this  region. 

Table  I  gives  the  coincidences  of  the  different  orders  of  the  spectra 
as  observed  with  several  concave  gratings  on  both  sides  of  the  normal, 
the  numbers  in  the  brackets  indicating  the  number  of  observations.  The 
observations  have  been  reduced  as  nearly  as  possible  to  what  I  consider 
the  true  wave-length,  the  small  difference  from  the  numbers  given  in 
Table  II  being  the  variation  of  the  observations  from  the  mean  value. 
The  true  way  of  reducing  these  observations  would  be  to  form  a  linear 
equation  for  each  series  and  reduce  by  the  method  of  least  squares.  A 
simpler  way  was,  however,  used  and  the  relative  wave-length  of  the 
standard  lines,  marked  S  in  Table  II,  was  obtained;  however,  some 
other  observations  were  also  included. 

Table  II  gives  the  wave-lengths  reduced  to  Bell's  value  for  the  abso- 
lute wave-length  of  the  D  line.  These  were  obtained  by  micrometric 
measurement  from  the  standards  as  described  before.  The  weights 
are  given  in  the  first  column  and  some  of  the  lines,  which  were  meas- 
ured double,  have  also  been  marked.  But  the  series  has  not  yet  been 
carefully  examined  for  doubles. 

The  method  is  so  much  more  accurate  than  by  means  of  angular 
measurement  that  the  latter  has  little  or  no  weight  in  comparison. 

This  table  is  to  be  used  in  connection  with  my  photographic  map  of 
the  normal  spectrum  to  determine  the  error  of  the  latter  at  any  point. 
The  map  was  made  by  placing  the  photograph  in  contact  with  the  scale, 
which  was  the  same  for  each  order  of  spectrum,  and  enlarging  the  two 
together.  In  this  way  the  map  has  no  local  irregularities,  although  the 
scale  may  be  displaced  slightly  from  its  true  position,  and  may  be  a  little 
too  long  or  short,  although  as  far  as  I  have  tested  it,  it  seems  to  have 
very  little  error  of  the  latter  sort.  The  scale  was  meant  in  all  cases, 
except  the  ultra  violet,  to  apply  to  Peirce's  absolute  value  and  so  the 
correction  is  generally  negative,  as  follows : 

Approximate  correction  to  the  photographic  map  of  the  normal  spectrum  to 
reduce  to  latest  absolute  value. 

Strip  3200  to  3330 Correction —-05 

"     3275  to  3530 "         —-05 

"     3475  to  3730 "         —-02 

"     3675  to  3930 <*          —-10 

"     3875  to  4130 "         —-16 

"     4075  to  4330..  "  ...—-04 


516  HENRY  A.  KOWLAND 

Strip  4275  to  4530 Correction —  -08 

"  4480  to  4735  «         —-10 

"  4685  to  4940 "         —-18 

"  4875  to  5130 " —-14 

"  5075  to  5330 „ "          —-15 

"  5215  to  5595  "         about —-05 

"  5415  to  5795 "         about —-04 

"  3710  to  3910  "         —-20 

"  3810  to  4000 "         —-14 

It  is  to  be  noted  that  the  third  spectrum  of  the  map  runs  into  the 
second,  so  that  it  must  not  be  used  beyond  wave-length  3200,  as  it  is 
mixed  with  the  second  in  that  region. 

[The  tables  are  omitted.] 


41 
TABLE   OF   STANDAKD   WAVE-LENGTHS 

[Johns  Hopkins  University  Circulars,  No.  73,  p.  69,  1889 ;  Philosophical  Magazine  [5], 

XXVII,  479-484,  1889] 

In  the  '  American  Journal  of  Science '  for  March,  1887,  and  the  '  Lon- 
don, Dublin  and  Edinburgh  Philosophical  Magazine '  for  the  same 
month,  I  have  published  a  preliminary  list  of  standards  as  far  as  could 
be  observed  with  the  eye,  with  a  few  imperfectly  observed  by  photog- 
raphy, the  whole  being  reduced  to  Bell's  and  Peirce's  values  for  absolute 
wave-lengths.  Mr.  Bell  has  continued  his  measurements  and  found  a 
slightly  greater  value  for  the  absolute  wave-length  of  the  D  line,  and  I 
have  reduced  my  standards  to  the  new  values. 

Nearly  the  whole  list  has  been  gone  over  again,  especially  at  the  ends 
around  the  A  line  and  in  the  ultra  violet.  The  wave-lengths  of  the  ultra 
violet  were  obtained  by  photographing  the  coincidence  with  the  lower 
wave-lengths,  a  method  which  gives  them  nearly  equal  weight  with 
those  of  the  visible  spectrum. 

The  full  set  of  observations  will  be  published  hereafter,  but  the  pres- 
ent series  of  standards  can  be  relied  on  for  relative  wave-lengths  to  -02 
division  of  Angstrom  in  most  cases,  though  it  is  possible  some  of  them 
may  be  out  more  than  this  amount,  especially  in  the  extreme  red. 

As  to  the  absolute  wave-length,  no  further  change  will  be  necessary, 
provided  spectroscopists  can  agree  to  use  that  of  my  table,  as  has  been 
done  by  many  of  them. 

By  the  method  of  coincidences  with  the  concave  grating  the  wave- 
lengths have  been  interwoven  with  each  other  throughout  the  whole 
table  so  that  no  single  figure  could  be  changed  without  affecting  many 
others  in  entirely  different  portions  of  the  spectrum.  The  principal  dif- 
ference from  the  preliminary  table  is  in  the  reduction  to  the  new  abso- 
lute wave-length  by  which  the  wave-lengths  are  about  1  in  80,000  larger 
than  the  preliminary  table.  I  hope  this  difference  will  not  be  felt  by 
those  who  have  used  the  old  table  because  measurements  to  less  than  A- 

o 

division  of  Angstrom  are  rare,  the  position  of  the  lines  of  many  metals 
being  unknown  to  a  whole  division  of  Angstrom.  As  the  new  map  of 
the  spectrum  has  been  made  according  to  this  new  table,  I  see  no  further 
reason  for  changing  the  table  in  the  future. 


518  HENRY  A.  ROWLAND 

No  attempt  has  been  made  to  reduce  the  figures  to  a  vacuum  as  the 
index  of  refraction  of  air  is  imperfectly  known,  but  this  should  be  done 
where  numerical  relations  of  time  period  are  desired. 

In  the  column  giving  the  weight,  the  primary  standards  are  marked 
8  and  the  other  numbers  give  the  number  of  separate  determination  of 
the  wave-length  and  thus,  to  some  extent,  the  weight. 

Many  of  these  standards  are  double  lines  and  some  of  them  have 
faint  components  near  them,  which  makes  the  accuracy  of  setting 
smaller.  This  is  specially  the  case  when  this  component  is  an 
atmospheric  line  whose  intensity  changes  with  the  altitude  of  the  sun. 
The  principal  doubles  are  marked  with  d,  but  the  examination  has  not 
been  completed  yet,  especially  at  the  red  end  of  the  spectrum. 

[A  table  of  the  standard  wave-lengths  is  given  on  p.  78  J.  H.  U.  Circ., 
but  is  omitted  in  this  volume.] 


42 

A  FEW  NOTES  ON  THE  USE  OF  GKATINGS 

[Johns  Hopkins  University  Circulars,  No.  73,  pp.  73,  74,  1889] 

The  ghosts  are  very  weak  in  most  of  my  gratings.  They  are  scarcely 
visible  in  the  lower  orders  of  spectra,  hut  increase  in  intensity  as  com- 
pared with  the  principal  line  as  the  square  of  the  order  of  the  spectrum. 
Hence,  to  avoid  them,  obtain  magnification  by  increasing  the  focal  dis- 
tances instead  of  going  to  the  higher  orders.  The  distances  from  the 
principal  line  in  my  gratings  are  the  same  as  the  distances  of  the  spectra 
from  the  image  of  the  slit  when  using  a  grating  of  20  lines  to  the  inch. 
They  are  always  symmetrical  on  the  two  sides,  and  about  -^  inch  for 
the  violet  and  £  inch  for  the  red  in  a  grating  of  21  ft.  6  in.  radius  in  all 
orders  of  spectra.  When  the  given  line  has  the  proper  exposure  on  the 
photographic  plate,  the  ghosts  will  not  show,  but  over-exposure  brings 
them  out  faintly  in  the  third  spectrum  of  a  20,000  grating  or  the  6th  of 
a  10,000  one.  They  never  cause  any  trouble,  as  they  are  easily  recog- 
nized and  never  appear  in  the  solar  spectrum.  In  some  cases  the  higher 
orders  of  ghosts  are  quite  as  apparent  as  those  of  the  first  order. 

The  gratings  with  10,000  lines  to  the  inch  often  have  better  definition 
than  those  of  20,000,  as  they  take  half  the  time  to  rule,  and  they  are 
quite  as  good  for  eye  observation.  They  can  also  be  used  for  photo- 
graphing the  spectrum  by  absorbing  the  overlying  spectra,  but  there 
are  very  few  materials  which  let  through  the  ultra  violet  and  absorb  the 
longer  wave-lengths.  The  10,000  gratings  have  the  advantage,  how- 
ever, in  the  measurement  of  wave-lengths  by  the  overlapping  spectra, 
although  this  method  is  unnecessary  since  the  completion  of  my  map  of 
the  spectrum.  By  far  the  best  is  to  use  a  20,000  grating  and  observe 
down  to  the  D  line  by  photography,  using  erythrosin  plates  from  the  F 
line  down  to  D.  Below  D,  cyanine  plates  can  be  used,  although  the  time 
of  exposure  is  from  10  to  60  minutes  with  a  narrow  slit.  The  solar 
spectrum  extends  to  wave-lengths  3000,  and  the  map  has  been  contin- 
ued to  this  point.  Beyond  this,  the  coincidence  with  the  solar  spectrum 
cannot  be  used,  but  those  of  the  1st  and  2d  or  2d  and  3d  spectra  can  be. 

Some  complaints  have  been  made  to  me  that  one  of  my  gratings  has 
no  spectrum  beyond  3400.  even  of  the  electric  arc.  I  have  never  found 
this  the  case,  as  the  one  I  use  gives  w.  1.  2200,  readily  with  30  minutes 
exposure  on  slow  plates,  requiring  5  minutes  for  the  most  sensitive 


520  HENRY  A.  KOWLAND 

part  and  using  the  electric  arc.  With  sensitive  plates,  the  time  can  be 
diminished  to  one-fifth  of  this. 

For  eye  observations,  a  very  low  power  eye-piece  of  1  or  2  in.  focus 
is  best.  This,  with  a  focus  of  21  ft.  6  in.  is  equivalent  to  a  plane  grat- 
ing with  a  telescope  of  a  power  of  100  or  200. 

In  measuring  the  spectra,  an  ordinary  dividing  engine  with  errors 
not  greater  than  10*00  inch  can  be  used,  going  over  the  measurements 
twice  with  the  plate  reversed  between  the  separate  series.  The  plates 
are  on  so  very  large  a  scale  that  the  microscope  must  have  a  very  low 
power.  The  one  I  use  has  a  1  inch  objective  and  a  2  inch  eye-piece. 
The  measured  part  of  the  plate  is  about  a  foot  long,  the  plates  being 
19  in.  long. 

All  the  spectrum  photographs  taken  at  different  times  coincide  per- 
fectly, and  this  can  be  used  for  such  problems  as  the  determination  of 
the  atmospheric  lines.  For  this  purpose,  negatives  at  high  and  low 
sun  are  compared  by  scraping  the  emulsion  off  from  half  the  plates  and 
clamping  them  together  with  the  edges  of  the  spectra  in  coincidence. 
The  two  spectra  coincide  exactly  line  for  line  except  where  the  atmo- 
spheric lines  occur. 

This  method  is  specially  valuable  for  picking  out  impurities  in  metal- 
lic spectra,  using  some  standard  impurity  in  all  the  substances  to  give 
a  set  of  fiducial  lines;  or  better,  obtaining  the  coincidence  of  all  the 
metals  with  some  one  metal,  such  as  iron.  Making  the  iron  spectrum 
coincide  on  the  two  plates,  the  other  spectra  can  be  compared.  This  is 
specially  possible  because  the  focus  of  a  properly  set  up  concave  grating 
need  not  be  altered  in  years  of  use,  for,  when  necessary,  it  can  be  ad- 
justed at  the  slit,  keeping  the  distance  of  the  grating  from  the  slit  con- 
stant. 

The  spectrum  of  the  carbon  poles  is  generally  too  complicated  for 
use  with  anything  except  the  more  pronounced  lines  of  metals,  there 
being,  at  a  rough  guess,  10,000  lines  in  its  spectrum.  However,  in  pho- 
tographing metallic  spectra  but  few  of  these  show  on  the  plate,  as  they 
are  mostly  faint.  The  spark  discharge  gives  very  nebulous  lines  for 
the  metals. 

Most  gratings  are  ruled  bright  in  the  higher  orders,  but  this  is  more 
or  less  difficult,  as  most  diamond  points  give  the  first  spectrum  the 
brightest.  Indeed,  it  is  very  easy  to  obtain  ruling  which  is  immensely 
bright  in  the  first  spectrum.  Such  gratings  might  be  used  for  gaseous 
spectra.  Short  focus  gratings  of  5  ft.  radius  of  curvature,  very  bright 
in  the  first  order,  require  only  a  fraction  of  a  second  exposure  for  the 
solar  spectrum  and  the  spectrum  of  a  gas  can  be  obtained  in  less  than 
an  hour. 


46 
KEPOET  OF  PROGRESS  IN  SPECTKUM  WORK 

[Johns  Hopkins  University  Circulars,  No.  85,  pp.  41,  42,  1891 ;  American  Journal  of 
Science  [3],  XLI,  243,  244,  1891 ;    The  Chemical  News,  LXIII,  133,  1891] 

During  the  past  year  or  two  a  great  deal  of  work  has  been  done  in 
the  photography  of  the  spectra  of  elements  and  the  identification  of  the 
lines  in  the  solar  spectrum,  which  it  will  take  a  long  time  to  work  up, 
ready  for  publication.  Hence,  I  have  thought  that  a  short  account  of 
what  has  been  done  up  to  the  present  time  might  be  of  interest  to  work- 
ers in  the  subject.  In  the  prosecution  of  the  work  financial  assistance 
has  been  received  from  the  Rumford  Fund  of  the  American  Academy  of 
Arts  and  Sciences,  as  well  as  from  the  fund  given  by  Miss  Bruce  to  the 
Harvard  Astronomical  Observatory  for  the  promotion  of  research  in 
astronomical  physics,  and  the  advanced  state  of  the  work  is  due  to  such 
assistance. 

The  work  may  be  summed  up  under  the  following  heads : 

1st.  The  spectra  of  all  known  elements,  with  the  exception  of  a  few 
gaseous  ones,  or  those  too  rare  to  be  yet  obtained,  have  been  photo- 
graphed in  connection  with  the  solar  spectrum,  from  the  extreme  ultra 
violet  down  to  the  D  line,  and  eye  observations  have  been  made  on  many 
to  the  limit  of  the  solar  spectrum. 

2d.  A  measuring  engine  has  been  constructed  with  a  screw  to  fit  the 
above  photographs,  which,  being  taken  with  the  concave  grating,  are  all 
normal  spectra  and  to  the  same  scale.  This  engine  measures  wave- 
1-engtlis  direct,  so  that  no  multiplication  is  necessary,  but  only  a  slight 
correction  to  get  figures  correct  to  y^g-  of  a  division  of  Angstrom. 

3d.  A  table  of  standard  wave-lengths  of  the  impurities  in  the  car- 
bons, extending  to  wave-length  2000,  has  been  constructed  to  measure 
wave-lengths  beyond  the  limits  of  the  solar  spectrum. 

4th.  Maps  of  the  spectra  of  some  of  the  elements  have  been  drawn 
on  a  large  scale  ready  for  publication. 

5th.  The  greater  part  of  the  lines  in  the  map  of  the  solar  spectrum 
have  been  identified  and  the  substance  producing  them  noted. 

6th.  The  following  rough  table  of  the  solar  elements  has  been  con- 
structed entirely  according  to  my  own  observations,  although,  of  course, 
most  of  them  have  been  given  by  others. 


522 


HENEY  A.  ROWLAND 


I  do  not  know  which  are  the  new  ones,  but  call  attention  to  Silicon, 
Vanadium,  Scandium,  Yttrium,  Zirconium,  Glucinum,  Germanium  and 
Erbium,  as  being  possibly  new. 

Silicon  has  lines  on  my  map  at  wave-lengths  3905-7,  4103-1,  5708-7, 
5772-3  and  5948-7.  That  at  3905-7  is  the  largest  and  most  certain. 
That  at  4103-1  is  also  claimed  by  Manganese. 

ELEMENTS  IN  THE  SUN,  ARRANGED  ACCORDING  TO  THE  INTENSITY 
AND  THE  NUMBER  OF  LINES  IN  THE  SOLAR  SPECTRUM. 


ACCOBDING  TO  INTENSITY. 

Calcium. 

Iron. 

Hydrogen. 

Sodium. 

Nickel. 

Magnesium. 

Cobalt. 

Silicon. 

Aluminium. 

Titanium. 

Chromium. 

Manganese. 

Strontium. 

Vanadium. 

Barium. 

Carbon. 

Scandium. 

Yttrium. 

Zirconium. 

Molybdenum. 

Lanthanum. 

Niobium. 

Palladium. 

Neodymium. 

Copper. 

Zinc. 

Cadmium. 

Cerium. 

Glucinum. 

Germanium. 


ACCORDING    TO    NUMBER. 

Iron  (2000   or  more). 

Nickel. 

Titanium. 

Manganese. 

Chromium. 

Cobalt. 

Carbon  (200  or  more). 

Vanadium. 

Zirconium. 

Cerium. 

Calcium  (75  or  more). 

Scandium. 

Neodymium. 

Lanthanum. 

Yttrium. 

Niobium. 

Molybdenum. 

Palladium. 

Magnesium  (20  or  more). 

Sodium  (11). 

Silicon. 

Strontium. 

Barium. 

Aluminium  (4). 

Cadmium. 

Rhodium. 

Erbium. 

Zinc. 

Copper  (2). 

Silver  (2). 


REPORT  OF  PROGRESS  IN  SPECTRUM  WORK  523 

ACCORDING   TO   INTENSITY.  ACCORDING   TO    NUMBER. 

Rhodium.  Glucinum  (2). 

Silver.  Germanium. 

Tin.  Tin. 

Lead.  Lead  (1). 

Erbium.  Potassium  (1). 
Potassium. 


DOUBTFUL  ELEMENTS. 

Iridium.  Ruthenium.  Tungsten. 

Osmium.  Tantalum.  Uranium. 

Platinum.  Thorium. 

NOT  IN  SOLAR  SPECTRUM. 

Antimony.  Caesium.  Rubidium. 

Arsenic.  Gold.  Selenium. 

Bismuth.  Indium.  Sulphur. 

Boron.  Mercury.  Thallium. 

Nitrogen  (vacuum  tube).  Phosphorus.  Praeseodymium. 

SUBSTANCES  NOT  YET  TRIED. 

Bromine.  Oxygen.  Holmium. 

Chlorine.  Tellurium.  Thulium. 

Iodine.  Gallium.  Terbium,  etc. 
Fluorine. 

These  tables  are  to  be  accepted  as  preliminary  only,  especially  the 
order  in  the  first  portion.  However,  being  made  with  such  a  powerful 
instrument,  and  with  such  care  in  the  determination  of  impurities,  they 
must  still  have  a  weight  superior  to  most  others  published. 

The  substances  under  the  head  of  "Not  in  Solar  Spectrum"  are 
often  placed  there  because  the  elements  have  few  strong  lines  or  none 
at  all  in  the  limit  of  the  solar  spectrum  when  the  arc  spectrum,  which 
I  have  used,  is  employed.  Thus  boron  has  only  two  strong  lines  at  2497. 
Again,  the  lines  of  bismuth  are  all  compound  and  so  too  diffuse  to  ap- 
pear in  the  solar  spectrum.  Indeed,  some  good  reason  generally  ap- 
pears for  their  absence  from  the  solar  spectrum.  Of  course,  this  is 
little  evidence  of  their  absence  from  the  sun  itself. 

Indeed,  were  the  whole  earth  heated  to  the  temperature  of  the  sun, 
its  spectrum  would  probably  resemble  that  of  the  sun  very  closely. 


524  HENRY  A.  ROWLAND 

With  the  high  dispersion  here  used  the  "basic  lines"  of  Lockyer  are 
widely  broken  up  and  cease  to  exist.  Indeed,  it  would  be  difficult  to 
prove  anything  except  accidental  coincidences  among  the  lines  of  the 
different  elements.  Accurate  investigation  generally  reveals  some  slight 
difference  of  wave-length  or  a  common  impurity. 

Furthermore,  the  strength  of  the  lines  in  the  solar  spectrum  is  gen- 
erally very  nearly  the  same  as  that  in  the  electric  arc,  with  only  a  few 
exceptions,  as  for  instance  calcium.  The  cases  mentioned  by  Lockyer 
are  generally  those  where  he  mistakes  groups  of  lines  for  single  lines 
or  even  mistakes  the  character  of  the  line  entirely.  Altogether  there 
seems  to  be  very  little  evidence  of  the  breaking  up  of  the  elements  in 
the  sun  as  far  as  my  experiments  go. 

Even  after  comparing  the  solar  spectrum  with  all  known  elements, 
there  are  still  many  important  lines  not  accounted  for.  Some  of  these 
I  have  accounted  for  by  silicon  and  there  are  probably  many  more.  Of 
all  known  substances  this  is  the  most  difficult  to  bring  out  the  lines  in 
the  visible  spectrum  although  it  has  a  fine  ultra-violet  one.  Possibly 
iron  may  account  for  many  more,  and  all  the  elements  at  a  higher  tem- 
perature might  develope  more.  Then,  again,  very  rare  elements  like 
scandium,  vanadium,  etc.,  when  they  have  a  strong  spectrum,  may  cause 
strong  solar  lines  and  thus  we  may  look  for  new  and  even  rare  elements 
to  account  for  very  many  more.  Indeed,  I  find  many  lines  accounted 
for  by  the  rare  elements  in  gadolinite,  samarskite  and  fergusonite  other 
than  yttrium,  erbium,  scandium,  praeseodymium,  neodymium,  lantha- 
num and  cerium,  which  I  cannot  identify  yet  and  which  may  be  without 
a  name.  For  this  reason,  and  to  discover  rare  elements,  I  intend  finally 
to  try  unknown  minerals,  as  my  process  gives  me  an  easy  method  of 
detecting  any  new  substance  or  analyzing  minerals  however  many  ele- 
ments they  may  contain. 

The  research  is  much  indebted  to  the  faithful  and  careful  work  of 
Mr.  L.  E.  Jewell  who  has  acted  as  my  assistant  for  several  years. 
Preliminary  publications  of  results  will  be  made  in  the  '  University 
Circulars.' 

Among  the  lastest  results  I  may  mention  the  spectroscopic  separation 
of  yttrium  into  three  components,  and  the  actual  separation  into  two. 


49 
GRATINGS  IN  THEORY  AND  PRACTICE  l 

[Philosophical  Magazine  [5],  XXXV,  397-419,  1893  ;  Astronomy  and  Astro  -Physics, 

XII,  129-149,  1893] 

PART  I1 

It  is  not  my  object  to  treat  the  theory  of  diffraction  in  general  but 
only  to  apply  the  simplest  ordinary  theory  to  gratings  made  by  ruling 
grooves  with  a  diamond  on  glass  or  metal.  This  study  I  at  first  made 
with  a  view  of  guiding  me  in  the  construction  of  the  dividing  engine 
for  the  manufacture  of  gratings,  and  I  have  given  the  present  theory 
for  years  in  my  lectures.  As  the  subject  is  not  generally  understood 
in  all  its  bearings  I  have  written  it  for  publication. 

Let  p  be  the  virtual  distance  reduced  to  vacuo  through  which  a  ray 
moves.  Then  the  effect  at  any  point  will  be  found  by  the  summation 
of  the  quantity 

A  C08&O—  Vt)  +  Bsinb(p  —  V£)  , 


o 
in  which  &  =  ~,  I  being  the  wave-length.     V  is  the  velocity  reduced  to 

L 

vacuo,  and  t  is  the  time.     Making  6  =  tan"1  -  -  we  can  write  this 


sin  [0  +  b  (  p  — 

The  energy  or  intensity  is  proportional  to  (A2  -f-  B2). 
Taking  the  expression 

(A  +iB)g~  »<!•-"), 

when  i  =  V  —  1,  its  real  part  will  be  the  previous  expression  for  the 
displacement.  Should  we  use  the  exponential  expression  instead  of  the 
circular  function  in  our  summation  we  see  that  we  can  always  obtain 

1  I  am  much  indebted  to  Dr.  Ames  for  looking  over  the  proofs  of  this  paper  and 
correcting  some  errors.  In  the  paper  I  have,  in  order  to  make  it  complete,  given 
some  results  obtained  previously  by  others,  especially  by  Lord  Rayleigh.  The  treat- 
ment is,  however,  new,  as  well  as  many  of  the  results.  My  object  was  originally  to 
obtain  some  guide  to  the  effect  of  errors  in  gratings  so  that  in  constructing  my 
dividing  engine  I  might  prevent  their  appearance  if  possible. 

5  [Part  II  was  never  written.] 


526  HENRY  A.  ROWLAND 

the  intensity  of  the  light  by  multiplying  the  final  result  by  itself  with 
—  i  in  place  of  -f-  i,  because  we  have 

(A  +  iB}  e~  ib  (p  ~  rt)  x(A  —  iff)  e'b  (f  ~  rt]  =  A*  +  &, 

In  cases  where  a  ray  of  light  falls  on  a  surface  where  it  is  broken 
up,  it  is  not  necessary  to  take  account  of  the  change  of  phase  at  the 
surface  but  only  to  sum  up  the  displacement  as  given  above. 

In  all  our  problems  let  the  grating  be  rather  small  compared  with 
the  distance  of  the  screen  receiving  the  light  so  that  the  displacements 
need  not  be  divided  into  their  components  before  summation. 

Let  the  point  x'  ,  y',  z'  be  the  source  of  light,  and  at  the  point  x,  y,  z 
let  it  be  broken  up  and  at  the  same  time  pass  from  a  medium  of  index 
of  refraction  I'  to  one  of  /.  Consider  the  disturbance  at  a  point  x",  y"  , 
z"  in  the  new  medium.  It  will  be 


where 

S  =  x"*  +  y'n  +  zm  +  a?  +  f  +  z*  -  2  (xx"  +  yy"  +  zz")  , 
p2  =  a/2  +  y'*  +  z'*  +  x*  +  f  +  z*  —  2  (xx'  +  yy'  +  zz')  . 

Let  the  point  x,  y,  z  be  near  the  origin  of  co-ordinates  as  compared 
with  x',  y',  z'  or  x"  ',  y"  ,  z"  and  let  a,  /?,  f  and  a!,  fl,  f  be  the  direction 
cosines  of  p  and  p.  Then,  writing 

R  =  I'  V  of*  +  y"  +  z'2  +  /Vz"2  +  ym  +  z"*, 

/I    =  la  +  I'a', 
p.   =  7/3  +  /'/?, 


we  have,  for  the  elementary  displacement, 

g—  ib  [  R  —  Vt  —  AZ  -  ny  —  vz  +  /trj] 


1 
n] 


where  _  ,  [~  _  P_  _       _  / 

L  V  z"  +  y"  +  z'z  +  V  x"'  +  y"3  +  z' 
and  r2  =  z2  +  y*  +  z\ 

This  equation  applies  to  light  in  any  direction.  In  the  special  case 
of  parallel  light,  for  which  *  =  0,  falling  on  a  plane  grating  with  lines 
in  the  direction  of  z,  one  condition  will  be  that  this  expression  must  be 
the  same  for  all  values  of  z. 

Hence  v  =  0  . 

If  N  is  the  order  of  the  spectrum  and  a  the  grating  space  we  shall 
see  further  on  that  we  also  have  the  condition 


GRATINGS  IN  THEORY  AND  PRACTICE  527 

The  direction  of  the  diffracted  light  will  then  be  defined  by  the 
equations 

«'2  +  p*  +  r*  =0, 


whence 


Fff^J-Jf-If, 

a 


In  the  ordinary  case  where  the  incident  and  diffracted  rays  are  per- 
pendicular to  the  lines  of  the  grating,  we  can  simplify  the  equations 
somewhat. 

Let  <p  be  the  angle  of  incidence  and  (p  of  diffraction  as  measured  from 
the  positive  direction  of  X. 

A  =  /'  cos  <f  +  I  cos  <p  , 

—  N  =  fi  =  /'  sin  y  +  /  sin  </>  , 
a 


where  I  is  the  wave-length  in  vacuo. 
In  case  of  the  reflecting  grating  1  =  1'  and  we  can  write 
A  =  I\coa<p  +  cos  <^}, 

—  N=.  ii  =  I\  sin  a>  +  sin  <p\. 
a 

This  is  only  a  very  elementary  expression  as  the  real  value  would 
depend  on  the  nature  of  the  obstacle,  the  angles,  etc.,  but  it  will  be  suffi- 
cient for  our  purpose. 

The  disturbance  due  to  any  grating  or  similar  body  will  then  be  very 
nearly 

(*  re—ib[R-  Vt  —  to-ny-vz  +  KW  +  y'  +  tfrtclg^ 
where  ds  is  a  differential  of  the  surface.     For  parallel  rays,  K  =  0. 

PLANE  GRATINGS 

In  this  case  the  integration  can  often  be  neglected  in  the  direction 
of  z  and  we  can  write  for  the  disturbance  in  case  of  parallel  rays, 

a—ib(R—  Vt)   I      I  (,—  il>[—  AX  —  ny]  /7« 
J  J 


528  HENRY  A.  ROWLAND 

CASE  I.  —  SIMPLE  PERIODIC  RULING 

Let  the  surface  be  divided  up  into  equal  parts  in  each  of  which  one 
or  more  lines  or  grooves  are  ruled  parallel  to  the  axis  of  z. 

The  integration  over  the  surface  will  then  resolve  itself  into  an 
integration  over  one  space  and  a  summation  with  respect  to  the  num- 
ber of  spaces.  For  in  this  case  we  can  replace  y  by  na  -\-  y  where  a  is 
the  width  of  a  space  and  the  displacement  becomes 

g-il)(R-Vt)   ve  +  ibnan   I      I  e+ib  (Ax  +  Ml/)  ds  , 

but  •        ~bnit. 


n-i  -         smw 


v  0+ibpan  — 


sin   ba;i 
Bin   -- 


Multiplying  the  disturbance  by  itself  with  —  i  in  place  of  -j-  i  we  have 
for  the  light  intensity 


I     C  e-n  l*x  +  «/>  ds  \     I    /(.+ ib  <Ax  +  *v)  ds\ 


sm    - 
The  first  term  indicates  spectral  lines  in  positions  given  by  the  equation 


with  intensities  given  by  the  last  integral.  The  intensity  of  the  spec- 
tral lines  then  depends  on  the  form  of  the  groove  as  given  by  the  equa- 
tion x  =  f(y)  and  upon  the  angles  of  incidence  and  diffraction.  The 
first  factor  has  been  often  discussed  and  it  is  only  necessary  to  call 
attention  to  a  few  of  its  properties. 

When  bafjt*=%7rN,  N  being  any  whole  number,  the  expression  be- 
comes n2.  On  either  side  of  this  value  the  intensity  decreases  until 
ribdfj! '=2xN,  wheniit  becomes  0. 

The  spectral  line  then  has  a  width  represented  by//  —  /M"=T 2^ nearly; 
on  either  side  of  this  line  smaller  maxima  exist  too  faintly  to  be  ob- 
served. When  two  spectral  lines  are  nearer  together  than  half  their 
width,  they  blend  and  form  one  line.  The  defining  power  of  the  spec- 
troscope can  be  expressed  in  terms  of  the  quotient  of  the  wave-length 
by  the  difference  of  wave-length  of  two  lines  that  can  just  be  seen  as 
divided.  The  defining  power  is,  then, 


3  An  expression  of  Lord  Rayleigh's. 


GRATINGS  ix  THEORY  AND  PRACTICE  529 

Now  na  is  the  width  of  the  grating.  Hence,  using  a  grating  at  a 
given  angle,  the  defining  power  is  independent  of  the  number  of  lines 
to  the  inch  and  only  depends  on  the  width  of  the  grating  and  the  wave- 
length. According  to  this,  the  only  object  of  ruling  many  lines  to  the 
inch  in  a  grating  is  to  separate  the  spectra  so  that,  with  a  given  angle, 
the  order  of  spectrum  shall  be  less. 

Practically  the  gratings  with  few  lines  to  the  inch  are  much  better 
than  those  with  many,  and  hence  have  better  definition  at  a  given 
angle  than  the  latter  except  that  the  spectra  are  more  mixed  up  and 
more  difficult  to  see. 

It  is  also  to  be  observed  that  the  defining  power  increases  with  shorter 
wave-lengths,  so  that  it  is  three  times  as  great  in  the  ultra  violet  as 
in  the  red  of  the  spectrum.  This  is  of  course  the  same  with  all  optical 
instruments  such  as  telescopes  and  microscopes. 

The  second  term  which  determines  the  strength  of  the  spectral  lines 
will,  however,  give  us  much  that  is  new. 

First  let  us  study  the  effect  of  the  shape  of  the  groove  on  the  bright- 
ness. If  N  is  the  order  of  The  spectrum  and  a  the  grating  space  we 
have 

Nl 

/j.  =  /(sin  <p  +  sin  0)  =  - 
•  a 

since  sin*?£  =  0 

<i 

and  the  intensity  of  the  light  becomes  proportional  to 

^  '  +^y)  ds      e~K"  (>  +  ^  v) 


It  is  to  be  noted  that  this  expression  is  not  only  a  function  of  N  but 
also  of  I,  the  wave-length.  This  shows  that  the  intensity  in  general 
may  vary  throughout  the  spectrum  according  to  the  wave-length  and 
that  the  sum  of  the  light  in  any  one  spectrum  is  not  always  white  light. 

This  is  a  peculiarity  often  noticed  in  gratings.  Thus  one  spectrum 
may  be  almost  wanting  in  the  green,  while  another  may  contain  an 
excess  of  this  color;  again  there  may  be  very  little  blu^  in  one  spectrum 
while  very  often  the  similar  spectrum  on  the  other  side  may  have  its 
own  share  and  that  of  the  other  one  also.  For  this  reason  I  have  found 
it  almost  impossible  to  predict  what  the  ultra  red  spectrum  may  be, 
for  it  is  often  weak  even  where  the  visible  spectrum  is  strong. 

The  integral  may  have  almost  any  form  although  it  will  naturally 
tend  to  be  such  as  to  make  the  lower  orders  the  brightest  when  the 
diamond  rules  a  single  and  simple  groove.  When  it  rules  several  lines 
34 


530  HENRY  A.  KOWLAND 

or  a  compound  groove,  the  higher  orders  may  exceed  the  lower  in 
brightness  and  it  is  mathematically  possible  to  have  the  grooves  of 
such  a  shape  that,  for  given  angles,  all  the  light  may  be  thrown  into 
one  spectrum. 

It  is  not  uncommon,  indeed,  very  easy,  to  rule  gratings  with  im- 
mensely bright  first  spectra,  and  I  have  one  grating  where  it  seems  as 
if  half  the  light  were  in  the  first  spectrum  on  one  side.  In  this  case 
there  is  no  reflection  of  any  account  from  the  grating  held  perpendicu- 
larly: indeed  to  see  one's  face,  the  plate  must  be  held  at  an  angle,  in 
which  case  the  various  features  of  the  face  are  seen  reflected  almost 
as  brightly  as  in  a  mirror  but  drawn  out  into  spectra.  In  this  case  all 
the  other  spectra  and  the  central  image  itself  are  very  weak. 

In  general  it  would  be  easy  to  prove  from  the  equation  that  want  of 
symmetry  in  the  grooves  produces  want  of  symmetry  in  the  spectra,  a 
fact  universally  observed  in  all  gratings  and  one  which  I  generally 
utilize  so  that  the  light  may  be  concentrated  in  a  few  spectra  only. 

EXAMPLE  1 — SQUARE  GROOVES 

When  the  light  falls  nearly  perpendicularly  on  the  plate,  we  need 
not  take  the  sides  into  account  but  only  sum  up  the  surface  of  the  plate 
and  the  bottom  of  the  groove.  Let  the  depth  "be  X  and  the  width  equal 

to*. 
m 

The  intensity  then  becomes  proportional  to 

'NT  S      T  ~rn          rT" 
This  vanishes  when 

N  =  m ,    2m ,    3m,  etc., 

or  —  =  0,  1,  2,  3,  etc. 

The  intensity  of  the  central  light,  for  which  N  =  0,  will  be 

«*        -  •/       *     ]T\ 

£rein»(*TXJ. 

This  can  be  made  to  vanish  for  only  one  angle  for  a  given  wave- 
length. Therefore,  the  central  image  will  be  colored  and  the  color 
will  change  with  the  angle,  an  effect  often  observed  in  actual  gratings. 
The  color  ought  to  change,  also,  on  placing  the  grating  in  a  liquid  of 
different  index  of  refraction  since  A  contains  7,  the  index  of  refraction. 

It  will  be  instructive  to  take  a  special  case,  such  as  light  falling  per- 
pendicularly on  the  plate.  For  this  case 


GRATINGS  IN  THEORY  AND  PRACTICE  531 


A77 

<p  =  0,  I  =1(1  +  cos  v'O  and  //  =  /  sin  0  =  ±11  . 


The  last  term  in  the  intensity  will  then  be 


As  an  example,  let  the  green  of  the  second  order  vanish.     In  this  case, 
Z= -00005.     N  =  2.     Let  a  =-0002  cm.  and  7=1. 

Then,  ^[20000  +  V  (20000)2  -  (10000)2]  =  n. 

Whence,  -% _       n 

~  37300. ' 

where  n  is  any  whole  number.     Make  it  1. 

Then  the  intensity,  as  far  as  this  term  is  concerned,  will  be  as 
follows : 

Minima  where  Intensity  is  0.  Maxima  where  Intensity  is  1. 

Wave-lengths.  Wave-lengths. 

1st  spec.              -0000526             -0000268  -0001000  -00003544  -00002137 

2nd    "                  -0000500              -0000266  -0000833  -00003463  -00002119 

3rd     "                  -0000462              -0000263  -0000651  -00003333  -00002089 

4th     «                  -0000416             -0000259  -0000499  -00003169  -00002050 

5th     "                     etc.  etc.  etc. 

The  central  light  will  contain  the  following  wave-lengths  as  a 
maximum : 

•0001072  -00003575  -0000214,  etc. 

Of  course  it  would  be  impossible  to  find  a  diamond  to  rule  a  rectangu- 
lar groove  as  above  and  the  calculations  can  only  be  looked  upon  as  a 
specimen  of  innumerable  light  distributions  according  to  the  shape  of 
groove. 

Every  change  in  position  of  the  diamond  gives  a  different  light  dis- 
tribution and  hundreds  of  changes  may  be  made  every  day  and  yet  the 
same  distribution  will  never  return,  although  one  may  try  for  years. 

EXAMPLE  2. — TRIANGULAR  GROOVE 

Let  the  space  a  be  cut  into  a  triangular  groove,  the  equations  of  the 
sides  being  x  =  —  cy,  and  x  =  c'(y  —  a),  the  two  cuttings  coming 
together  at  the  point  y  =  u.  Hence  we  have  —  cu  =  c'(u  —  a),  and 
ds  =  dy  V 1  +  <?  or  dy  ^1+c12.  Hence  the  intensity  is  proportional  to 


532  HENRY  A.  ROWLAND 

.  — cA) 


1 J         * sin8 


2 


I  Q  + 


A  —  <-•#)(>  + 

cos 


-^-  [(/*  +  c'  A)  (a  —  w)  —  w  (//  —  c/)]  I  . 


This  expression  is  not  symmetrical  with  respect  to  the  normal  to  the 
grating,  unless  the  groove  is  symmetrical,  in  which  case  c  =  c'  and 

.=«. 

In  this  case,  as  in  the  other,  the  colors  of  the  spectrum  are  of  vari- 
able intensity,  and  some  of  them  may  vanish  as  in  the  first  example, 
but  the  distribution  of  intensity  is  in  other  respects  quite  different. 

CASE  II.  —  MULTIPLE  PERIODIC  RULING 

Instead  of  having  only  one  groove  ruled  on  the  plate  in  this  space  a, 
let  us  now  suppose  that  a  series  of  similar  lines  are  ruled. 

We  have,  then,  to  obtain  the  displacement  by  the  same  expression  as 
before,  that  is 


sn 

2 


r 
I     I  eib  ^x  +  *»»)  ds, 

* 


except  that  the  last  integral  will  extend  over  the  whole  number  of  lines 
ruled  within  the  space  a. 

In  the  spaces  a  let  a  number  of  equal  grooves  be  ruled  commencing 
at  the  points  y  =  0,  ylt  y2,  yz,  etc.,  and  extending  to  the  points  w,  yl  -f-  w, 
yz  -f-  w,  etc.  The  surface  integral  will  then  be  divided  into  portions 
from  w  to  yu  from  yl  -f-  w,  to  yz,  etc.,  on  the  original  surface  of  the 
plate  for  which  x  =  0,  and  from  w  to  0,  from  y±  -\-  w  to  yu  etc.,  for 
the  grooves. 

The  first  series  of  integrals  will  be 


/e 


dv  =  4—  (  —  6a>iiW  +  efoMi  —  fc«^(i/i+«>)  +  gib^  —  etc. 
tOft 


But,  eib^a  =  1  since  &/*«  =  2^-JV  for  any  maximum,  and  thus  the  inte- 
gral becomes 

f 


<    1  4-  fribnyi  4-  gib^y^  -\-  etc. 


GRATINGS  IN  THEORY  AND  PRACTICE'  533 

The  second  series  of  integrals  will  be 

/• 

The  total  integral  will  then  be 

8inw^ri    ««*« 

sin^i   L     *&»,       ^  Jo  6  JL 

i 

As  before,  multiply  this  by  the  same  with  the  sign  of  i  changed  to 
get  the  intensity. 

EXAMPLE  1. — EQUAL  DISTANCES 
The  space,  a,  contains  n'  —  1  equidistant  grooves,  so  that  y^  =  yz  —  y\ 

=  etc.,  =  -, 
n' 

metals  with  some  one  metal,  such  as  iron.     Malting  the  iron  spectrum 


„•-.       a 
v    tt>n^    n 


Hence  the  displacement  becomes 

bttu 
sin  n  —. 


As  the  last  term  is  simply  the  integral  over  the  space  — -,  in  a  different 

form  from  before,  this  is  a  return  to  the  form  we  previously  had  except 
that  it  is  for  a  grating  of  nn'  lines  instead  of  n  lines,  the  grating  space 

being  £ . 

EXAMPLE  2. — Two  GROOVES 


But  ba/jt  =  2 ATT.     Hence  this  becomes 

.      v\_  y 

a 

The  square  of  the  last  term  is  a  factor  in  the  intensity.     Hence  the 
spectrum  will  vanish  when  we  have 

~n~ ' 
4  A  theorem  of  Lord  Rayleigh's. 


534  HENRY  A.  ROWLAND 

or  N_    la         3     a         5      a        , 

"   ~cT     J        ~~c\~    >         TT"    »  *"*" 

2     y,         2     y,        2     y, 
Thus  when  —  =  2,  the  1st,  3d,  etc.,  spectra  will  disappear,  making 

y\ 

a  grating  of  twice  the  number  of  lines  to  the  cm. 

When  —  =4,   the   2d,    6th,    10th,   etc.,   spectra   disappear.     When 

y\ 

—  =  6,  the  3d,  9th,  etc.,  spectra  disappear. 

y\ 

The  case  in  which  —  =  4,  as  Lord  Rayleigh  has  shown,  would  be  very 

y\ 

useful  as  the  second  spectrum  disappears  leaving  the  red  of  the  first 
and  the  ultra  violet  of  the  third  without  contamination  by  the  second. 
In  this  case  two  lines  are  ruled  and  two  left  out.  This  would  be  easy 
to  do  but  the  advantages  would  hardly  pay  for  the  trouble  owing  to 
the  following  reasons:  Suppose  the  machine  was  ruling  20,000  lines 
to  the  inch.  Leaving  out  two  lines  and  ruling  two  would  reduce  the 
dispersion  down  to  a  grating  with  5000  lines  to  the  inch.  Again,  the 
above  theory  assumes  that  the  grooves  do  not  overlap.  Now  I  believe 
that  in  nearly,  if  not  all,  gratings  with  20,000  lines  to  the  inch  the 
whole  surface  is  cut  away  and  the  grooves  overlap.  This  would  cause 
the  second  spectrum  to  appear  again  after  all  our  trouble. 

Let  the  grooves  be  nearly  equidistant,  one  being  slightly  displaced. 


In  this  case  yt  =  ?  -j-  v- 


,      Ny,        I         7TJV          i:Nv  .     nN    •     ff 

cos2  TT  —  S3  =  [  oos-s-  cos  -  —  sin  -4-  am  - 

a         \        2  a  % 

For  the  even  spectra  this  is  very  nearly  unity,  but  for  the  odd  it 
becomes 


Hence  the  grating  has  its  principal  spectra  like  a  grating  of  space  ^ 

but  there  are  still  the  intermediate  spectra  due  to  the  space  a,  and  of 
intensities  depending  on  the  squares  of  the  order  of  spectrum,  and  the 
squares  of  the  relative  displacement,  a  law  which  I  shall  show  applies 
to  the  effect  of  all  errors  of  the  ruling. 

This  particular  effect  was  brought  to  my  attention  by  trying  to  use 
a  tangent  screw  on  the  head  of  my  dividing  engine  to  rule  a  grating 
with  say  28,872  lines  to  the  inch,  when  a  single  tooth  gave  only  14,436 
to  the  inch.  However  carefully  I  ground  the  tangent  screw  I  never  was 


GRATINGS  IN  THEORY  AND  PRACTICE  535 

able  to  entirely  eliminate  the  intermediate  spectra  due  to  14,436  lines, 
and  make  a  pure  spectrum  due  to  28,872  lines  to  the  inch,  although  I 
could  nearly  succeed. 

EXAMPLE  3.  —  ONE  GROOVE  IN  m  MISPLACED 

Let  the  space  a  contain  m  grooves  equidistant  except  one  which  is 
displaced  a  distance  v.     The  displacement  is  now  proportional  to 


Multiplying  this  by  itself  with  —  i  in  place  of  -+-  i,  and  adding  the 
factors  in  the  intensity,  we  have  the  whole  expression  for  the  intensity. 
One  of  the  terms  entering  the  expression  will  be 


sm 


sin^       sin** 
2m  2 

Now  the  first  two  terms  have  finite  values  only  around  the  points 

_^=  rw^Vrr,  where  mN  is  a  whole  number.     But  2p  —  m  -\-  1  is  also  a 
2 

whole  number,  and  hence  the  last  term  is  zero  at  these  points.     Hence 
the  term  vanishes  and  leaves  the  intensity,  omitting  the  groove  factor, 


•    baa  .  .  ba 

sin  ~  sin*  - 

2  in  2 


The  first  term  gives  the  principal  spectra  as  due  to  a  grating  space 
of  —  and  number  of  lines  nm  as  if  the  grating  were  perfect.     The  last 

term  gives  entirely  new  spectra  due  to  the  grating  space,  a,  and  with 
lines  of  breadth  due  to  a  grating  of  n  lines  and  intensities  equal  to 


Hence,  when  the  tangent  screw  is  used  on  my  machine  for  14,436 
lines  to  the  inch,  there  will  still  be  present  weak  spectra  due  to  the 
14,436  spacing  although  I  should  rule  say  400  lines  to  the  mm.  This 
I  have  practically  observed  also. 

The  same  law  holds  as  before  that  the  relative  intensity  in  these 


536  HENRY  A.  ROWLAND 

subsidiary  spectra  varies  as  the  square  of  the  order  of  the  spectrum  and 
the  square  of  the  deviation  of  the  line,  or  lines  from  their  true  position. 

So  sensitive  is  a  dividing  engine  to  periodic  disturbances  that  all  the 
belts  driving  the  machine  must  never  revolve  in  periods  containing  an 
aliquot  number  of  lines  of  the  grating;  otherwise  they  are  sure  to  make 
spectra  due  to  their  period. 

As  a  particular  case  of  this  section  we  have  also  to  consider 

PERIODIC  ERRORS  OF  RULING.  —  THEORY  OF  "  GHOSTS  " 

In  all  dividing  engines  the  errors  are  apt  to  be  periodic  due  to 
"  drunken  "  screws,  eccentric  heads,  imperfect  bearings,  or  other  causes. 
We  can  then  write 

y  =  atn  +  a^  sin  (e^ri)  +  a^  sin  (e?n),  +  etc. 

The  quantities  e1?  ez)  etc.,  give  the  periods,  and  a1}  a2,  etc.,  the  ampli- 
tudes of  the  errors.  We  can  then  divide  the  integral  into  two  parts  as 
before,  an  integral  over  the  groove  and  spaces  and  a  summation  with 
respect  to  the  numbers. 

ds  . 


I  I  'e~ib  <Ax  +  w)  ds  =  le-tbw  j        " 

Vy1  */0 


It  is  possible  to  perform  these  operations  exactly,  but  it  is  less  com- 
plicated to  make  an  approximation,  and  take  y"-  —  yr  =  a,  a  constant 
as  it  is  very  nearly  in  all  gratings.  Indeed  the  error  introduced  is 
vanishingly  small.  The  integral  which  depends  on  tho  shape  of  the 
groove,  will  then  go  outside  the  summation  sign  and  we  have  to  per- 
form the  summation 


sine^  +  os  sine2 

Let  Jn  be  a  Bessel's  function.     Then 

cos  (u  sin  ?)  =  «70  («•)  +  2  [J"2  (w)  cos2  y  +  Jt  (w)  cos*  ^  +  etc.] 
sin  (w  sin  </>)  =  2  [Ji  (w)  sin  ^  +  /,  (w)  sin3  ^  +  etc.] 

But  e~ iu  sin<f>  =  cos  (u  sin  ^ )  —  i sin  (w  sin  ^>)  . 

Hence  the  summation  becomes 


X  [Jo  (^«0  +  2  (—  iJi  (S/iOi)  sin  e^n  +  Jt  (ft/taj  cos  'Ze^n  —  etc.)] 
X  [J0  (bvctt*)  +  2  (—  iJt  (b/jifty)  sin  ezn  +  Jt  (J//a2)  cos  Zeji  —  etc.)] 
X  [/» (bra,*)  +  etc.] 
X  [etc.] 


GRATINGS  IN  THEORY  AND  PRACTICE 


537 


CASE  I. — SINGLE  PERIODIC  ERROR 
In  this  case  only  a0  and  a^  exist.     We  have  the  formula 


Hence  the  expression  for  the  intensity  becomes 


sn  n 


sin  n 


Mo  —  el  }  « 


+  etc. 


2 


J 


As  n  is  large,  this  represents  various  very  narrow  spectral  lines  whose 
light  does  not  overlap  and  thus  the  different  terms  are  independent  of 
each  other.  Indeed  in  obtaining  this  expression  the  products  of  quan- 
tities have  been  neglected  for  this  reason  because  one  or  the  other  is 
zero  at  all  points.  These  lines  are  all  alike  in  relative  distribution 
of  light  and  their  intensities  and  positions  are  given  by  the  following 
table : 

Places.  Intensities.  Designations. 

Primary  line 

Ghosts  of  1st  order. 
Ghosts  of  2d  order. 

Ghosts  of  3d  order, 
etc.  etc.  etc. 


=  I*  ± 


=  ;*±-E-1      J.'QwJ 


Hence  the  light  which  would  have  gone  into  the  primary  line  now 
goes  to  making  the  ghosts,  so  that  the  total  light  in  the  line  and  its 
ghosts  is  the  same  as  in  the  original  without  ghosts. 

The  relative  intensities  of  the  ghosts  as  compared  with  the  primary 
line  is 


538  HENRY  A.  ROWLAND 

This  for  very  weak  ghosts  of  the  first,  second,  third,  etc.,  order, 
becomes 


The  intensity  of  the  ghosts  of  the  first  order  varies  as  the  square  of 
the  order  of  the  spectrum  and  as  the  square  of  the  relative  displace- 
ment as  compared  with  the  grating  space  a0.  This  is  the  same  law  as 
we  before  found  for  other  errors  of  ruling,  and  it  is  easy  to  prove  that 
it  is  general.  Hence 

The  effect  of  small  errors  of  ruling  is  to  produce  diffused  light  around 
the  spectral  lines.  This  diffused  light  is  subtracted  from  the  light  of  the 
primary  line,  and  its  comparative  amount  varies  as  the  square  of  the 
relative  error  of  ruling  and  the  square  of  the  order  of  the  spectrum. 

Thus  the  effect  of  the  periodic  error  is  to  dimmish  the  intensity  of 
the  ordinary  spectral  lines  (primary  lines)  from  the  intensity  1  to 
t702(fy"ai)j  and  surround  it  with  a  symmetrical  system  of  lines  called 
ghosts,  whose  intensities  are  given  above. 

When  the  ghosts  are  very  near  the  primary  line,  as  they  nearly  always 
are  in  ordinary  gratings  ruled  on  a  dividing  engine  with  a  large  number 
of  teeth  in  the  head  of  the  screw,  we  shall  have 

f-  +  A)  +  Jftai  (f*—  j^}  =  IJfta^  nearly. 
oaj  \         baj 

Hence  the  total  light  is  by  a  known  theorem, 


Thus,  in  all  gratings,  the  intensity  of  the  ghosts  as  well  as  the 
diffused  light  increases  rapidly  with  the  order  of  the  spectrum.  This 
is  often  marked  in  gratings  showing  too  much  crystalline  structure. 
For  the  ruling  brings  out  the  structure  and  causes  local  difference  of 
ruling  which  is  equivalent  to  error  of  ruling  as  far  as  diffused  light  is 
concerned. 

For  these  reasons  it  is  best  to  get  defining  power  by  using  broad 
gratings  and  a  low  order  of  spectra  although  the  increased  perfection  of 
the  smaller  gratings  makes  up  for  this  defect  in  some  respects. 

There  is  seldom  advantage  in  making  both  the  angle  of  incidence 
and  diffraction  more  than  45°,  but,  if  the  angle  of  incidence  is  0,  the 
other  angle  may  be  60°,  or  even  70°,  as  in  concave  gratings.  Both 
theory  and  practice  agree  in  these  statements. 

Ghosts  are  particularly  objectionable  in  photographic  plates,  especi- 


GRATINGS  IN  THEORY  AND  PRACTICE  539 

ally  when  they  are  exposed  very  long.     In  this  case  ghosts  may  be 
brought  out  which  would  be  scarcely  visible  to  the  eye. 
As  a  special  case,  take  the  following  numerical  results: 


1 

2 

3 

1 

1 

1 

1 

1 

1 

1 

1 

1 

25' 

50  ' 

100 

25' 

50' 

100 

25' 

50' 

100' 

1 

1 

1 

1 

1 

1 

1 

1 

1 

63  ' 

252' 

1008 

16' 

63' 

252 

7  ' 

28' 

102* 

In  a  grating  with  20,000  lines  to  the  inch,  using  the  third  spectrum, 

we  may  suppose  that  the  ghosts  corresponding  to  ai=~   will  be  visible 

a0     50 

and  those  for  -1  =  -^  very  troublesome.     The  first  error  is  a,  =TTnrinnnr 
a0     25 

in.  and  the  second  a^  =  5  0  0*0  o  o  in.  Hence  a  periodic  displacement  of 
one  millionth  of  an  inch  will  produce  visible  ghosts  and  one  five  hun- 
dred thousandth  of  an  inch  will  produce  ghosts  which  are  seen  in  the 
second  spectrum  and  are  troublesome  in  the  third.  With  very  bright 
spectra  these  might  even  be  seen  in  the  first  spectrum.  Indeed  an  over 
exposed  photographic  plate  would  readily  bring  them  out. 

When  the  error  is  very  great,  the  primary  line  may  be  very  faint  or 
disappear  altogether,  the  ghosts  to  the  number  of  twenty  or  fifty  or 
more  being  often  more  prominent  than  the  original  line.  Thus,  when 

bfial  =  2-405,  5-52,  8-65,  etc.  =  2*N  -^  , 

00 

the  primary  line  disappears.     When 

=  0,   3-83,   7-02,   etc.  =  ZxN  ^L  , 


the  ghosts  of  the  first  order  will  disappear.     Indeed  we  can  make  any 
ghost  disappear  by  the  proper  amount  of  error. 
Of  course,  in  general 

r  -  2  CM  -  1)    r  j 

Un  --  -  t/B_i  —  «/„_•>  • 

V 

Thus  a  table  of  ghosts  can  be  formed  readily  and  we  may  always  tell 
when  the  calculation  is  complete  by  taking  the  sum  of  the  light  and 
finding  unity. 


540  HENRY  A.  ROWLAND 

72         72         T2         TV          72  72          72         72         72         72        /2  72  72  72        72 

t/0         "1         "2          "8          "4  "5  "6         "7         "8         "9         "10         "11        "12         "13      "U 


0 

a 

i 

1-000 

•2 

•980 

•010 

•4 

•038 

6 

•832 

089 

•002 

8 

•716 

136 

•005 

1- 

0 

•586 

•194 

•019 

a 

•0 

•050 

•333 

•1  94 

•017 

•001 

2 

•605 

•000 

•969 

•186 

•040 

•003 

•068 

•115 

•236 

•095 

•017 

•002 

8 

•832 

•162 

•000 

•169 

•176 

•065 

•013 

•002     

4 

•0 

•158 

•004 

•133 

•185 

•079 

•018 

•002     

r, 

•0 

•031 

•107 

•009 

•133 

•153 

•068 

•017  -003     

5 

fi 

520 
0 

•000 
•022 

•116 
•077 

etc. 
•059 

•013 

•128 

•131 

•061   -017  -003     

7- 
8 

016 

•090 
•029 

.000 
•055 

•090 
•013 

etc. 
•085 

•Oil 

•035 

•114  -103  -050  -016  -003  -001     

8' 

10 

654 

•000 
•060 

•075 
•002 

etc. 
•065 

•003 

•048 

•055 

•002  -047  -101   -091   -051  -022  -Oil  -009    -022 

This  table  shows  how  the  primary  line  weakens  and  the  ghosts 
strengthen  as  the  periodic  error  increases,  becoming  0  at  2nJVa  —  2-405. 

tt 

It  then  strengthens  and  weakens  periodically,  the  greatest  strength 
being  transferred  to  one  of  the  ghosts  of  higher  and  higher  order  as 
the  error  increases. 

Thus  one  may  obtain  an  estimate  of  the  error  from  the  appearance 
of  the  ghost. 

Some  of  these  wonderful  effects  with  20  to  50  ghosts  stronger  than 
the  primary  line  I  have  actually  observed  in  a  grating  ruled  on  one  of 
my  machines  before  the  bearing  end  of  the  screw  had  been  smoothed. 
The  effect  was  very  similar  to  these  calculated  results. 

DOUBLE  PERIODIC  ERROR 

Supposing  as  before  that  there  is  no  overlapping  of  the  lines,  we 
have  the  following: 

Places.  Intensities. 

[/„  (ba^  ,/„  (toirif  }  Primary  line. 


=  ,,.  ±      -      [«7i  (ba^J  ,70 

(.  Ghosts  of  1st  order. 

/> 

=  fi±  ~       [J0  (ba^)  /!  (ba^J 


GRATINGS  IN  THEORY  AND  PRACTICE 


541 


Places. 


=  /j.  ± 


Intensities. 


gt± 

baa 


l4  =  /JL±^L        [J,  (&z1(«J  ^  (fo2,O]2  j-  Ghosts  of  2d  order. 

,5  =  ft  ±  |£*        [  J 

'fi     /*     ^t  7  I   « 


f  Ghosts  of  3d  order. 


&*„ 

A*9  =  ,U    ±    T-^2 

etc. 


etc. 


Each  term  in  this  table  of  ghosts  simply  expresses  the  fact  that  each 
periodic  error  produces  the  same  ghosts  in  the  same  place  as  if  it  were 
the  only  error,  while  others  are  added  which  are  the  ghosts  of  ghosts. 
The  intensities,  however,  are  modified  in  the  presence  of  these  others. 

Writing  ^  =  balP.  and  c2  =  ba^. 

The  total  light,  is 


7 

«/0 


+  etc. 


which  we  can  prove  to  be  equal  to  1. 

Hence  the  sum  of  all  the  light  is  still  unity,  a  general  proposition 
which  applies  to  any  number  of  errors. 

The  positions  of  the  lines  when  there  is  any  number  of  periodic 
errors  can  always  be  found  by  calculating  first  the  ghosts  due  to  each 
error  separately;  then  the  ghosts  due  to  these  primary  ghosts  for  it  as 
if  it  were  the  primary  line,  and  so  on  ad  infinitum. 

In  case  the  ghosts  fall  on  top  of  each  other  the  expression  for  the 
intensity  fails.  Thus  when  e2  =  2elt  e3  =  3e^  etc.,  the  formula  will 
need  modification.  The  positions  are  in  this  case  only  those  due  to  a 
single  periodic  error,  but  the  intensities  are  very  different. 

Places.  Intensities. 

P  =  -£— 
baa 


542  HENRY  A.  ROWLAND 

Places.  Intensities. 

A£I  _  fJL  ±  A.     [«/!  (K,"i)  «/o  (fas.«i)  —  J3  (ba^J  «72  (ba&J  +  etc.]2 

*"°          +  [</i  C^iAti)  t/x  (ifl^x)  —  <73  (>iAO  /i  (far,*0  +  etc.]8, 
etc.  etc. 

We  have  hitherto  considered  cases  in  which  the  error  could  not  be 
corrected  by  any  change  of  focus  in  the  objective.  It  is  to  be  noted, 
however,  that  for  any  given  angle  and  focus,  every  error  of  ruling  can 
be  neutralized  by  a  proper  error  of  the  surface,  and  that  all  the  results 
we  have  hitherto  obtained  for  errors  of  ruling  can  be  produced  by  errors 
of  surface,  and  many  of  them  by  errors  in  size  of  groove  cut  by  the  dia- 
mond. Thus  ghosts  are  produced  not  only  by  periodic  errors  of  ruling 
but  by  periodic  waves  in  the  surface,  or  even  by  a  periodic  variation  in 
the  depth  of  ruling.  In  general,  however,  a  given  solution  will  apply 
only  to  one  angle  and,  consequently,  the  several  results  will  not  be 
identical;  in  some  cases,  however,  they  are  perfectly  so. 

Let  us  now  take  up  some  cases  in  which  change  of  focus  can  occur. 
The  term  *r*  in  the  original  formula  must  now  be  retained. 

Let  the  lines  of  the  grating  be  parallel  to  each  other.  We  can  then 
neglect  the  terms  in  z  and  can  write  r2  =  y2  very  nearly.  Hence  the 
general  expression  becomes 


where  *  depends  on  the  focal  length.     This  is  supposed  to  be  very 
large,  and  hence  K  is  small. 

This  integral  can  be  divided  into  two  parts,  an  integral  over  the 
groove  and  the  intervening  space,  and  a  summation  for  all  the  grooves. 
The  first  integral  will  slightly  vary  with  change  in  the  distance  of  the 
grooves  apart,  but  this  effect  is  vanishingly  small  compared  with  the 
effect  on  the  summation,  and  can  thus  be  neglected.  The  displace- 
ment is  thus  proportional  to 

Ky*\ 


CASE  I.  —  LINES  AT  VARIABLE  DISTANCES 
In  this  case  we  can  write  in  general 

y  =  an  +  atf  +  a^n3  +  etc. 

As  K,  au  a2,  etc.,  are  small,  we  have  for  the  displacement,  neglecting 
the  products  of  small  quantities, 

(an  +  Oina  +  aan8  +  etc.)  —  «a3«2]  . 


GRATINGS  IN  THEORY  AND  PRACTICE  543 

Hence  the  term  a^n2  can  be  neutralized  by  a  change  of  forms  ex- 
pressed by  fjia1=K  a2.  Thus  a  grating  having  such  an  error  will  have 
a  different  focus  according  to  the  angle  n,  and  the  change  will  be  -f-  on 
one  side  and  —  on  the  other. 

This  error  often  appears  in  gratings  and,  in  fact,  few  are  without  it. 

A  similar  error  is  produced  by  the  plate  being  concave,  but  it  can 
be  distinguished  from  the  above  error  by  its  having  the  focus  at  the 
same  angle  on  the  two  sides  the  same  instead  of  different. 

According  to  this  error,  a^n2,  the  spaces  between  the  lines  from  one 
side  to  the  other  of  the  grating,  increase  uniformly  in  the  same  manner 
as  the  lines  in  the  B  group  of  the  solar  spectrum  are  distributed.  For- 
tunately it  is  the  easiest  error  to  make  in  ruling,  and  produces  the  least 
damage. 

The  expression  to  be  summed  can  be  put  in  the  form 


ib  (>«!  —  «a2)  n2  +  ib/tatf  +  ib  Oa3  -f  ib  (/^  —  <«*)']  n*+  etc.] 

The  summation  of  the  different  terms  can  be  obtained  as  shown 
below,  but,  in  general,  the  best  result  is  usually  sought  by  changing 
the  focus.  This  amounts  to  the  same  as  varying  K  until  //ax  —  *a2  =  0 
as  before.  For  the  summation  we  can  obtain  the  following  formula  from 
the  one  already  given.  Thus 


Hence 


vn -\eZipn  —  sm  nP  eip (n  - 1). 

sin  p 


=  e«p(»  -i) 

m 


dp  J  I      amp 

When  n  is  very  large,  writing  *^  =  pn  =  n  Nn  -f  q,  we  have 


dq 
Whence  writing 


c     = 

c'   •=.   /JLCii, 

c"  =  b  &a3  +  i 

c'"  =  etc., 


544 

the  summation  is 


HENRY  A.  ROWLAND 


•( 


+  etc. 


sn 


dq 

rf*    sin  <y  __ 
~dq*      q 


_  <7  cos  <y  —  sin  q 


S*D 


—  2q  cos  <y  +  (2  —  g2  )  sin  g 
q*  ' 

g  (6  —  g2)  cos  q  —  (6  —  3g2)  sin 
~~ 


< 


etc. 


etc. 


These  equations  serve  to  calculate  the  distribution  of  light  intensity 
in  a  grating  with  any  error  of  line  distribution  suitable  to  this  method 
of  expansion  and  at  any  focal  length.  For  this  purpose  the  above 
summation  must  be  multiplied  by  itself  with  -f-  i  in  place  of  —  i. 

The  result  is  for  the  light  intensity 

j^  sin  q 
dq      q 


+  2c      -  +  etc. 


16 
n* 


Uq3 


9 

sin  q 


16 

As  might  have  been  anticipated,  the  effect  of  the  additional  terms  is 
to  broaden  out  the  line  and  convert  it  into  a  rather  complicated  group 
of  lines,  as  can  sometimes  be  observed  with  a  bad  grating.  At  any 
given  angle  the  same  effect  can  be  produced  by  variation  o'f  the  plate 
from  a  perfect  plane.  Likewise  the  effect  of  errors  in  the  ruling  may 
be  neutralized  for  a  given  angle  by  errors  of  the  ruled  surface,  as  noted 
in  the  earlier  portions  of  the  paper. 


50 
A  NEW  TABLE  OF  STAND AKD  WAVE-LENGTHS 

[Johns  Hopkins  University  Circulars,  No.  106,  p.  110,  1893;   Philosophical  Magazine  [5], 
XXXVI,  49-75,  1893;  Astronomy  and  Astro- Physics,  XII,  321-347,  1893] 

PREFATORY  NOTE 

During  the  last  ten  years  I  have  made  many  observations  of  wave- 
lengths, and  have  published  a  preliminary  and  a  final  table  of  the  wave- 
lengths of  several  hundred  lines  in  the  solar  spectrum. 

For  the  purpose  of  a  new  table  I  have  worked  over  all  my  old  observa- 
tions, besides  many  thousand  new  ones,  principally  made  on  photo- 
graphs, and  have  added  measurements  of  metallic  lines  so  as  to  make 
the  number  of  standards  nearly  one  thousand. 

Nearly  all  the  new  measurements  have  been  made  on  a  new  measur- 
ing machine  whose  screw  was  specially  made  by  my  process1  to  cor- 
respond with  the  plates  and  to  measure  wave-lengths  direct  with  only 
a  small  correction. 

The  new  measures  were  made  by  Mr.  L.  E.  Jewell,  who  has  now  be- 
come so  expert  as  to  have  the  probable  error  of  one  setting  about  Tir?nF 
division  of  Angstrom,  or  1  part  in  5,000,000  of  the  wave-length.  Many 
of  these  observations,  however,  being  made  with  different  measuring 
instruments,  and  before  such  experience  had  been  obtained,  have  a 
greater  probable  error.  This  is  especially  true  of  those  measurements 
made  with  eye  observations  on  the  spectrum  direct.  The  reductions  of 
the  reading  were  made  by  myself. 

Many  gratings  of  6  in.  diameter  and  21^  feet  radius  were  used;  and 
the  observations  were  extended  over  about  ten  years. 

The  standard  wave-length  was  obtained  as  follows:  Dr.  Bell's  value 
of  D1  was  first  slightly  corrected  and  became  5896-20.  C.  S.  Peirce's 
valfce  of  the  same  line  was  corrected  as  the  result  of  some  measurements 
made  on  his  grating  and  became  5896-20.  The  values  of  the  wave-length 
then  become 


•See  Encyc.  Brit.,  art.  Screw. 
35 


546  HENKY  A.  EOWLAND 

Weight.  Observer.  D. 

o 

1  Angstrom,  corrected  by  Thalen   5895-81 

2  Miiller  &  Kempf     5896-25 

2  Kurlbaum     .  5895-90 

5  Peirce   5896-20 

10  Bell  .  ..5896-20 


Mean   5896-156 

As  the  relative  values  are  more  important  for  spectroscopic  work 
than  the  absolute,  I  take  this  value  without  further  remark.  It  was 
utilized  as  follows: 

1st.  By  the  method  of  coincidences  with  the  concave  grating,  the 
wave-lengths  of  14  more  lines  throughout  the  visible  spectrum  were 
determined  from  this  with  great  accuracy  for  primary  standards. 

2d.  The  solar  standards  were  measured  from  one  end  of  the  spectrum 
to  the  other  many  times;  and  a  curve  of  error  drawn  to  correct  to  these 
primary  standards. 

3d.  Flat  gratings  were  also  used. 

4th.  Measurements  of  photographic  plates  from  10  to  19  inches  long 
were  made.  These  plates  had  upon  them  two  portions  of  the  solar 
spectrum  of  different  orders.  Thus  the  blue,  violet  and  ultra  violet 
spectra  were  compared  with  the  visible  spectrum,  giving  many  checks 
on  the  first  series  of  standards. 

5th.  Measurements  were  made  of  photographic  plates  having  the 
solar  spectrum  in  coincidence  with  metallic  spectra,  often  of  three 
orders,  thus  giving  the  relative  wave-lengths  of  three  points  in  the 
spectrum. 

Often  the  same  line  in  the  ultra  violet  had  its  wave-length  deter- 
mined by  two  different  routes  back  to  two  different  lines  of  the  visible 
spectrum.  The  agreement  of  these  to  y-j^  division  of  Angstrom  in 
nearly  every  case  showed  the  accuracy  of  the  work. 

6th.  Finally,  the  important  lines  had  from  10  to  20  measurements  on 
them,  connecting  them  with  their  neighbors  and  many  points  in  the 
spectrum,  both  visible  and  invisible;  and  the  mean  values  bound  the 
whole  system  together  so  intimately  that  no  changes  could  be  made  in 
any  part  without  changing  the  whole. 

This  unique  way  of  working  has  resulted  in  a  table  of  wave-lengths 
from  2100  to  7700  whose  accuracy  might  be  estimated  as  follows: 

Distribute  less  than  ^^  division  of  Angstrom  properly  throughout 


A  NEW  TABLE  OF  STANDARD  WAVE-LENGTHS  547 

the  table  as  a  correction,  and  it  will  become  perfect  within  the  limits 
2400  and  7000. 

The  above  is  only  a  sketch  of  the  methods  used.  The  complete  de- 
tails of  the  work  are  ready  for  publication  but  I  have  not  yet  found  any 
journal  or  society  willing  to  undertake  it.2 

[The  tables  of  wave-lengths  are  omitted.] 

2  [These  details  were  finally  published  in  the  Memoirs  of  the  American  Academy  of 
Arts  and  Sciences,  XII,  101-186,  1896,  under  the  title,  '  On  a  Table  of  Standard  Wave- 
Lengths  of  the  Spectral  Lines.'] 


51 

ON  A  TABLE  OF  STANDARD  WAVE-LENGTHS  OF  THE 

SPECTRAL  LINES1 

• 

[Memoirs  of  the  American  Academy  of  Arts  and  Sciences,  XII,  101-186,  1896] 
PRESENTED  MAY  10,  1898 

Investigations  on  Light  and  Heat,  made  and  published  wholly  or  in  part  with  appro- 
priation from  the  Rumford  Fund 

Some  years  since,  having  made  a  machine  for  ruling  gratings  and  dis- 
covered the  concave  grating,  which  placed  in  my  hands  an  excellent 
process  for  photographing  spectra,  I  applied  myself  to  photograph  the 
solar  spectrum.  The  property  of  the  concave  grating,  mounted  in  the 
method  which  I  use,  of  producing  a  normal  spectrum  gave  me  the 
means  of  adding  a  scale  of  wave-lengths,  and  so  producing  a.  photo- 
graphic map  of  the  solar  spectrum  on  a  very  large  scale  and  of  great 
accuracy.  I  soon  after  constructed  a  very  much  better  ruling  engine, 
which  is  kept  at  a  uniform  temperature  in  the  vault  of  the  new  physical 
laboratory  of  the  Johns  Hopkins  University,  with  which  I  have  made 
very  much  better  gratings.  I  therefore  went  over  the  whole  process 
once  more,  extending  the  map  to  include  B,  and  making  new  negatives 
of  the  whole  spectrum  very  much  better  than  the  old.  This  set  of  ten 
photographic  plates  is  now  familiar  to  most  spectroscopists. 

In  order  to  place  the  scale  on  the  negatives,  it  was  necessary  to  know 
the  wave-lengths  of  certain  standard  lines.  Of  course  my  first  thought 
was  of  Angstrom,  whose  measurements  were  the  wonder  of  his  time. 
On  trying  to  place  my  scale  according  to  his  figures,  I  found  it  impos- 
sible to  make  them  and  my  photographs  agree ;  and  I  finally  was  forced 
to  the  conclusion  that  a  new  series  of  standards  was  needed  before  I 
could  go  further.  Here  again  the  concave  grating  came  to  my  rescue. 
All  the  spectra  are  in  focus  at  once,  and  relative  measures  can  thus  be 
made  at  once  by  micrometric  measures  of  the  overlapping  spectra. 
Again,  the  spectrum  is  normal,  and  so  a  micrometer  of  very  long  range 
could  be  used.  To  obtain  the  primary  standards  by  means  of  overlap- 
ping spectra,  I  have  used  gratings  with  from  3000  up  to  20,000  lines  to 

1  An  abstract  of  this  paper  has  recently  appeared  in  'Astronomy  and  Astro-Physics,' 
and  in  the  'London  Philosophical  Magazine.' 


TABLE  OF  STANDARD  WAVE-LENGTHS  OF  THE  SPECTRAL  LINES    549 

the  inch,  and  from  13  to  21|  feet  focus.  The  first  series  made  with  the 
13-foot  grating  by  Mr.  Koyl  in  1882  was  not  found  quite  accurate 
enough,  and  I  have  since  made  personally  a  long  series  with  gratings 
of  21|  feet  focus  which  is  mnch  more  accurate.  These  long  focus  grat- 
ings had  from  7000  to  20,000  lines  to  the  inch,  and  were  ruled  on  two 
dividing  engines,  while  the  13-foot  one  had  a  less  number,  possibly 
3000.  There  are  two  principal  errors  to  guard  against  in  this  method, 
the  first  peculiar  to  the  method  of  coincidences,  and  the  second  to  any 
method  where  gratings  are  used.2  The  first  is  that,  where  spectra  are 
over  each  other  and  the  lines  therefore  often  on  top  of  each  other,  the 
line  of  one  spectrum  may  be  apparently  slightly  displaced  by  the 
presence  of  one  from  another  spectrum,  although  the  latter  may  be 
almost  invisible.  The  use  of  proper  absorbents  obviates  this  difficulty. 
The  second  source  of  error  is  more  subtle,  and  arises  from  the  diamond 
ruling  differently  on  different  parts  of  the  grating.  It  is  more  apt  to 
occur  in  concave  gratings  than  plane  ones,  although  few  are  perfectly 
free  from  the  error,  as  it  is  very  difficult  to  get  a  diamond  to  rule  a 
concave  grating  uniformly.  Looking  at  the  grating  in  spectra  of 
different  orders,  the  grating  may  appear  uniform  from  end  to  end  in 
one,  and  possibly  brighter  at  one  end  than  the  other  in  another  spec- 
trum. This  gives  a  chance  for  any  imperfection  in  the  form  of  the 
surface  of  the  grating,  or  any  errors  in  its  ruling,  or  indeed  the  spheri- 
cal aberration  of  the  lenses  or  concave  grating,  to  affect  the  measure- 
ment of  relative  wave-length.3  This  error  I  have  guarded  against  by 
using  only  uniformly  ruled  gratings,  reversing  them,  and  using  a  great 
number  of  them.  I  have  also  used  the  coincidence  of  only  the  lower 
orders  of  spectra,  such  as  the  2d,  3d,  4th,  oth,  and  6th.  Coincidences 
up  to  the  12th  were,  however,  observed  by  Mr.  Koyl  with  the  13-foot 
concave,  and  probably  have  some  errors  of  this  nature. 

In  this  way  I  established  about  fifteen  points  in  the  visible  spectrum 
which  served  as  primary  standards.  These  were  so  interwoven  by  the 
coincidences  that  I  have  great  confidence  in  the  value  of  most  of  them. 

2  The  variation  of  the  dispersion  of  the  air  with  the  thermometer  and  barometer 
is  probably  not  worth  considering  for  the  visible  part  of  the  spectrum,  although  it 
might  be  worth  investigating  for  the  two  extremities  of  the  spectrum. 

3  The  error  of    using  gratings  of    variable  brightness  in  different  parts,  or  those 
with  imperfect  ruling  of  any  kind,  I  have  constantly  guarded  against.     Such  I  be- 
lieve to  be  the   principal   causes  of    the  great  errors  in  relative  and  absolute  wave- 
lengths in  Vogel's  tables,  as  the  gratings  he  used,  made  by  Wandschaft,  were  full  of 
errors  of  all  kinds. 


550  HENEY  A.  ROWLAND 

Indeed,  no  process  of  angular  measurement  could  approach  the  accuracy 
of  this  one. 

Thus,  using  a  line  P  to  start  with,  I  determine  other  groups  of  lines, 
a',  V,  c',  d',  etc.  From  these  again  I  find  groups,  some  of  which  may 
be  the  same  as  the  first;  then  again  from  these,  other  groups.  The 
process  can  he  continued  further,  hut  we  are  apt  to  come  hack  to  the 
same  lines  again,  and  we  are  further  limited  by  the  visibility  of  the 
lines.  Thus  the  limit  of  great  accuracy  by  eye  observation  in  either 
direction  is  practically  4200  and  7000;  although  in  a  dark  room,  especi- 
ally in  the  first  spectrum,  one  can  see  much  further,  even  beyond  the  A 
group,  although  it  is  difficult  to  set  on  the  lines,  and  one  is  apt  to  mis- 
take groups  of  lines  for  single  lines.4  When  one  uses  a  group  as  a 
standard,  and  one  or  more  of  the  group  is  an  atmospheric  line  which 
varies,  the  measures  will  of  course  vary  also,  unless  the  atmospheric 
line  is  in  the  centre  of  the  group.  This  is  a  very  common  source  of 
error,  and  has  caused  me.  much  trouble.  In  a  grating  with  a  very 
bright  second  spectrum,  I  have,  however,  obtained  the  coincidence  of  A 
with  the  region  whose  wave-length  is  about  5080,  and  have  thus  con- 
firmed the  value  given  in  my  preliminary  table,  which  was  obtained  by 
a  very  long  interpolation  passing  from  the  first  into  the  second  spec- 
trum. 

The  accuracy  of  these  primary  standards  can  be  estimated  from  the 
equations  given  in  Table  VII.  It  is  there  seen  that  there  is  scarcely 
any  difference  in  the  different  measures  as  derived  from  different  lines. 

It  is  to  be  specially  noted  that  the  wave-length  of  P  and  the  lines 
directly  determined  from  it  have  no  more  weight  than  any  of  the 
others.  The  table  might  just  as  well  have  been  arranged  with  the  D 
line,  or  any  other,  first.  The  true  way  of  discussing  the  results  is  to 
form  a  series  of  linear  equations,  about  twenty-six  in  all,  and  solve 
them.  This  is  the  method  I  have  used,  although  I  have  not  discussed 
them  by  the  method  of  least  squares.5 

Some  miscellaneous  observations  not  included  in  the  table  allowed 
me  to  add  a  few  more  line?  to  these  primary  standards. 

Having  completed  these  primary  standards,  I  then  observed  several 

• 

4 la  a  very  bright  grating  I  have  faintly  seen,  and  even  measured,  lines  down  to 
wave-length  8500.  My  assistant,  Mr.  L.  E.  Jewell,  can  see  far  into  what  is  called 
the  ultra  violet,  even  to  wave-length  3500  or  beyond. 

5  The  calculations  of  this  paper  have  involved  about  a  million  figures,  of  which  I 
have  personally  written  more  than  half.  Hence  I  am  not  anxious  for  more  labor  of 
this  kind. 


TABLE  OF  STANDARD  WAVE-LENGTHS  OF  THE  SPECTRAL  LINES    551 

hundred  standard  lines  in  the  visible  spectrum,  including  these  primary 
standards,  with  a  micrometer  having  a  range  of  five  inches,  and  very 
accurately  made.  The  spectrum  being  strictly  normal,  the  readings  so 
made  were  proportional  to  the  wave-length.  They  could  have  been  used 
simply  to  interpolate  between  the  primary  standards,  but  I  preferred 
another  method.  The  readings  of  the  micrometer  were  made  to  over- 
lap, so  that,  by  adding  a  constant  to  each  set,-  a  continuous  series  could 
be  formed  for  the  whole  spectrum  which  would  be  proportional  to  the 
wave-length  except  for  some  slight  errors  due  to  the  working  of  the 
apparatus  for  keeping  the  focus  constant.  Making  this  series  coincide 
with  two  standards  at  the  ends,  the  wave-lengths  of  all  could  be  obtained 
by  simply  multiplying  the  whole  series  by  one  number  and  adding  a 
constant.  This  usually  gave  the  wave-lengths  of  the  whole  spectrum 
within  0-1  or  0-2  divisions  of  Angstrom.  The  differences  of  this  series 
from  the  primary  standards  were  then  plotted,  and  a  smooth  curve 
drawn  through  the  points  thus  found.  The  ordinates  of  this  curve 
then  gave  the  correction  to  be  applied  at  any  point. 

It  is  to  be  noted  that  the  departure  from  the  normal  spectrum  was 
very  small,  and  the  correction  thus  found  was  very  certain.  The  cause 
of  the  departure  was  not  apparent,  but  may  have  been  the  slight  tilting 
of  the  spectrum,  by  which  it  was  measured  somewhat  obliquely  at 
places. 

The  visible  spectrum  was  thus  gone  over  five  or  more  times  in  this 
manner,  with  several  different  gratings  and  in  different  orders  of  spectra. 
The  results  are  given  in  Table  X,  Columns  C,  R,  p,  q,  m,  0,  e,  h,  i,  etc. 
The  spectrum  from  the  green  down  to  and  including  A  was  also  ob- 
served on  a  large  instrument  for  flat  gratings,  having  lenses  six  and 
one-half  inches  in  diameter  and  of  eight  feet  focus.  These  latter 
observations  are  marked  C".  This  region  I  intend  at  some  future  time 
to  observe  further. 

It  was  now  required  to  observe  the  ultra  violet  to  complete  the  series. 
For  this  purpose  the  coincidences  of  the  3d,  3d,  4th,  5th,  and  6th 
spectra  of  a  7000,  21$  feet  radius,  grating  were  photographed.  My  in- 
strument will  take  in  photographic  plates  twenty  inches  long,  but  there 
will  be  a  slight  departure  from  a  normal  spectrum  in  so  long  a  plate. 
Hence  plates  ten  inches  long  were  mostly  used  for  this  special  series. 
Before  the  camera  was  placed  a  revolving  plate  of  metal  about  three- 
sixteenths  of  an  inch  thick,  and  having  a  slit  in  it  of  the  same  width.' 

6  This  is  described  in  the  Johns  Hopkins  Circular  of  May,  1889,  by  Dr.  Ames. 


552  HENRY  A.  BOWL  AND 

When  the  flat  side  was  parallel  to  the  camera  plate,  a  strip  of  the 
spectrum  three-sixteenths  of  an  inch  wide  fell  on  the  plate.  When 
turned  ninety  degrees,  the  plate  shielded  this  portion  and  exposed  the 
rest.  Using  absorbents.,  it  was  thus  possible  to  photograph  a  strip  of 
say  the  4th  spectrum  between  two  strips  of  the  5th.  This  arrangement 
is  better  than  having  only  two  edges  come  together.  To  correct  any 
movement  of  the  apparatus  during  the  time  of  exposure,  I  expose  on 
one  spectrum,  then  on  the  other,  and  back  again  on  the  first. 
•  Placing  the  negatives  so  obtained  on  a  dividing  engine  with  a  micro- 
scope of  very  low  power  and  a  tightly  stretched  cross-hair,  the  coin- 
cidence of  the  two  spectra  can  be  measured.  Owing  to  the  large  scale 
of  the  photographs,— about  that  of  Angstrom, — an  ordinary  dividing 
engine  having  errors  not  greater  than  y^Vo"  incn  can  be  used,  but  the 
negatives  should  be  gone  over  at  least  twice,  reversing  them  end  for 
end.  Two  screws  were  used  in  the  engine  and  finally  another  com- 
plete machine  was  constructed,  giving  wave-lengths  direct  with  only  a 
slight  correction.  For  determining  the  wave-length  of  metallic  lines, 
the  same  process  can  be  used  with  wonderful  accuracy. 

The  results  are  given  in  the  columns  marked  PL  with  the  number 
of  the  plates.  The  accuracy  is  very  remarkable,  and  I  think  the  figures 
establish  the  assertion  that  the  coincidence  of  solar  and  metallic  lines 
can  be  determined  with  a  probable  error  of  one  part  in  500,000  by  only 
one  observation. 

This  process  not  only  gave  me  measures  of  the  ultra  violet,  but  also 
new  observations  of  the  visible  spectrum.  So  far  in  my  work  on  these 
coincidences,  I  have  only  used  erythrosin  plates  going  a  little  below  D; 
but  cyanine  plates  might  be  used  to  B,  or  even  in  the  ultra  red,  as  Trow- 
bridge  has  recently  shown.  One  plate,  No.  20,  however,  connects  wave- 
lengths 6400  and  3200. 

Thus  I  have  constructed  a  table  of  about  one  thousand  lines,  more 
or  less,  which  are  intertwined  with  each  other  in  an  immense  number 
of  ways.  They  have  been  tested  in  every  way  I  can  think  of  during 
eight  or  nine  years,  and  have  stood  all  the  tests;  and  I  think  I  can 
present  the  results  to  the  world  with  confidence  that  the  results  of  the 
relative  measures  will  never  be  altered  very  much.  I  believe  that  no 
systematic  error  in  the  relative  wave-lengths  of  more  than  about  ±'01 
exists  anywhere  except  in  the  red  end  as  we  approach  A.  Possibly 
±  -03,  or  even  less,  might  cover  that  region. 

The  relative  measures  having  thus  been  obtained,  we  have  means  in 
the  concave  grating  of  obtaining  the  wave-lengths  of  the  lines  of  metals 


TABLE  OF  STANDARD  WAVE-LENGTHS  OF  THE  SPECTRAL  LIXES    553 

to  a  degree  of  accuracy  hitherto  unknown,  and  thus  of  solving  the  great 
problem  of  the  mathematical  distribution  of  these  lines. 

But  for  the  comparison  of  spectra,  as  measured  by  different  observers, 
some  absolute  scale  is  needed.  Hitherto  Angstrom  has  been  used. 
But  it  is  now  very  well  known  that  his  standard  measure  was  wrong. 
As  his  relative  measures  are  also  very  wrong,  I  have  concluded  that  the 
time  has  come  to  change  not  only  the  relative  measures,  but  the  abso- 
lute also.  To  this  end  Dr.  Louis  Bell  worked  in  my  laboratory  for 
several  years  with  the  best  apparatus  of  modern  science,  using  two 
glass  and  two  speculum  metal  gratings,  ruled  on  two  dividing  engines 
with  four  varieties  of  spacing,  three  of  which  were  incommensurable 
or  nearly  so,  with  two  spectrometers  of  entirely  different  form,  with  a 
variety  of  standard  bars  compared  in  this  country  and  in  Europe,  and 
with  a  special  comparator  made  for  the  measure  of  gratings.  His  result 
agrees  very  well  with  the  next  best  determination,  that  of  Mr.  C.  S. 
Peirce  of  the  U.  S.  Coast  Survey.  His  final  result  agrees  within  1  in 
50,000  with  his  preliminary  value.7  This  most  recent  value,  combined 
with  those  of  Peirce,  Miiller  and  Kempf,  Kurlbaum  and  Angstrom,  I 
have  adopted  to  reduce  my  final  results  to,  although  the  calculations  are 
made  according  to  Bell's  preliminary  value.  See  Appendix  A. 

But  it  rests  with  scientific  men  at  large  »to  adopt  some  absolute 
standard.  The  absolute  standard  is,  of  course,  not  so  important  as  the 
relative,  and  possibly  the  average  of  Angstrom  might  be  adopted.  But 
for  myself  I  do  not  believe  in  continuing  an  error  of  this  sort  indefi- 
nitely. All  the  results  obtained  before  the  concave  grating  came  into 
use  were  so  imperfect,  that  they  must  be  replaced  by  others  very  soon. 
With  a  good  concave  grating  one  man  in  a  few  years  could  obtain  the 
wave-lengths  of  the  elements  with  far  greater  accuracy  than  now 
known. 

As  an  aid  to  this  work,  I  have  constructed  the  table  of  wave-lengths 
given  in  this  paper,  which  have  already  been  adopted  by  the  British 
Association  and  by  the  most  noted  writers  of  Germany  and  other 
countries,  and  sincerely  hope  that  it  will  aid  in  the  work  of  making 
the  wave-length  of  a  spectrum  line  a  definite  quantity  within  a  few 
hundredths  of  a  division  of  Angstrom. 

ABSOLUTE  WAVE-LENGTH  OF  D 

The  following  is  an  estimate  of  the  absolute  wave-length  of  the  D  line 
from  the  best  determinations.  First,  I  shall  recalculate  the  portion  of 

1  American  Journal  of  Science,  1887. 


554  HENRY  A.  ROWLAND 

Dr.  Bell's  paper  s  in  which  the  calibration  of  the  grating  space  is  taken 
into  account.  The  method  of  correction  is  founded  on  the  principle 
that  a  linear  error  in  the  spaces  only  affects  the  focal  length,  and  not 
the  angle,  and  that  small  portions  which  have  an  error,  and  thus  throw 
the  light  far  to  one  side,  should  be  rejected.  The  corrections  Dr.  Bell 
has  used  seem  to  me  very  proper,  except  to  grating  III,  which  appears 
to  me  to  be  twice  too  great.  I  find  the  following : 

Grating.  D.  Correction.         Final  Values. 


I. 

5896-20 

—  •02 

5896-18 

II. 

5896-14 

+  -09 

5896-23 

III. 

5896-28 

-•06 

5896-22 

IV. 

5896-14 

-f  -03 

5896-17 

Mean  value,  5896-20. 

This  is  very  nearly  the  value  given  by  Dr.  Bell. 

The  determination  of  Mr.  C.  S.  Peirce  of  the  TJ.  S.  Coast  Survey  is 
certainly  a  very  accurate  one.  Dr.  Bell  and  myself  have  made  some 
attempts  to  calibrate  his  gratings,  which  he  sent  to  us  for  the  purpose, 
and  to  correct  for  the  scale  used  by  him.  There  is  great  uncertainty 
in  this  process,  as  we  had  only  a  portion  of  the  necessary  data.  The 
correction  of  his  scale  was  also  uncertain,  because  the  glass  scales  used 
by  him  may  have  changed  since  he  used  them,  in  the  manner  thermom- 
eter bulbs  are  known  to  change.  Correcting,  then,  only  for  the  error  of 
ruling  in  the  gratings,  we  have: 

Peirce's  value    5896-27 

Correction  *  — -07 


5896-20 

The  correction  for  the  scale  would  be  about  as  much  more  in  the  same 
direction,  provided  the  glass  scales  had  not  changed.  But  it  is  too 
uncertain  to  be  used,  although  I  have  applied  it  in  my  preliminary 
paper. 

Kurlbaum's  result,  made  with  two  good  modern  gratings,  has  the 
defect  that  the  gratings  were  42  and  43  mm.  broad,  quantities  which 
it  is  impossible  to  compare  accurately  with  a  metre.  His  small  objec- 
tives, one  inch  in  diameter,  could  not  take  in  light  from  the  whole 
grating,  and  so  the  grating  space  was  not  determined  from  the  portion 

8  American  Journal  of  Science,  1888. 

9  Bell,  American  Journal  of  Science,  May,  1888,  p.  365. 


TABLE  OF  STANDARD  WAVE-LENTGTHS  OF  THE  SPECTRAL  LINES    555 

of  the  grating  used.  The  spectrometer  was  poor,  and  the  errors  of 
the  grating  undetermined. 

Miiller  and  Kempf  used  four  gratings,  evidently  of  very  poor  quality, 
as  they  give  results  which  differ  1  in  10,000. 

The  result  of  Angstrom  was  a  marvel  at  the  time,  but  the  Nobert 
gratings  used  by  him  would  now  be  considered  very  poor.  Taking 
Thalen's  correction  for  error  of  scale,  we  have  for  the  mean  of  the  E 
lines  5269-80,  which  gives,  by  my  table  of  relative  wave-lengths,  D  = 
5895-81.  It  is  rather  disagreeable  to  estimate  the  relative  accuracy 
of  observations  made  by  different  observers  and  in  different  countries, 
but  in  the  interest  of  scientific  progress  I  have  attempted  it,  as  follows : 

o  Wt- 

Angstrom   5895-81  1 

Miiller  and  Kempf 5896-25  2 

Kurlbaum       5895-90  2 

Peirce      5896-20  5 

Bell      5896-20         10 

Mean,  5896-156  in  air  at  20°  and  760  mm.  pressure. 

This  must  be  very  nearly  right,  and  I  believe  the  wave-length  to  be 
as  well  determined  as  the  length  of  most  standard  bars.  Indeed,  fur- 
ther discussion  of  the  question  would  involve  a  very  elaborate  discus- 
sion of  standard  metres,  a  question  involving  endless  dispute.  I  think  we 
may  say  that  the  above  result  is  within  1  in  100,000  of  the  correct  value, 
which  is  very  nearly  the  limit  of  accuracy  of  linear  measurements.  This 
should  be  so,  as  the  probable  error  of  the  angular  measures  affects  the 
wave-length  only  to  1  in  2,000,000,10  and  hence  nearly  the  whole  accuracy 
rests  on  the  linear  measures. 

RESUME  OF  PROCESS  FOR  OBTAINING  RELATIVE  WAVE-LENGTHS 

1.  Determination  of  about  20  lines  in  the  visible  spectrum  by  coin- 
cidences by  Koyl." 

10  Is  not  a  grating  and  spectrometer  thus  the  best  standard  of  length,  and  almost 
independent  of  the  temperature?     Gratings  of  10  cm.  length  can   now  be   ruled  on 
my  new  engine  with  almost  perfect  accuracy,  as  seen  in  the  calibration  of  Grating 
IV  in  Dr.  Bell's  paper,  and  it  seems  to  me  the  time  has  come  for  their  practical  use. 

11  These  observations  of  Mr.  Koyl  were  finally  given  no  weight,  on  account  of  the 
inferior  apparatus  used.     They  serve  a  useful  purpose,  however,  as  checks  on  the 
other  work. 


556  HENEY  A.  ROWLAND 

2.  Determination  of  about  15  lines  in  the  visible  spectrum  by  coin- 
cidences by  Rowland,  using  several  gratings  of  21^  feet  focus. 

3.  Interpolation  by  direct  eye  observations  with  concave  gratings  of 
21£  feet  focus  and  micrometer  of  5  inches  range  and  of  almost  perfect 
accuracy. 

4.  Interpolation  by  means  of  flat  gratings. 

5.  Measurement  of  photographic  plates  from  10  to  19  inches  long, 
having  two  or  three  portions  of  the  spectrum  in  different  orders  on 
them,  thus  connecting  the  ultra  violet  and  blue  with  the  visible  spec- 
trum.    The  fact  that  nearly  the  same  values  are  obtained  for  the  violet 
and  ultra  violet  by  use  of  different  parts  of  the  visible  spectrum  proves 
the  accuracy  of  the  latter. 

6.  Measurement  of  photographic  plates  having  the  solar  visible  spec- 
trum in  coincidence  with  the  metal  lines  of  different  orders  of  spectra. 
The  fact  that  the  wave-lengths  of  the  metal  lines  are  very  nearly  the 
same  as  obtained  from  any  portion  of  the  visible  or  ultra  violet  spec- 
trum proves  the  accuracy  of  the  latter,  as  well  as  that  of  the  metallic 
wave-lengths. 

7.  Measurement  of  plates  having  metallic  spectra  of  different  orders. 

ADVANTAGES  OF  THE  PKOCESS 

The  only  other  process  of  obtaining  relative  wave-lengths  is  by 
means  of  angular  measures.  Supposing  the  angle  to  be  about  45°,  an 
error  of  1"  will  make  an  error  of  about  1  in  200,000  in  the  sine  of  the 
angle.  When  one  considers  the  changes  of  temperature  and  barometer 
measuring  on  one  line  and  then  another,  together  with  the  errors  of 
graduation,  it  would  be  a  difficult  matter  to  measure  this  angle  to  2", 
making  an  error  of  1  in  100,000,  or  about  ^  division  of  Angstrom. 

Looking  over  the  observations  of  principal  standards  made  under 
the  direction  of  Professor  Vogel  in  Potsdam,  with  very  poor  gratings 
but  an  excellent  spectrometer,  we  find  the  average  probable  error  to 
be  about  =b  T-g- uVinr  °f  ^ne  wave-length,  which  is  not  far  from  the  other 
estimate.  This  does  not  include  constant  errors,  and  I  believe  the 
probable  error  to  be  really  greater  than  this. 

The  method  of  coincidences  by  the  concave  grating  gives  far  superior 
results.  The  distance  to  be  measured  is  very  small,  and  the  equivalent 
focal  length  of  a  telescope  to  correspond  would  be  very  great  (21£ 
feet).  Furthermore,  all  changes  of  barometer  and  thermometer  are 
eliminated  at  once,  except  the  small  effect  on  the  dispersion  of  the  air, 
which,  when  known,  can  be  corrected  for.  It  is  not  to  be  wondered  at 


TABLE  OF  STANDABD  WAVE-LENGTHS  OF  THE  SPECTEAL  LINES    557 

that  this  method  is  far  superior  to  the  former.  The  probable  error  is, 
indeed,  reduced  to  ±  Tinnhnnr?  or  even  ^ess  ^or  the  best  lines.  Where 
the  interpolation  can  be  made  on  photographs,  this  probable  error  is 
scarcely  increased  at  all ;  but  even  taking  it  at  twice  the  above  estimate, 
the  method  even  then  remains  from  three  to  five  times  as  accurate  as 
that  of  angular  measurement.  Indeed,  the  impression  made  on  my 
mind  in  looking  over  Vogel's  Potsdam  observations  is,  that  my  tables 
and  process  are  ten  times  as  accurate  as  theirs;  and  I  think  any  careful 
student  of  both  processes  will  come  to  a  similar  conclusion. 

The  wonderful  result  that  can  be  obtained  by  the  measurement  of 
photographs  on  the  new  micrometer,  which  can  measure  plates  over 
twenty  inches  long,  is  partly  seen  in  the  table.  Where  the  distance  is 
only  a  few  inches,  the  wave-length  of  a  series  of  lines  can  be  measured 
with  a  probable  error  of  less  than  T^¥  of  a  division  of  Angstrom. 
Indeed,  a  series  would  determine  any  line  so  that  the  probable  error 
would  be  even  ±-0000001  of  the  whole.  This  would  detect  a  motion 
in  the  line  of  sight  of  ±  140  feet  per  second! 

From  the  tests  I  have  made  on  my  standards,  I  am  led  to  believe 
that  down  +o  wave-length  7000,  a  correction  not  exceeding  ±  -01 
division  of  Angstrom  (1  part  in  500,000),  properly  distributed,  would 
reduce  every  part  to  perfect  relative  accuracy. 

To  ascend  to  the  next  degree  of  accuracy  would  need  many  small  cor- 
rections which  would  scarcely  pay.  It  is  reasonable  to  assume  that  a 
higher  degree  of  accuracy  will  not  be  needed  for  twenty-five  years,  as 
the  present  degree  is  sufficient  to  distinguish  the  lines  of  the  different 
elements  from  one  another  in  all  cases  that  I  have  yet  tried. 

DETAILS  OF  WOEK 

To  reduce  all  the  observations  in  a  given  region  to  one  line,  relative 
observations  extending  a  short  distance  either  side  of  the  standard 
region  are  necessary.  Thus  the  mean  of  4215  and  4222  can  be  taken  as 
the  standard,  and,  if  only  one  is  observed,  it  can  be  reduced  to  the 
standard  by  a  correction  -f  3-358  or  — 3-358.  But  it  is  not  necessary 
to  take  the  mean  of  the  lines  as  a  standard,  as  any  one  of  them  may 
be  so  taken,  or  even  any  other  point  where  there  is  no  line,  as  the  point 
is  only  to  be  used  in  the  mathematical  work,  and  finally  disappears 
altogether. 

Table  II  gives  results  of  this  nature.  The  letters  at  the  top  of  each 
series,  e,  g,  h,  ;,  etc.,  are  the  arbitrary  names  of  the  standards.  The 
first  columns  refer  to  the  series  of  observations,  "  Co."  being  observa- 


558  HENRY  A.  KOWLAND 

tions  made  at  the  time  of  measuring  the  coincidences;  Plates  9,  10,  etc., 
refer  to  photographic  plates;  C,  R,  etc.,  refer  to  the  series  as  given  in 
the  final  table,  although  they  may  differ  very  slightly  from  the  latter, 
as  the  final  table  contains  slight  corrections.  Figures  in  parentheses 
are  the  number  of  readings.  The  photographs  were  usually  measured 
from  two  to  six  times. 

Table  III  gives  the  first  series  of  observations  made  in  1884  with 
a  21£  foot  concave,  14,436  lines  to  the  inch.  The  numbers  taken  for 
the  standards  are  only  preliminary,  and  agree  as  nearly  as  practicable 
with  my  Table  of  Preliminary  Standards.  As  only  differences  are 
finally  used,  they  are  sufficiently  near.  The  fractions  give  the  order 
of  the  spectra  observed. 

Thus,  the  first  observation  on  Ji  and  t  is  worked  up  as  follows : 

4691-590  7027-778 

Correction  to  standard.  .    . .     —626  +2-785 


4690-964  7030-563 

4691-590  4690-326  7027-778 

—  626  +-626  +2-785 

4690-964  4690-952  7030-563 


4691-590 
—  626 

7040-092 
—9-547 

4690-964 

7030-545 

Weight. 
1 

h 

4690-964 

t 
7030-563 

2 

4690-958 

7030-563 

2 

4690-964 

7030-545 

4690-962  7030-556 

The  equation  3  Ji  —  2  t  =  11-774  then  readily  follows. 

Tables  IV  and  V  are  from  a  21£  foot  concave  with  7218  lines  to  the 
inch,  used  on  both  sides,  and  thus  equivalent  to  two  gratings  used  on 
one  side  only.  I  have  not  yet  determined  theoretically  whether  the 
minor  errors  are  perfectly  neutralized  in  this  manner,  but  it  would  evi- 
dently have  a  tendency  in  this  direction. 

The  photographic  coincidences  are  given  in  the  main  table  (X),  as 
not  only  the  standards  are  compared  by  this  process,  but  whole  regions 


TABLE  OF  STANDARD  WAVE-LEXGTHS  OF  THE  SPECTRAL  LINES    559 

are  photographed  side  by  side.  •  Both  a  10,000  and  a  20,000  concave 
were  used  for  this  work. 

Table  VI  gives  the  collection  of  the  equations  relating  to  the  visible 
spectrum,  the  final  results  being  given  in  Table  VII. 

The  proper  method  of  treating  these  twenty-six  equations  would  be 
by  the  method  of  least  squares.  But  it  would  be  so  long  and  tedious, 
and  so  liable  to  mistake,  that  I  have  adopted  the  method  of  starting  at 
one  point  and  going  forward  until  all  the  equations  are  reached.  Thus 
(Table  VII),  starting  with  an  assumed  value  of  e,  we  can  calculate  p,  n, 
1, 1c,  ;',  o,  t. 

Using  the  eight  values  thus  found  once  more,  from  p  we  have  g,  Jc,  Z; 
from  n  we  have  h,  t,  g;  with  similar  results  for  the  others.  Collecting, 
we  then  have  e,  f,  g,  h,  j,  Tc,  I,  n,  o,  p,  q,  t.  Using  these  once  more,  we 
have  values  of  all  the  standards.  We  could  do  this  any  number  of 
times,  keeping  the  proper  weights,  but  I  thought  this  number  was  suffi- 
cient. The  second  calculation  is  done  in  the  same  manner,  starting  from 
o,  however,  and  is  given  in  Table  VIII. 

The  results  of  the  two  calculations  are  given  in  Table  IX.  Taking 
the  mean  and  adding  the  results  of  local  micrometer  measurements,  we 
obtain  the  column  marked  "  Eelative  Wave-Lengths." 

Reducing  these  values  by  1  part  in  200,000,  we  make  them  agree 
with  the  absolute  value  of  the  standard  as  before  agreed  upon.  Thus 
the  column  of  standards  is  obtained  for  use  in  the  visible  spectrum. 

For  ordinary  interpolation  with  the  short  and  imperfect  micrometers 
generally  used,  and  working  with  a  flat  grating  and  a  spectrum  not  nor- 
mal, the  standards  would  be  too  far  apart.  But  with  such  a  long  and 
perfect  micrometer  as  I  use,  and  working  with  the  normal  spectrum  of 
a  concave  grating,  they  are  entirely  sufficient.  However,  I  have  filled 
in  the  interval  from  7030  to  7621  by  some  extra  substandards  at  7230. 

The  micrometer  for  eye  observations  has  a  range  of  five  inches,  and 
the  machine  for  measuring  photographs  of  more  than  twenty  inches, 
both  with  practically  perfect  screws  made  by  my  process.  The  eye  ob- 
servations are  not  an  interpolation,  in  the  ordinary  sense,  between  the 
standards,  but  the  whole  series  is  continuous,  the  micrometer  observa- 
tions overlapping  so  that  they  join  together  to  any  length  desired.  By 
measuring  from  the  D  line  in  one  spectrum  to  the  D  line  in  the  next, 
and  including  the  overlapping  spectra,  no  further  standards  would  be 
necessary,  as  all  the  lines  of  the  spectrum  would  be  determined  at  once, 
knowing  the  wave-length  of  the  D  line.  But  I  usually  plotted  the 
difference  of  the  standards  from  the  micrometer  determination,  usually 


560  HEXEY  A.  ROWLAND 

o 

amounting  to  less  than  one-  or  two-tenths  of  a  division  of  Angstrom,  and 
so  corrected  the  whole  series  to  the  standards.  Sometimes  two,  or  even 
three,  overlapping  spectra  were  measured  at  once. 

To  make  Table  X,  the  following  process  was  used: 

1st.  From  all  the  observations  at  my  disposal,  I  determined  a  few 
more  lines  around  the  main  standards,  and  put  them  in  the  second  col- 
umn, marked  St.,  so  that  I  should  have  a  greater  number  of  points  to 
draw  my  curve  through. 

2d.  I  then  put  down  a  few  observations  which  were  made  by  meas- 
uring overlapping  spectra. 

3d.  Then  the  main  eye  observations  were  put  down  as  follows: — 

p  extending  from  4071  to  7040,  3d  spectrum,  14,436  grating. 
q  «  "          4999  to  7035,          "          "          "          "          " 

0  "  "         4859  to  7040,          "          "          "          "          " 
c           "  "         4859  to  6079,  (fragmentary^. 

"  «  6855  to  6909,  2d  spectrum,   14,436  grating. 

«  «  5162  to  7201,          "         "         "         "         " 

«  «  5742  to  7628,  1st  spectrum,  14,436  grating. 

1  "  "  6065  to  7671,         "         "         '<         "         " 
C'         «'  "  6855  to  7714,  plane  grating. 

R'  '<  "  5139  to  5296,  2d  spectrum,  14,436  grating. 

t  "  "  6499  to  6929,  "         "  "         "         " 

a  "  "  6278  to  6322,  "         "  "         "         " 

E  "  "  4048  to  4824,  "         "  "         "         " 

4th.  The  series  of  photographs  containing  coincident  spectra,  mostly 
on  plates  so  short  as  to  make  the  spectra  nearly  normal,  were  now  in- 
troduced. The  plates  were  numbered  from  1  to  20,  ISTos.  7  and  19  being 
rejected  because  imperfect. 

This  series  of  plates  was  obtained  by  photographing  a  narrow  strip 
of  one  spectrum  between  two  strips  of  another,  the  overlapping  spectra 
being  separated  by  absorption.  In  order  to  eliminate  any  change  in 
the  apparatus  during  the  exposure,  the  latter  was  divided  into  three 
parts,  the  first  and  third  being  given  to  the  same  spectrum. 

This  series  of  plates  gives  me  a  continuous  series  of  photographs  from 
wave-length  7200  to  the  extremity  of  the  ultra  violet  spectrum,  each 
part  being  interwoven  with  one  or  two  other  parts  of  the  spectrum. 
Thus,  wave-length  3900  comes  from  5200  and  5850  with  only  a  slight 
difference  in  values.  There  is  scarcely  any  difference  in  any  wave- 
length as  derived  from  any  portion  of  the  spectrum;  thus  proving  the 
accuracy  of  the  whole  table.  The  description  of  the  plates  is  as  follows: 


TABLE  OF  STANDARD  WAVE-LENGTHS  OF  THE  SPECTRAL  LINES    561 

PHOTOGRAPHIC  COINCIDENCES 
CONCAVE,  GRATING  10,000  LINES  TO  THE  INCH 


Spectra 

Plate 

Standard 

f 

1 

4407  to 

4643  and 

3331  to 

3486 

f,9 

it 

2 

4637  « 

4890  i' 

3478  « 

3667 

h>J 

11 

3 

4823  " 

5068  " 

3612  « 

3805 

j,  ft 

tt 

4 

4919  " 

5133  " 

3683  " 

3875 

j,  * 

M 

5 

5050  'i 

5288  " 

3780  i« 

4005 

k,l 

II 

6 

5097  " 

5333  " 

3821  " 

4157 

ft,  I 

it 

7 

it 

8 

5242  1  1 

5477  " 

3937  " 

4121 

Z,  m 

tt 

9 

5405  " 

5662  'i 

4073  " 

4222 

m,  n,  e 

ll 

10 

5582  'i 

5816  « 

4293  « 

4376 

n,f 

It 

11 

5782  » 

5934  " 

4343  " 

4447 

°>f 

II 

12 

4157  " 

4267  " 

3129  " 

3218 

e 

II 

13 

4157  " 

4325  " 

3094  " 

3246 

e 

ll 

14 

3218  " 

3318 

ll 

15 

4391  i' 

4643  'i 

3292  " 

3478 

f,ff 

i 

16 

5788  « 

5977  " 

3864  " 

3977 

0 

17 

5788  « 

5977  " 

3864  " 

3984 

o 

ll 

18 

5715  " 

5977  » 

3875  " 

3977 

0 

ll 

19 

20 


5853 


6569 


3024    "    3267 


Plates  7,  14  and  19  were  imperfect,  owing  to  clouds  passing  over  the 
sun,  although  a  part  (3218  to  3318)  of  Plate  14  was  used  for  interpola- 
tion, as  observations  were  scanty  in  that  region. 

It  is  seen  that  some  of  the  plates  have  only  one  standard  upon  them. 
With  a  plane  grating  it  would  be  impossible  to  work  them  up,  but  with 
the  normal  spectrum  produced  by  the  concave  grating  only  one  is 
necessary,  as  the  multiplier  to  reduce  readings  to  wave-lengths  is  nearly 
a  constant.  In  working  up  a  whole  series  of  plates,  there  is  no  trouble 
in  giving  a  proper  value  to  the  constant  for  any  plate  in  the  series 
which  has  only  one  standard. 

Plate  17  was  measured  twice  by  two  dividing  engines,  and  as  it  was 
a  specially  good  plate,  each  measure  was  given  a  weight  equal  to  one 
of  the  other  plates.  The  principal  error  to  be  feared  in  these  plates  is 
a  displacement  of  the  instrument  between  the  time  of  the  exposure  on 
the  two  spectra.  This  was  guarded  against  by  the  method  above  de- 
scribed. In  Plates  17  and  20  there  was  a  portion  of  the  plate  on  which 
both  the  spectra  fell  all  the  time,  and  thus  gave  a  test  of  the  displace- 
ment. This  was  found  to  be  zero.  The  other  plates  overlap  so  much 
that  there  are  generally  two  or  more  determinations  of  each  line.  A 
36 


562  HEXRY  A.  EOWLAXD 

comparison  of  these  values  shows  little  or  no  systematic  variation  in  the 
different  plates  exceeding  ^  division  of  Angstrom.  Plates  16,  17,  18, 
and  5,  6,  8,  all  give  the  region  3900  as  derived  from  5200  and  5850,  and 
thus  give  a  test  of  the  relative  accuracy  of  these  latter  regions.  It  is 
seen  that  the  two  results  of  the  region  3900  differ  by  about  -015  division 
of  Angstrom.  Were  the  wave-lengths  of  the  region  5170  to  5270  to  be 
increased  by  -020  the  discrepancy  would  cease.  The  amount  of  this 
quantity  seems  rather  large  to  be  accounted  for  by  any  displacement  of 
the  spectra  on  the  plates,  but  still  this  may  be  the  cause.  Again,  it  is 
possible  that  different  gratings  may  give  this  difference  of  wave-length 
from  the  cause  I  have  mentioned  above.  This  cause,  as  I  have  shown, 
exists  in  the  same  degree  in  plane  gratings  as  in  concave.  I  have  not 
attempted  to  correct  it  in  this  case,  but  have  simply  taken  the  mean  of 
the  two  values  for  the  region  3900,  and  so  distributed  the  error.  This 
is  the  greatest  discrepancy  I  have  found  in  the  results  except  in  the 
extreme  red. 

Thus  the  region  3100  to  3200,  a  portion  for  which  Plate  20  is  to  be 
relied  upon,  gives  the  wave-length  of  the  ultra  violet  -01  division  of 
Angstrom  higher  from  the  region  4200  than  from  6300.  As  the  dis- 
crepancies in  this  region  before  the  invention  of  the  concave  grating  were 
often  a  whole  division  of  Angstrom,  I  have  regarded  this  result  as  satis- 
factory. Indeed,  until  we  are  able  to  make  all  sorts  of  corrections  due 
to  the  change  in  the  index  of  refraction  of  the  air  with  the  Barometer 
and  thermometer,  it  seems  to  me  useless  to  attempt  further  accuracy. 

With  the  advent  of  photographic  plates  into  the  table,  especially  the 
longer  ones  required  for  metallic  spectra,  it  becomes  necessary  to  cor- 
rect them  for  the  departure  from  the  normal  spectrum  due  to  the  use 
of  long  plates.  The  plates  in  the  box  are  bent  to  the  arc  of  a  circle  of 
radius  r.  When  afterwards  straightened  we  measure  the  distance  by  a 
linear  dividing  engine.  Hence,  what  we  measure  is  the  arc  with  radius  r. 
Let  «  and  ft  be  the  angles  of  incidence  and  diffraction  from  the  grating. 
We  have  then  to  express  ft  in  terms  of  d.  Let  X  be  the  wave-length, 
and  n  and  N  the  number  of  lines  on  the  grating  to  1  mm.  and  the  order 
of  the  spectrum  respectively.  Then 

A  =  — T7  (sin  a  +  sin  /?  ) ; 

nN 

%r         <5         / 

sin  j3  =  -Tr  sin  —  cos  [r  +  p  •—  ~ 
H  A  \ 

In  these  formula?  a  is  the  angle  to  the  centre  of  the  photographic 
plate,  and  ft  and  d  are  also  measured  from  the  centre,  f  is  the  angle 


TABLE  OF  STANDARD  WAVE-LENGTHS  OF  THE  SPECTRAL  LINES    563 

between  the  radius  from  the  centre  of  the  photographic  plate  and  the 
line  drawn  from  that  point  to  the  centre  of  the  grating.  When  prop- 
erly adjusted,  f  will  be  zero.  Also,  we  make  2  r  =  R,  to  obtain  perfect 
focus  throughout.  So  that 

/  =  — ^  (sin  «  4-  sin  -g-j . 

nN\  2  / 

Calling  ^Othe  wave-length  at  the  centre  of  the  plate,  we  have  ap- 
proximately 


* 

The  first  quantity,  - „,  is  the  value  of  / — ^0,  assuming  the  spectrum  to 

^  ?l  jLJ 

be  normal.  The  last  term  is  the  required  correction  expressed  in  terms 
of  the  provisional  wave-length.  The  correction  in  actual  practice  has 
been  made  from  a  plot  of  the  correction  on  a  large  scale,  and  never 
amounted  to  more  than  a  few  hundredths  of  a  division  of  Angstrom,  even 
for  the  longest  plate. 

In  two  or  three  plates  the  camera  was  displaced,  so  that  7-  had  a  value. 
In  such  cases  no  attempt  was  made  to  measure  f  ,  but  the  plates  were 
only  used  for  local  interpolation  by  drawing  a  curve  through  certain 
points  used  as  substandards. 

These  substandards  Mere  principally  used  for  working  up  the  last 
set  of  photographic  plates  containing  the  solar  spectrum  and  the  metal 
spectra  of  the  same  or  higher  orders,  or  both.  Some  of  them  contained 
three  metallic  spectra. 

Thus  the  region  3900  in  the  solar  spectrum  has  been  obtained  from 
both  wave-lengths  5200  and  5850.  The  mean  of  these  gave  values  of 
the  substandards  for  working  up  the  plates  taken  at  this  point,  and 
containing  also  metallic  lines  at  2700. 

Again,  the  boron  lines  2496  and  2497  have  been  obtained  from  the 
regions  4800,  3200  and  3600.  The  mean  values  give  substandards  for 
working  up  the  metallic  spectra  of  that  region.  Also  the  near  coinci- 
dence in  the  values  of  the  wave-lengths  of  these  lines  indicate  the  rela- 
tive accuracy  of  the  regions  2496,  3200,  3600,  and  4800. 

The  use  of  these  substandards  is  as  follows:  The  photographic  plates, 
mostly  19  inches  long,  were  measured  mostly  on  a  machine  giving  wave- 
lengths direct.  The  differences  of  the  results  from  the  substandards 
were  then  plotted  on  a  paper  having  the  curve  of  correction  for  length 
upon  it  in  such  a  way  that  the  final  marks  should  theoretically  be  a 
straight  line.  This  was  actually  the  case  in  all  but  a  few  plates,  in 


564  HENKY  A.  ROWLAND 

which  the  camera  was  displaced.  A  straight  line  was  then  passed  through 
all  the  marks  as  nearly  as  may  be,  and  the  correction  taken  off.  This 
correction  could  thus  be  obtained  to  T^TF  division  of  Angstrom,  and 
amounted  to  only  a  few  hundredths  of  a  division  at  most.  Possibly  T10- 
division  of  Angstrom  was  the  greatest  correction  required  for  length. 

In  this  way  each  plate  represents  the  average  of  all  the  wave-length 
determinations  throughout  its  extent,  and  will  not  admit  of  any  correc- 
tion save  a  linear  one,  should  such  ever  be  required  in  working  over  the 
table  again. 

In  every  plate  having  a  solar  and  metallic  spectrum  upon  it,  there  is 
often — indeed  always — a  slight  displacement.  This  is  due  either  to 
some  slight  displacement  of  the  apparatus  in  changing  from  one  spectrum 
to  the  other,  or  to  the  fact  that  the  solar  and  the  electric  light  pass 
through  the  slit  and  fall  on  the  grating  differently.  In  all  cases  an  at- 
tempt was  made  to  eliminate  it  by  exposing  on  the  solar  spectrum,  both 
before  and  after  the  axe,  but  there  still  remained  a  displacement  of 
TTTF  to  yf-g-  division  of  Angstrom,  which  was  determined  and  corrected 
for  by  measuring  the  difference  between  the  metallic  and  coinciding  solar 
lines,  selecting  a  great  number  of  them,  if  possible. 

The  changes  from  sun  to  arc  light  are  much  more  extensive  than  from 
one  order  of  solar  spectrum  to  another.  In  two  cases  I  have  tested  the 
latter  and  found  no  displacement,  and  have  no  fear  that  it  exists  in 
the  others. 

In  working  up  the  plates,  I  have  started  at  the  plates  whose  centre  is 
at  wave-length  4600,  and  proceeded  either  way  from  that  point.  For 
this  purpose  I  have  used  the  plates  originally  obtained  for  metallic 
spectra,  generally  using  the  lines  due  to  the  impurities.  The  method, 
I  believe,  is  obvious  from  the  table.  For  a  long  region  no  substandard^ 
are  necessary,  but  are  used  whenever  they  become  so. 

[The  tables  are  omitted.! 


52 

THE  SEPAKATION  OF  THE  EAEE  EAETHS 

[Johns  Hopkins  University  Circulars,  No.  112,  pp.  73,  74,  1894] 

In  the  course  of  several  years'  investigations  of  the  so-called  "  rare 
earths,"  such  as  yttrium,  erbium,  holmium,  cerium,  etc.,  I  have  devised 
several  methods  for  their  separation.  I  wish  to  give  an  account  of  these 
now,  and  hope  soon  to  be  able  to  publish  a  complete  description  of  my 
work  and  its  results. 

It  was  evident  very  early  in  the  work  that  cerium,  lanthanium,  praseo- 
dymium, neodymium  and  thorium  differed  from  the  yttrium  group,  and 
I  have  seen  no  reason  to  suppose  that  they  can  be  divided  any  further. 
All  of  these  "earths"  appear,  in  varying  proportions,  in  such  minerals  as 
gadolinite,  samarskite,  yttrialite,  cerite,  etc.  Besides  the  elements  of 
the  cerium  group  here  present  there  are  at  least  seven  other  substances. 
For  the  present  I  shall  speak  of  them  as 

a,  6,  i,  d,  h,  n,  c,  fc. 
Their  properties  are  as  follows: 

PKOPEBTIES  OF  ELEMENTS 

Substance  a 

This  is  the  principal  element  of  yttrium  and  may  possibly  be  divided 
into  two  in  the  future,  as  I  have  observed  a  variation  in  the  arc  spec- 
trum on  adding  potash  or  soda.  However,  this  is  no  more  evidence  than 
occurs  in  the  case  of  iron  or  zirconium.  I  give  a  process  below  for  pro- 
ducing this  pure. 

Properties. — No  absorption  bands.  Oxalate  and  oxide  pure  white. 
It  occurs  in  the  sun.  Its  properties  are  those  of  yttrium  as  hitherto  ob- 
tained, but  I  am  the  first  to  obtain  it  with  any  approach  to  purity. 

Mixture  of  I,  i  and  d 

These  seem  to  be  the  principal  ingredients  in  so-called  "erbium." 
Oxalate  is  red.     Oxide  is  pure  white.     Absorption  band  is  that  of 
"erbium."     It  colors  the  electric  arc  green,  and  shows  the  "erbium" 
emission  bands  on  heating  white  hot.    The  substance  b  is  strong  in  gado- 


566  HENRY  A.  EOWLAISTD 

Unite  and  weak  in  samarskite.  The  solution  has  the  absorption  bands 
of  "  erbium  "  and  most  of  these  seem  to  belong  to  &  rather  than  i.  How- 
ever, we  can  readily  prove  that  the  absorption  bands  of  erbium  belong 
to  two  substances,  as  we  can  produce  a  decided  variation  in  it. 

I  cannot  reconcile  this  with  my  spectrum  work  without  assuming  a 
fourth  ingredient  in  "  erbium." 

Substance  &  is  in  the  sun,  but  not  i.  With  6  and  i  the  substance  d 
always  occurs. 

Substance  d 

This  is  the  principal  impurity  of  a  sample  of  yttrium,  kindly  furnished 
me  by  Dr.  Kriiss,  which  my  process  of  making  yttrium  separates  out.  It 
has  not  been  obtained  pure,  but  occurs  strongly  in  the  yellow  part  of 
the  oxides.  It  is  in  the  sun. 

By  aid  of  ferrocyanide  of  potassium  the  substance  a  can  be  obtained 
pure  from  d.  With  this  exception  d  occurs  in  all  the  preparations  of 
the  yttrium  group  and  cannot  be  separated  from  &,  i,  c,  n,  h,  or  any 
of  the  other  substances.  Indeed,  I  have  found  it  in  some  specimens  of 
cerium  and  lanthanium,  although  in  traces  only. 

On  account  of  the  trouble  caused  by  it  and  its  universal  presence,  I 
propose  the  name  demonium  for  it. 

Its  principal  spectrum  line  is  at  w.  1.  4000-6  nearly. 

Substance  h 

This  occurs  mainly  in  samarskite.  Hints  toward  its  separation  will 
be  given  below,  but  I  have  otherwise  obtained  none  of  its  properties. 

Substances  n,  Ic  and  c 

These  always  occur  with  d  and  form  a  group  intermediate  between  the 
yttrium  and  cerium  groups.  They  can  be  separated  from  these  by  sul- 
phate of  potassium  or  sodium  by  always  taking  in  intermediate  portions 
of  the  precipitate.  They  seem  to  have  a  weak  absorption  spectrum  in 
the  visible  spectrum  and  strong  in  the  ultra  violet,  especially  If. 

Chemical  Separation 

The  first  process  that  suggests  itself  is  that  by  the  sulphates  of  soda 
or  potash.  This  is  the  usual  method  for  separating  the  cerium  from 
the  yttrium  groups.  When  the  solution  of  earth  and  the  sulphate 
solution  are  both  hot  and  concentrated,  everything  except  some  scan- 
dium comes  down.  When  done  in  the  cold  with  weaker  solutions,  there 
is  more  or  less  complete  separation  of  the  cerium  group.  Let  the  mixed 


THE  SEPARATION  OF  THE  RARE  EARTHS  567 

earths  be  dissolved  in  a  very  slight  excess  of  nitric  acid  and  diluted  some- 
what (possibly  1  k.  to  2  or  3  litres).  Place  in  a  warm  place,  add  lumps 
of  sulphate  of  soda,  and  stir  until  no  more  will  dissolve.  Continue  to 
add  and  stir  for  a  day  or  two  until  the  absorption  lines  of  neodymium 
disappear  from  the  solution.  Filter  off  and  call  the  solution  No.  1. 
Add  caustic  potash  to  the  precipitated  sulphates  and  wash  so  as  to  leave 
the  oxides  once  more.  Dissolve  in  nitric  acid  and  precipitate  again  with 
sulphate  of  soda,  calling  the  nitrate  No.  2.  Proceed  in  this  way  pos- 
sibly 10  or  more  times.  The  nitrates  contain  less  and  less  earths;  and 
the  precipitate  is  more  and  more  the  pure  cerium  group;  but  a  dozen 
precipitations  still  leave  some  impurity. 

The  portions  1,  2,  3,  etc.,  show  decreasing  "erbium"  absorption  bands, 
and  the  spectrum  shows  that  the  substances  a,  6,  d,  i  are  gradually  sepa- 
rated out  with  parts  1,  2,  etc.,  while  the  numerous  fine  lines  belonging  to 
d,  n,  c,  etc.,  with  the  cerium  group,  fill  the  spectrum  of  the  portions 
8,  9,  10,  etc.  This  intermediate  group  has  only  very  weak  absorption 
bands  and  evidently  has  three  or  four  elements  in  it,  as  I  have  produced 
at  least  that  number  of  variations  in  its  spectrum.  The  group  can  be 
obtained  fairly  free  from  «,  5,  and  i,  but  the  substance  d  persists  in  all 
the  filtrates  and  in  the  precipitated  cerium  group  also.  This  interme- 
diate group  d,  n,  etc.,  seems  to  be  in  greater  proportion  in  samarskite 
than  in  gadolinite,  and  there  seem  to  be  more  elements  in  samarskite 
than  in  gadolinite.  One  of  these  I  have  called  li. 

The  oxides,  especially  for  samarskite,  are  very  yellow  and  dark. 

Sulphate  of  potash  has  a  decided  action  in  separating  a  and  i  from  6, 
a  and  i  coming  down  first.  After  two  months,  the  solution  gradually 
drying,  the  proportion  of  &  to  a  in  the  filtrate  increased  many  times. 
Sulphate  of  soda  has  an  action  of  the  same  kind,  but  much  weaker. 
After  leaving  two  months  over  sulphate  of  potash  and  soda,  the  follow- 
ing was  the  result  of  analysis  of  the  soluble  part  as  compared  with  the 
original  mixture: 

Sulphate  of  Potash.  Sulphate  of  Soda. 

Ge.,  La.,  etc.  o  o 

a  Weak  Medium  weak 

b  Much  stronger  Stronger 

c  oo 

d  Unchanged  Unchanged 

t  Weaker  Medium  strong 

o  Stronger  Weaker 

The  oxide  of  the  members  of  this  group  which  are  only  slightly  pre- 
cipitated by  the  sulphates  of  soda  and  potash  is  pure  snow-white,  and 
hence  those  of  &  and  i  must  be  so. 


568  HENRY  A.  KOWLAND 

The  substance  d  comes  down  slightly  sooner  than  a  by  sulphate  of 
soda,  but  slightly  slower  by  sulphate  of  potash.  Hence,  in  purifying 
yttrium  (substance  a)  for  the  last  time  from  the  ce.  group,  sulphate  of 
potash  will  increase  d  in  the  filtrate  and  sulphate  of  soda  will  decrease  it. 

Action  of  oxalic  acid 

When  the  oxalates  of  the  mixed  earths,  free  from  the  ce.  group,  are 
boiled  in  water  to  which  nitric  acid  is  added,  they  are  more  or  less  dis- 
solved, leaving  a  coarse,  heavy,  red  oxalate  yielding  a  pale  yellow  oxide. 
The  nitrate,  set  aside  to  cool,  deposits  more  of  the  oxalates  and  leaves  a 
filtrate  which  contains  several  of  the  unknown  elements,  as  also  what  re- 
mains of  the  ce.  group.  On  separating  the  ce.  group  the  remainder  is 
quite  different  from  the  heavy  red  oxalate,  but  there  is  far  from  complete 
separation.  The  analysis  showed  the  following: 

a,  &,  c,  d,  li,  i,  n. 

I  have  not  found  the  separation  particularly  useful,  and  it  seems  to  be 
more  apparent  than  real  as  tested  by  the  spectroscope. 

Ferrocyanide  of  potassium 

This  is  the  most  useful  process  and  easily  separates  the  element  a, 
pure  and  free  from  all  others.  To  obtain  pure  a  from  the  mineral  gado- 
linite,  Fergusonite  or  Samarskite: 

First  obtain  the  crude  mixed  earths  in  the  usual  manner.  Then  sepa- 
rate the  cerium  group  as  usual  until  the  absorption  bands  of  neodymium 
no  longer  appear.  For  the  complete  separation  without  loss  this  must 
be  done  several  times,  as  much  of  the  yttrium  group  is  carried  down 
with  the  first  precipitate,  as  we  have  before  seen. 

The  separation  of  the  yttrium  (a)  from  the  other  elements  is  effected 
by  precipitating  the  latter  from  a  weak  acid  solution  by  ferrocyanide  of 
potassium.  For  this  purpose  the  filtrate,  after  separating  the  cerium 
group,  can  be  used  at  once  by  slightly  acidulating  with  nitric  acid,  dilut- 
ing and  adding  a  weak  solution  of  ferrocyanide  of  potassium.  No  pre- 
cipitate should  appear  at  once,  but  by  standing  for  an  hour  or  so  some 
will  come  down.  Add  more  ferrocyanide  of  potassium  and  repeat  until 
the  filtrate  no  longer  shows  the  bands  of  so-called  erbium.  After  this 
it  is  best  to  precipitate  with  oxalic  acid  or  oxalate  of  potassium  and 
ignite  the  precipitate  so  as  to  get  the  earth.  Dissolve  this  in  nitric  acid 
and  add  only  water  enough  to  make  a  very  concentrated  syrupy  solution. 


THE  SEPARATION  OF  THE  RARE  EARTHS  569 

Place  in  a  beaker  at  least  three  inches  in  diameter  and  examine  with  a 
spectroscope  of  low  power  for  absorption  bands.  Probably  the  bands  of 
neodymium  and  "  erbium  "  will  appear.  Separate  the  first  by  sulphate 
of  sodium  as  usual,  and  the  last  by  ferrocyanide  of  potassium  from  an 
acid  solution  as  above.  The  filtrate  will  then  contain  the  pure  yttrium 
a,  whose  calcined  oxalate  will  be  pure  white  without  trace  of  yellow. 
After  separation  of  iron,  calcium,  and  possibly  manganese,  the  earth  will 
be  a  pure  element  as  far  as  I  can  tell  spectroscopically.  However,  like 
Zr,  Fe  and  many  other  substances,  the  addition  of  Na  or  K  to  the  elec- 
tric arc  while  obtaining  the  spectrum  will  change  the  intensity  of  cer- 
tain lines  of  the  spectrum,  while  others  are  unchanged.  If  this  is  con- 
sidered as  evidence  of  the  existence  of  two  elements,  then  the  same  evi- 
dence will  apply  to  Fe  and  Zr.  The  reason  for  believing  that  the  sub- 
stance thus  found  is  an  element  is  based  on  the  fact  that  its  spectrum 
remains  unaltered  in  all  minerals  and  after  all  chemical  operations  that 
I  have  been  able  to  devise.  Furthermore,  I  believe  that  the  new  pro- 
cess is  not  only  more  easy  than  any  other,  but  also  that  it  has  given  a 
single  element  for  the  first  time,  as  it  eliminates  the  element  d.  The 
yield  will  of  course  depend  on  the  amount  of  purity  required.  From  the 
earths  of  gadolinite  about  one-tenth  of  quite  pure  yttrium  (a)  can  be  ob- 
tained and  about  one-twentieth  of  very  pure. 

I  have  determined  spectroscopically  that  when,  by  the  above  process, 
the  absorption  band  of  "erbium"  at  last  disappears  from  3  in.  of  strong 
solution,  all  the  other  elements  have  also  disappeared. 

By  taking  the  first  precipitate  several  times  by  ferrocyanide  of  potas- 
sium from  an  acid  solution,  a  mixture  of  many  elements  is  obtained 
which  contains  much  of  that  element  to  which  the  so-called  "erbium" 
band  is  due.  By  dissolving  a  weighed  quantity  of  this  mixture  in  nitric 
acid  and  water  and  examining  the  band  spectrum,  I  have  determined  the 
limit  when  the  band  can  no  longer  be  seen.  Thus  I  have  proved  that 
when  the  band  vanishes  from  3  inches  of  concentrated  syrupy  solution 
of  yttrium  there  cannot  exist  in  it  more  than  -|  per  cent  of  the  mixed 
element  as  compared  with  the  yttrium,  and  there  is  probably  less. 

I  have  not  found  ferrocyanide  of  potassium  useful  in  the  further 
separation  of  the  elements,  but  only  in  separating  out  a  from  the  others. 

When  the  neodymium  band  has  disappeared  by  use  of  sulphate  of 
sodium,  all  the  other  elements  of  the  cerium  group  have  disappeared. 
The  element  thorium  is  sometimes  present  in  the  crude  earths,  but  dis- 
appears after  a  while  from  the  purified  earths.  The  conditions  for  its 
disappearance  I  have  not  determined. 


570  HENRY  A.  ROWLAND 

The  elements  which  persist  to  the  last  by  the  ferrocyanide  process  are 
&  and  i,  while  by  Kriiss'  process  the  element  d  persists  the  longest.  As 
&  -J-  i  has  an  absorption  spectrum  and  d  probably  not,  the  test  of  purity 
by  absorption  bands  is  very  complete  in  the  new  process. 

Note. — For  help  in  this  investigation  my  thanks  are  due  to  a  large  number  of  gen- 
tlemen. Professor  Schapleigh  has  sent  me  a  large  collection  of  substances,  Mr. 
Hidden,  Professor  Wolcott  Gibbs,  and  Professor  F.  W.  Clarke  many  minerals,  Profes- 
sor Kriiss  several  specimens,  and  Professor  Barker  and  others  have  helped  me  in 
many  ways. 


57 

NOTES  OF  OBSERVATION  ON  THE  RONTGEN  RAYS 

BY  HENRY  A.  ROWLAND,  N.  R.  CARMICIIAEL,  AND  L.  J.  BRIGGS 

[American  Journal  of  Science  [4],  /,  247,  248,  1896  ;   Philosophical  Magazine  |5],  XLI, 

381,  382,  1896] 

The  discovery  of  Hertz  some  years  since  that  the  cathode  rays  pene- 
trated some  opaque  bodies  like  aluminium,  has  opened  up  a  wonderful 
field  of  research,  which  has  now  culminated  in  the  discovery  by  Rontgen 
of  still  other  rays  having  even  more  remarkable  properties.  We  have 
confirmed,  in  many  respects,  the  researches  of  the  latter  on  these  rays, 
and  have,  repeated  his  experiment  in  photographing  through  wood, 
aluminium,  cardboard,  hard  rubber,  and  even  the  larger  part  of  a  milli- 
meter of  sheet  copper. 

Some  of  these  photographs  have  been  indistinct,  indicating  a  source 
of  these  rays  of  considerable  extent,  while  others  have  been  so  sharp 
and  clear  cut  that  the  shadow  of  a  coin  at  the  distance  of  2  cm.  from 
the  photographic  plate  has  no  penumbra  whatever,  but  appears  perfectly 
sharp  even  with  a  low  power  miscroscope. 

So  far  as  yet  observed  the  rays  proceed  in  straight  lines  and  all  efforts 
to  deflect  them  by  a  strong  magnet  either  within  or  without  the  tube 
have  failed.  Likewise  prisms  of  wood  and  vulcanite  have  no  action 
whatever  so  far  as  seen,  and,  contrary  to  Rontgen,  no  trace  of  reflection 
from  a  steel  mirror  at  a  large  angle  of  incidence  could  be  observed.  In 
this  latter  experiment  the  mirror  was  on  the  side  of  the  photographic 
plate  next  to  the  source  of  the  rays,  and  not  behind  it,  as  in  Rontgen's 
method. 

We  have,  in  the  short  time  we  have  been  at  work,  principally  devoted 
ourselves  to  finding  the  source  of  the  rays.  For  this  purpose  one  of 
our  tubes  made  for  showing  that  electricity  will  not  pass  through  a 
vacuum  was  found  to  give  remarkable  results.  This  tube  had  the 
aluminium  poles  within  1  mm.  of  each  other  and  had  such  a  perfect 
vacuum  that  sparks  generally  preferred  10  cm.  in  air  to  passage  through 
the  tube.  By  using  potential  enough,  however,  the  discharge  from  an 
ordinary  Ruhmkorff  coil  could  be  forced  through.  The  resistance  being 


572  HENEY  A.  ROWLAND 

so  high  the  discharge  was  not  oscillatory  as  in  ordinary  tubes  but  only 
went  in  one  direction. 

In  this  tube  we  demonstrated  conclusively  that  the  main  source  of 
the  rays  was  a  minute  point  on  the  anode  nearest  to  the  cathode.  At 
times  a  minute  point  of  light  appeared  at  this  point,  but  not  always. 

Added  to  this  source  the  whole  of  the  anode  gave  out  a  few  rays. 
From  the  cathode  no  rays  whatever  came,  neither  were  there  any  from 
the  glass  of  the  tube  where  the  cathode  rays  struck  it  as  Rontgen 
thought.  This  tube  as  a  source  of  rays  far  exceeded  all  our  other  collec- 
tion of  Crookes'  tubes  and  gave  the  plate  a  full  exposure  at  5  or  10  cm. 
in  about  5  or  10  minutes  with  a  slow-acting  coil  giving  only  about  4 
sparks  per  second. 

The  next  most  satisfactory  tube  had  aluminium  poles  with  ends  about 
3  cm.  apart.  It  was  not  straight,  but  had  three  bulbs,  the  poles  being  in 
the  end  bulbs  and  the  passage  between  them  being  rather  wide.  In  this 
case  the  discharge  was  slightly  oscillatory,  but  more  electricity  went  one 
way  than  the  other.  Here  the  source  of  rays  was  two  points  in  the  tube, 
a  little  on  the  cathode  side  of  the  narrow  parts. 

In  the  other  tubes  there  seemed  to  be  diffuse  sources,  probably  due 
in  part  to  the  oscillatory  discharge,  but  in  no  case  did  the  cathode  rays 
seem  to  have  anything  to  do  with  the  Rontgen  rays.  Judging  from  the 
first  two  most  definite  tubes  the  source  of  the  rays  seems  to  be  more 
connected  with  the  anode  than  the  cathode,  and  in  both  of  the  tubes  the 
rays  came  from  where  the  discharge  from  the  anode  expanded  itself  to- 
ward the  cathode,  if  we  may  roughly  use  such  language. 

As  to  what  these  rays  are  it  is  too  early  to  even  guess.  That  they  and 
the  cathode  rays  are  destined  to  give  us  a  far  deeper  insight  into  nature 
nobody  can  doubt. 

Baltimore,  Feb.  20,  1896. 


58 
NOTES  ON  RONTGEN  KAYS 

BY  H.  A.  ROWLAND,  N.  R.  CARMICHAEL,  AND  L.  J.  BRIGGS 
[Electrical  World,  XXVII,  452,  1896] 

In  the  '  American  Journal  of  Science '  for  March  we  made  a  few  notes 
of  our  researches  on  the  Rb'ntgen  rays,  reaching  the  provisional  con- 
clusion that  the  main  source  of  the  rays  was  at  the  anode,  and  that  the 
cathode  rays  seemed  to  have  nothing  to  do  with  the  phenomena  pre- 
sented. A  further  study  of  the  source  of  the  rays  in  many  other  tubes 
has  led  us  to  modify  this  conclusion  somewhat,  for,  while  we  still  think 
the  anode  or  its  equivalent  is  the  main  source  of  the  rays,  yet  we  now 
have  evidence  in  some  of  the  tubes  that  it  is  necessary  for  the  cathode 
rays  to  fall  on  the  anode  in  order  that  the  Rontgen  rays  may  be  formed. 

In  our  tubes  with  a  very  high  vacuum  the  other  sources  of  rays  are 
very  faint  indeed.  We  have  never  obtained  any  rays  from  the  cathode 
except  in  one  case,  where  undoubtedly  there  were  electrical  oscillations 
which  made  the  cathode  momentarily  an  anode.  It  can  be  readily  proved 
that  these  oscillations  always  exist  in  the  case  of  low  resistance  tubes, 
and  these  are  probably  the  cause  of  many  errors  in  estimating  the 
source  of  the  rays. 

In  some  cases  we  have  found  very  faint  sources  of  rays  as  Rontgen 
found  them,  where  the  cathode  rays  struck  the  glass,  but  not  where  they 
struck  a  piece  of  platinum  kept  at  nearly  zero  potential.  On  the  anode 
theory,  this  might  be  explained  by  the  fact  that  the  bombarding  cathode 
rays,  coming  in  periodical  electrified  showers,  alternately  raise  and 
lower  the  potential  of  the  glass,  thus  making  it  alternately  an  anode  and 
cathode.  In  the  case  of  the  platinum,  this  could  not  occur  to  the  same 
extent. 

That  feeble  Rontgen  rays  emanate  from  some  bodies  when  bombarded 
by  the  cathode  rays,  we  are  willing  to  admit,  and,  in  fact,  had  long  ago 
come  to  that  conclusion.  But  we  do  not  agree  with  Prof.  Elihu  Thom- 
son's general  conclusion  that  these  rays  are  always  given  out  from  bom- 
barded surfaces,  as  we  have  a  tube,  with  platinum  in  the  focus  of  a  con- 
cave electrode,  which  emits  no  rays  whatever  from  the  platinum,  even 


574  HENRY  A.  Rovv  LAND 

when  the  platinum  is  red  hot  from  the  bombardment,  the  concave  elec- 
trode being  the  cathode  and  a  third  wire  the  anode. 

The  same  tube,  with  the  platinum  made  an  anode  and  the  concave 
electrode  a  cathode,  produces  a  profuse  radiation  of  Rontgen  rays  in  all 
directions  on  the  side  of  the  platinum  bombarded  by  the  cathode  rays, 
and  none  on  the  other  side.  In  the  first  case  we  obtained  no  rays  from 
the  cathode,  no  rays  from  the  bombarded  surface,  and  only  a  very  weak 
effect  from  the  anode,  indeed  almost  nothing.  Hence  the  condition 
for  the  production  of  the  rays  seems  to  be  neither  the  one  or  the  other 
but  a  combination  of  the  two,  and  we  now  believe  as  far  as  we  can  yet 
see  that  the  necessary  condition  for  their  production  is  an  anode  bom- 
barded by  the  cathode  discharge.  The  anode  may  be,  however,  an  in- 
duced anode  formed  on  the  glass,  and  the  cathode  rays  may  vary  a  great 
deal  and  cease  to  present  the  usual  appearance  of  cathode  rays. 

Thus,  in  the  best  tube  that  we  have,  originally  made  for  showing  that 
electricity  will  not  pass  through  a  vacuum,  the  main  source  is  a  point  on 
the  end  of  the  anode,  where  a  little  point  of  light  appears.  Sometimes, 
across  the  little  interval  of  1  mm.  between  the  electrodes,  a  faint  spark 
or  arc  crosses  from  one  electrode  to  the  other,  and  we  think  that  the 
rays  come  out  especially  well  under  these  conditions.  Here  the  action  of 
the  bombarding  cathode  discharge  is  rather  obscure.  This  little  point  of 
light  also  sometimes  appears  on  the  red  hot  platinum  anode  men- 
tioned above,  and  we  have  seen  it  in  other  tubes,  always  at  the  place 
where  Rontgen  rays  are  apparently  found. 

Prof.  Elihu  Thomson  has  kindly  sent  us  some  sketches  of  tubes  hav- 
ing the  anode  bombarded  by  the  cathode,  and  we  had  previously  de- 
signed some  tubes  of  similar  shape,  but  have  not  yet  found  anybody 
in  this  country  capable  of  making  a  sufficiently  good  vacuum.  In  many 
of  our  best  tubes  the  vacuum  is  so  perfect  as  to  cause  a  resistance  equal 
to  a  five  or  six  inch  spark  in  the  air.  The  better  the  vacuum  the 
greater  the  number  of  rays  sent  out. 

However,  for  sharpness  of  detail,  nothing  equals  the  perfect  vacuum 
tube,  having  its  electrodes  one  mm.  apart.  Such  a  tube  has  been  de- 
signed by  one  of  us,  but  we  have  not  been  able  to  get  the  proper 
exhaustion. 

As  to  other  sources  of  Rontgen  rays,  we  have  tried  a  torrent  of  elec- 
tric sparks  in  air,  from  a  large  battery,  and  have  obtained  none.  Of 
course,  coins  laid  on  or  near  the  plate  under  these  circumstances,  pro- 
duce impressions,  but  these  are,  of  course,  induction  phenomena. 

As   to   sunlight,    Tyndall,    Abney,    Graham   Bell   and   others,   have 


NOTES  ox  KONTGEN  KAYS  575 

shown  that  some  of  the  rays  penetrate  vulcanite  and  other  opaque 
bodies,  and  we  have  only  to  look  at  an  unpainted  door,  on  the  other 
side  of  which  the  sun  is  shining,  to  convince  ourselves  that  sunlight 
penetrates  wood  to  a  considerable  depth. 

As  to  the  theory  of  the  Eontgen  rays  we  know  little.  If  the  rays 
are  vibrations  we  can  readily  determine  a  rough  limit  to  their  length, 
from  the  sharpness  of  the  shadows. 

Thus  our  photographs  have  such  sharpness  that  the  complete  waves 
cannot  be  more  than  -0005  cm.  long,  but  are  probably  much  shorter. 
This  is  independent  of  whether  the  waves  are  longitudinal  like  sound 
or  transverse  like  light,  and  of  course  only  applies  to  that  portion  of 
them  which  affects  the  photographic  plate.  There  may  be  others  of 
larger  size  that  do  not  affect  the  plate. 

All  efforts  to  bend  the  rays  from  their  course,  either  within  or  with- 
out the  tube,  by  means  of  a  strong  magnetic  field,  have  failed,  both  in 
our  hands  and  in  those  of  others,  and  thus,  if  the  rays  are  radiant  parti- 
cles of  matter,  they  cannot  be  highly  charged  particles  like  the  cathode 
rays.  The  rays  are  not  refracted  by  any  solid  bodies  so  far  tried,  and 
this  seems  to  be  against  their  being  waves  either  in  air  or  ether.  They 
pass  through  solid  bodies,  and  thus  their  wave-lengths  cannot  be  very 
small.  We  have  before  seen  that  it  cannot  be  very  great.  They  cannot 
be  sound  waves  as  they  proceed  for  some  distance  through  a  very  perfect 
vacuum. 

Altogether  we  are  at  a  loss  for  a  theory.  If  we  have  not  yet  got  a 
satisfactory  theory  of  light  after  more  than  a  hundred  years  of  labor, 
how  can  we  hope  to  have  a  theory  of  the  Kontgen  rays  after  knowing 
of  them  for  only  a  few  months?  Let  us  suspend  our  judgment  for  a 
while,  and  let  us,  above  all  things,  be  willing  to  alter  our  opinions  at 
any  moment  when  fresh  light  appears. 


59 

THE  RONTGEN  RAY,  AND  ITS  RELATION  TO  PHYSICS 

(A  TOPICAL  DISCUSSION) 

[Transactions  of  the  American  Institute  of  Electrical  Engineers,  XIII, 
403-410,  430,  431,  1896] 

OPENING  REMABKS  BY  PROF.  HENRY  A.  ROWLAND 

MR.  PRESIDENT  AND  GENTLEMEN:  A  gentleman  asked  me  a  few  mo- 
ments ago  if  I  knew  anything  about  the  X-ray.  I  told  him  no;  that  what 
I  was  going  to  tell  to-night  was  what  I  did  not  know  about  the  X-ray. 
I  do  not  suppose  anybody  can  do  any  more  than  that,  because  all  of  us 
know  very  little  about  it.  We  were  very  much  surprised,  something 
like  a  year  ago,  by  this  very  great  discovery.  But  I  cannot  say  that  we 
know  very  much  more  about  it  now  than  we  did  then.  The  whole 
world  seems  to  have  been  working  on  it  for  all  this  time  without  having 
discovered  very  much  more  with  respect  to  it. 

Now,  I  suppose  it  is  not  necessary  for  me  to  go  into  the  history  of 
the  thing.  We  all  know  it;  how  Lenard  first,  probably,  discovered  these 
rays,  or  discovered  something  very  similar  to  them;  how  Rontgen  after- 
wards found  their  particular  use,  their  penetrating  power,  and  so  on, 
although  Lenard  had  found  something  similar  to  that  before.  It  is 
thus  not  necessary  for  me  to  go  into  the  history  of  the  matter,  but 
simply  to  go  over,  to  some  extent,  what  we  know  with  regard  to  these 
rays  at  the  present  time.  First,  there  was  some  discussion,  some  time 
ago,  as  to  the  source  of  these  rays.  Rontgen  found  that  their  source 
was  any  point  that,  the  cathode  rays  struck  upon;  and  you  will  remember 
that  when  we  first  knew  about  these  rays  they  were  often  called  cathode 
rays.  Many  persons  thought  that  the  cathode  rays  came  through  the 
glass,  and  Lenard  first  thought  that  they  did  come  through  his  little 
window,  and  it  is  probable  that  they  do  at  the  present  time.  But  the 
kind  of  rays  that  we  are  considering  are  very  different  from  the  cathode 
rays.  Six  months  ago  there  was  quite  a  discussion  in  regard  to  the 
source,  and  I  believe  it  was  finally  determined  that  they  came  from 
points  where  the  cathode  rays  strike.  At  the  same  time  I  was  rather 
opposed  to  that.  In  one  of  my  tubes  I  found  that  the  rays  came  from 


THE  RONTGEN  RAY  AND  ITS  RELATION  TO  PHYSICS          577 

the  anode.  I  had  only  the  ordinary  assortment  of  Crookes'  tubes,  and 
one  of  the  tubes  had  aluminum  wires  which  were  a  millimeter  apart. 
In  one  of  these  the  source  of  the  rays  was  a  point  upon  the  anode — 
not  upon  the  cathode  at  all.  It  was  a  very  small  point.  The  photo- 
graphs which  I  obtained  by  that  tube  were  sharper  than  any  I  had  seen 
before.  They  are  so  very  sharp  that  in  estimating  the  shadow  of  an 
object  I  determined  that  the  point  could  not  have  been  a  thousandth 
of  an  inch  in  diameter.  Therefore  the  source  in  this  case  was  a  very 
minute  point  upon  the  anode,  and  that  point  was  nearer  the  cathode, 
and  I  suppose  some  of  the  cathode  rays  might  have  struck  upon  it,  and 
it  might  have  obeyed  the  law  that  the  point  where  these  X-rays  are 
formed  is  the  point  on  the  anode  where  the  cathode  rays  strike. 

I  had  another  very  interesting  tube,  and  I  was  going  to  bring  some 
of  the  photographs  here  to-night;  but  I  thought  they  were  so  small  that 
it  would  be  almost  impossible  to  see  them.  I  tried  the  three  cases  in 
this  tube:  First,  the  case  where  the  cathode  rays  strike  upon  the  anode. 
In  that  case  I  got  very  many  Rontgen  rays.  Then  I  tried  the  case 
where  the  cathode  rays  strike  upon  an  object — a  piece  of  platinum.  I 
did  not  get  any  rays  whatever  then.  Now,  some  people  say  that  they 
come  from  the  point  where  the  cathode  ray  strikes.  I  did  not  get  any 
whatever  in  that  case.  In  this  case  the  cathode  ray  struck  upon  a  piece 
of  platinum  in  the  centre  of  a  bulb,  and  no  rays  were  given  out  by  the 
anode  either.  Therefore  I  seemed  to  have  a  crucial  experiment  in  each; 
I  seemed  to  have  the  case  where  the  cathode  ray  strikes  upon  the  anode, 
and  I  got  lots  of  rays.  Then  I  had  the  case  where  the  cathode  rays 
strike  on  a  piece  of  platinum,  and  I  did  not  get  anything  at  all.  Then 
where  the  anode  itself  was  free  and  no  cathode  rays  struck  it,  I  did  not 
get  anything  from  it.  It  seemed  to  me  as  if  the  source  was  most  abun- 
dant when  the  cathode  ray  struck  upon  the  anode;  and  that  is  the 
theory,  we  know,  upon  which  nearly  all  tubes  are  formed  at  the  present 
time.  You  have  the  focus  tubes  in  which  you  focus  the  cathode  rays 
upon  the  anode,  and  in  that  case  you  have  a  very  abundant  source  of 
rays;  but  I  do  not  believe  you  ever  could  get  as  small  a  source  of  rays 
as  I  got  with  that  first  tube,  where  I  had  a  source  of  a  thousandth  of  an 
inch  diameter.  Having  such  a  small  source  of  rays,  it  gave  me  a  limit 
to  the  wave-length,  if  there  were  waves  at  all;  it  would  give  me  a  limit 
to  the  wave-length  of  which  I  will  speak  in  a  moment.  As  to  whether 
there  are  any  rays  where  the  cathode  rays  strike  on  any  other  objects, 
we  know  that  there  are  very  feeble  ones.  It  seems  to  be  almost  neces- 
sary in  order  to  get  an  abundant  source  that  you  should  have  cathode 
37 


578  HENRY  A.  EOWLAND 

rays  strike  on  the  anode.  However,  that  is  a  point  of  discussion.  Now, 
as  to  the  source  of  electricity,  we  have  generally  the  Euhmkorff  coil. 
There  is  one  source  of  which  I  saw  a  little  note  in  (  Nature,'  where  a 
man  had  used  a  large  Holtz  machine  with  very  good  effects.  Now  it  is 
very  much  easier  for  many  persons  to  use  a  Holtz  machine  than  to  use 
a  Euhmkorff  coil.  There  are  many  cases  where  one  cannot  have  a  large 
battery;  and  this  man  said  that  with  the  Holtz  machine  he  got  as  great 
an  effect  as  with  the  Euhmkorff  coil.  Then  we  have  the  Tesla  coil,  etc. 
By  the  way,  speaking  of  the  Tesla  coil,  I  am  not  sure  but  that  you 
might  look  back  and  find  that  it  is  very  similar  to  the  Henry  coil. 
Henry  originally  experimented  on  the  induction  of  electricity,  transmit- 
ting a  spark  of  electricity  from  one  coil  and  getting  a  spark  from  an- 
other, and  the  Tesla  coil  is  something  like  that,  except  that  it  is  made 
so  as  to  produce  a  much  more  voluminous  spark. 

We  all  know  the  properties  of  the  Eontgen  rays — they  go  in  a  straight 
line.  Every  effort  to  deviate  them  from  a  straight  line,  by  any  means 
whatever,  has  failed,  except  that  when  they  strike  upon  an  object  they 
are  reflected.  Now,  it  is  a  question  for  discussion  as  to  whether  there  is 
any  regular  reflection.  They  strike  upon  an  object,  and  you  get  some- 
thing from  that  object  which  will  affect  a  photographic  plate.  Are 
those  rays  which  you  get  from  the  object  Eontgen  rays  still,  or  do  the 
Eontgen  rays  strike  upon  this  object  and  generate  in  it  some  sort  of 
rays  which  come  out,  different  from  the  Eontgen  rays,  and  affect  the 
plate?  We  do  not  know  that.  Neither  are  we  quite  positive  whether 
there  is  any  reflection  of  the  rays.  We  know  there  is  turbid  reflection — 
you  may  call  it — rays  strike  on  the  object,  and  the  object  becomes  a 
source  of  rays  of  some  kind.  Nobody  has  ever  found  out  what  sort  of 
rays  come  from  the  object.  Something  comes  from  it,  and  we  generally 
imagine,  and  indeed  we  often  state,  that  they  are  Eontgen  rays  that 
come  off  the  object.  But  we  have  good  reason  to  suppose  that  they 
may  be  something  else;  and  they  may  or  may  not  be  regular  reflections; 
some  persons  say  they  are  and  some  that  they  are  not.  I  have  seen 
some  photographs  made  in  this  city  which  indicated  regular  reflections. 
At  the  same  time  I  would  not  be  positive  as  to  whether  there  was  any 
regular  reflection.  It  is  rather  doubtful.  It  is  a  point  to  be  determined. 

Then  the  fluorescence — that  is  the  way  Eontgen  originally  found  the 
ray.  You  know  the  way  they  produce  fluorescence — the  photographic 
effect — you  all  know  that.  You  all  know  that  the  magnet  does  not 
affect  them — does  not  turn  these  rays  from  a  straight  line. 

The  polarization  of  the  rays:     We  have  no  evidence  whatever  as  to 


THE  RONTGEN  KAY  AND  ITS  RELATION  TO  PHYSICS          579 

the  polarization.  If  they  were  very  small  waves,  transverse  waves,  like 
light,  we  ought  to  be  able  to  polarize  them.  Becquerel,  by  exposing 
certain  phosphorescent  substances  to  the  sun,  obtained  from  them  cer- 
tain rays  which  penetrated  objects  like  aluminium,. etc.  But  these  rays 
were  evidently  small  rays  of  light,  because  he  could  polarize  them,  and 
he  could  refract  them,  and  they  were  probably  very  short  waves  of  ultra 
violet  light.  But  we  never  have  been  able  to  discover  that  there  was 
any  such  effect  in  a  Rontgen  ray.  Some  persons  have  claimed  that  they 
got  polarization;  but  if  there  ever  was  any  polarization,  it  is  very  small, 
indeed.  One  of  the  principal  advances  in  respect  to  these  rays  is  that 
made  by  J.  J.  Thomson,  in  considering  the  electric  discharge  of  bodies. 
He  has  published  most  valuable  results  with  regard  to  the  effect  of 
these  rays  upon  gases.  When  the  rays  fall  upon  a  gas,  they  affect  the 
gas  in  some  way  so  that  it  becomes  a  conductor.  Now,  you  can  subject 
the  gas  to  these  rays  and  allow  the  gas  to  go  through  a  tube  off  into 
another  vessel,  so  that  it  will  discharge  an  electrified  body  in  that  vessel. 
But  he  has  found  the  most  interesting  result  that  it  will  not  continue 
long  to  affect  these  bodies.  After  one  has  allowed  a  certain  amount 
of  electricity  to  pass  through  it,  it  then  becomes  an  insulator  again. 
It  only  allows  a  certain  amount  of  electricity  to  go  through  it.  That  is 
easily  explained — or  you  can  explain  it — by  the  Rontgen  rays  liberating 
the  ions,  and  only  a  certain  amount  of  them.  Just  as  soon  as  these 
are  used  up  in  the  conduction  of  the  gas,  then  it  ceases  to  conduct.  So 
that  a  certain  amount  of  gas  will  conduct  a  certain  amount  of  electricity, 
and  then  it  stops  conducting.  That  is  a  most  interesting  result.  It  is 
one  of  the  great  advances  we  have  made  since  Rontgen's  discovery. 
Rontgen  knew  nearly  all  we  know  now  about  these  rays.  We  have 
discovered  very  little  indeed;  but  that  point  I  think  we  have  at  least 
discovered. 

Then  it  is  said  that  these  rays  affect  a  selenite  cell  in  the  same  way 
that  light  affects  it — it  changes  the  resistance  of  the  selenite  cell. 

Of  course,  we  are  only  considering  the  theory  to-night;  at  least  I 
am,  and  we  do  not  have  to  consider  the  bones,  and  so  on.  I  have  had 
some  students  at  work  in  my  laboratory,  and  it  was  with  the  utmost 
difficulty  that  I  kept  them  from  photographing  bones.  Bones  seemed 
to  be  the  principal  object  to  be  photographed  by  the  Rontgen  rays  when 
they  were  first  discovered,  and  I  suppose  it  is  the  same  now.  Most 
people  connect  Rontgen  rays  with  bones;  but  I  do  not  intend  to  say  very 
much  about  them. 

Now,  one  important  point  with  respect  to  these  rays  is  as  to  whether 


580  HENRY  A.  ROWLAND 

they  are  homogeneous.  Are  they  like  light  which  can  he  divided  up 
into  a  large  number  of  different  wave-lengths,  or  are  they  homogeneous? 
There  seems  to  be  a  great  deal  of  evidence  that  they  are  not  all  the 
same;  that  one  ought  to  get  a  spectrum  of  them  in  some  way.  We  can 
filter  them  a  little  bit  through  objects.  After  they  are  filtered  through 
an  object,  they  are  probably  a  little  different  from  what  they  were 
before,  and  some  objects  probably  let  through  different  rays  from  others. 
In  '  Nature '  Mr.  Porter,  I  believe,  has  shown  experiments  upon  that.  He 
divides  rays  into  three  kinds.  At  least  he  finds  that  under  certain 
circumstances  the  rays  will  penetrate  bones  better  than  in  other  cases  — 
bones  or  any  other  object — they  have  more  penetrating  power,  and  they 
go  through  many  of  those  objects  that  ordinarily  stop  them.  By  heat- 
ing up  the  tube,  and  by  various  arrangements  of  his  spark-gaps,  etc,, 
and  putting  little  wires  around  his  tubes,  and  so  on,  he  can  cause  them 
to  generate  different  kinds  of  rays.  That  is  a  very  important  point,  if 
it  is  substantiated,  and  there  seems  to  be  little  reason  to  doubt  that  a 
number  of  rays  really  do  exist;  that  whatever  they  are  that  come  from 
the  object,  they  are  not  all  the  same;  some  of  them  penetrate  bodies 
better  than  others,  and  very  likely  some  one  will  get  up  some  sort  of 
filter  that  will  filter  them  out,  and  allow  us  to  use  them  and  to  find  if 
they  have  different  properties.  At  the  present  we  are  rather  in  the 
dark  with  regard  to  this  point. 

Now  I  come  to  the  theory  of  these  rays.  What  is  the  cause  of  all 
these  phenomena?  There  was  a  time  when  we  were  rather  self- 
satisfied,  I"  think,  with  regard  to  theories  of  light.  We  thought  that 
Fresnel  and  others  had  discovered  what  light  was — some  sort  of  vibra- 
tion in  the  ether;  we  called  it  ether;  if  it  had  these,  waves  going  through 
it,  then  it  would  produce  light,  and  we  were  pretty  well  convinced  that 
the  waves  were  transverse,  because  we  would  polarize  them;  so  that  we 
began  to  be  satisfied  that  we  knew  something  about  light.  Then  Max- 
well was  born,  and  he  proved  that  these  rays  were  electromagnetic — 
very  nearly  proved  it.  Then  Hertz  came  along  and  actually  showed  us 
how  to  experiment  with  these  Maxwell  waves,  most  of  which  were 
longer  than  those  of  light.  At  the  same  time  they  were  of  the  same 
nature.  Well,  we  got  a  rather  complicated  sort  of  ether  by  that  time. 
The  ether  had  to  do  lots  of  things.  One  must  put  upon  the  ether  all  the 
communication  between  bodies.  For  instance,  what  communication  is 
there  between  this  earth  and  the  sun?  Why,  you  have  light  coming 
from  it  and  heat.  Radiation  you  might  call  it  all.  We  have  radiation. 
Then  some  people  thought  they  discovered  electromagnetic  disturbance 


THE  RONTGEN  RAY  AND  ITS  RELATION  TO  PHYSICS          581 

from  the  sun.  Sometimes  they  have  seen  a  sun  spot  and  noted  a  deflec- 
tion of  the  magnetic  needle  on  the  earth.  Very  likely  that  is  true.  I 
don't  know  that  they  have  discovered  any  electrostatic  effect.  But  we 
know  that  electrostatic  effects  will  be  carried  on  through  as  perfect  a 
vacuum  as  you  can  get.  Then  we  have  gravitation  action  too.  Now, 
you  have  got  all  those  things — electromagnetic  action,  light  which 
would  be  an  electromagnetic  phenomenon,  and  then  we  have  gravitation, 
and  we  have  got  to  load  the  ether  with  all  those  things.  Then  we  have 
got  to  put  matter  in  the  ether  and  have  got  to  get  some  connection 
between  the  matter  and  the  ether.  By  that  time  one's  mind  is  in  a 
whirl,  and  we  give  it  up. 

Now  we  have  got  something  worse  yet — we  have  got  Rontgen  rays  on 
top  of  all  that.  Here  is  something  that  goes  through  the  ether,  and  it 
not  only  goes  through  the  ether  but  shoots  in  a  straight  line  right 
through  a  body.  Now,  what  sort  of  earthly  thing  can  that  be?  A  body 
will  stop  light  or  do  something  to  it  as  it  goes  through;  but  what  on 
earth  can  it  be  that  goes  through  matter  in  a  straight  line?  Why,  our 
imagination  doesn't  give  us  any  chance  to  do  anything  with  that  pro- 
blem. It  is  a  most  wonderful  phenomenon.  Now,  we  can  suppose  that 
they  are  ultra  violet  light.  Indeed,  we  can  get  a  limit  to  the  wave- 
length to  some  extent.  Nobody,  however,  has  ever  proved  that  the  Ront- 
gen rays  are  waves.  But  we  can  get  a  limit  of  the  wave-length  if  they  are 
waves,  because  when  I  have  a  tube  that  gives  me  a  shadow  which  is  only 
a  thousandth  of  an  inch  broad,  or  rather  from  the  greatest  intensity 
out  to  clear  glass  a  thousandth  of  an  inch  broad,  I  can  calculate  the 
wave-length  of  the  thing  that  would  produce  such  a  shadow.  It  has 
got  to  be  very  small  indeed;  one  knows  that  right  away,  because  any 
ordinary  light  would  make  a  few  waves  at  the  edge  of  the  shadow,  and 
by  measuring  those  waves  you  could  get  the  wave-lengths  of  the  light. 
But  there  was  no  appearance  whatever  on  any  of  my  photographs  of  any 
such  phenomenon  as  that.  I  did  not  have  any  of  these  waves  at  the 
edge  of  the  shadow  whatever.  It  went  directly  from  blackness  to  light. 
But  putting  it  under  the  microscope  and  measuring  from  almost  imag- 
inary points,  from  lightness  to  darkness,  I  could  get  a  limit  to  the  wave- 
length. Now,  as  to  that  limit,  I  published  it  in  one  of  the  journals 
six  months  ago,  or  more,  and  it  came  at  about  one-seventh,  I  think, 
that  of  yellow  light.  Others  have  determined  the  wave-length  and  got 
even  below  one-seventh  that  of  yellow  light.  Some  have  got  one- 
thirtieth  that  of  yellow  light,  and  so  on.  Some  of  them  I  am  rather 
doubtful  about,  because  they  say  they  have  bands.  If  they  have  bands 


582  HENRY  A.  ROWLAND 

and  diffraction  bands,  that  would  prove  instantly  that  the  Rontgen  rays 
are  waves.  But  I  have  never  seen  the  slightest  phenomenon  of  that 
sort.  It  is  very  doubtful  that  it  exists,  and  those  persons  who  have  had 
it  will  have  to  show  their  photographs  very  clearly  to  make  us  believe 
it.  And  therefore  we  have  no  evidence  whatever  that  the  rays  are 
waves.  At  the  same  time  we  have  no  evidence  that  they  are  not  waves. 
They  might  be  very  short  waves — infinitely  short  waves.  Let  us  see 
what  would  happen  if  they  were  infinitely  short  waves.  They  might 
be  so  very  short  as  to  be  too  fine-grained  for  any  of  our  methods  of 
polarization  or  reflection.  Waves  are  reflected  from  a  solid  body — 
regularly  reflected,  because  they  interfere  after  they  come  from  the 
body.  You  can  get  the  direction — the  angle  of  incidence  equals  the 
angle  of  reflection;  you  can  get  that  by  means  of  considering  them  as 
waves  and  as  interfering  after  they  come  from  the  object.  Well,  if  the 
object,  however,  is  a  very  rough  sort  of  thing  compared  with  the  wave- 
length, you  will  not  get  a  regular  reflection.  That  is  what  might  hap- 
pen in  the  case  of  Rontgen  rays.  And  then  again,  with  regard  to 
refraction  of  the  light,  the  theory  of  refraction  which  comes  from  con- 
sidering molecules  imbedded  in  the  ether  will  give  you  some  limit. 
When  we  go  beyond  that  limit,  we  get  no  refraction.  The  bending  of 
the  violet  rays  increases  up  to  a  certain  point  and  then  goes  back.  We 
have  a  case  of  anomalous  refraction  very  often  in  some  substances  like 
fuchsine,  aniline  dyes,  and  so  on.  Therefore  the  action  of  refraction 
can  be  accounted  for  by  having  very  short  waves.  But  when  we  treat 
of  the  theory  of  the  case  we  have  the  little  molecules  of  a  gas  knocking 
against  each  other,  and  they  can  only  go  a  little  distance.  We  call  that 
the  free  path  of  the  gas — a  very  small  distance  in  the  ordinary  air. 
Those  molecules  cannot  go  more  than  this  very  small  distance  before 
they  stop.  Well,  now,  why  should  little,  short  waves  of  light  pass 
through  the  gas  and  not  be  stopped  too?  When  the  waves  are  very 
short  indeed,  it  seems  to  me  that  the  object  would  be  entirely  opaque 
to  them,  because  they  would  strike  upon  those  molecules,  unless  they 
could  pass  directly  through  the  molecules.  You  would  therefore  neces- 
sarily have  these  little  short  waves  going  directly  through  the  mole- 
cules, which  we  generally  think  is  almost  impossible  in  case  of  light. 
And  that  is  one  very  great  objection  that  I  have  to  that  theory. 

Then  we  have  another  theory — that  these  are  not  transverse  waves 
at  all;  that  they  are  waves  like  sound,  and  very  short  indeed.  Well, 
what  would  happen  then?  If  they  are  very  short  indeed,  you  have  the 
same  objection:  They  would  all  strike  against  the  molecules,  and  they 


THE  ROXTGEN  RAY  AND  ITS  RELATION  TO  PHYSICS          583 

would  be  dispersed  very  quickly.  The  shorter  the  wave-lengths,  the 
more  they  are  dispersed.  Take,  for  instance,  short  waves  that  bob 
against  a  boat  and  are  reflected  back.  Thus,  if  you  have  a  big,  long 
ocean  wave,  it  sweeps  around  a  boat  and  goes  on  without  being  troubled 
by  the  boat  at  all.  The  shorter  the  waves,  the  more  they  are  bothered 
by  the  boat,  and  so  it  is  with  respect  to  other  waves — the  short  waves 
would  probably  be  stopped  by  the  molecules.  So  I  do  not  see  what  we 
can  do  with  regard  to  it  in  that  respect.  According  to  Maxwell's  law, 
waves  like  sound  do  not  exist  in  the  kind  of  ether  that  he  suggested. 
But  that  is  all  based  upon  a  certain  theory  that  the  lines  of  force  were 
always  closed.  He  introduced  into  his  equation  an  expression  which 
indicated  that  every  line  of  force  was  a  closed  path  coming  back  upon 
itself  or  ending  in  electricity,  one  or  the  other.  Now,  if  we  throw  out 
that,  then  we  can  get  this  kind  of  compressional  waves  in  the  ether. 
Now,  it  is  not  at  all  impossible  that  they  exist,  and  as  to  whether  they 
would  go  through  molecules  any  better  than  light  waves  do,  nobody  can 
tell;  but  it  is  possible  that  they  might.  But  if  there  are  waves  at  all, 
they  must  be  very  short  waves.  You  cannot  get  over  that  fact — if  they 
are  waves  at  all,  they  must  be  short. 

Then,  of  course,  you  have  the  other  theory — of  little  particles  of 
matter  flying  out  from  the  body,  passing  through  the  glass  and  all  other 
bodies,  until  they  reach  a  photographic  plate  or  any  other  place  where 
we  are  notified  of  their  presence,  and  these  little  particles  make  their 
way  through  the  air  or  any  other  substance.  Now,  why  should  not  the 
little  particles  be  stopped  very  quickly  by  bodies  as  well  as  if  the  rays 
were  waves?  You  see  we  are  in  trouble  here  too.  Why  are  not  the 
waves  stopped?  Why  are  not  the  little  particles  stopped?  Stokes  has 
given  some  sort  of  a  theory  with  regard  to  this — that,  instead  of  having 
a  wave  motion  in  the  ether,  the  rays  are  impulses — a  sudden  impulse — 
one  wave,  for  instance — not  a  series  of  waves  at  all,  but  one  impulse 
coming  out  from  the  tube.  I  think  if  he  had  seen  any  very  sharp 
shadows  obtained  from  the  Rontgen  rays  he  would  not  have  given  that 
theory.  He  probably  has  seen  only  those  very  hazy  outlines  that  very 
many  persons  take  for  Rontgen  photographs.  But  if  he  had  seen  any 
very  defined  ones — very  sharp  ones — he  probably  would  not  have  given 
that  theory,  because  if  the  Rontgen  rays  are  waves  at  all,  they  must  be 
short,  and  there  must  be  a  long  series  of  them  to  make  sharp  shadows. 
This  is  why  Newton  gave  up  the  wave  theory  of  light.  You  remember 
he  gave  up  this  theory  because  he  found  that  light  went  straight  past 
an  object  instead  of  curving  around  into  the  shadow  as  much  as  sound 


584  HENRY  A.  ROWLAND 

does.  But  he  was  not  quite  up  to  his  usual  pitch  when  he  made  that 
statement,  because  if  he  had  thought  a  moment  he  would  have  seen  that 
very  short  waves  will  go  more  nearly  in  a  straight  line  than  long  ones. 
But  any  single  impulse,  such  as  Stokes  suggests,  would  go  into  the 
shadow.  The  only  wave  motion  that  would  go  in  a  straight  line  is  a 
series  of  waves,  one  after  another.  Therefore,  these  rays  cannot  he 
single  impulses  coming  irregularly. 

Prof.  Michelson  has  suggested  a  theory  of  rays  based  on  something 
like  vortex  rings  in  the  ether.  Now,  if  we  have  an  ether  that  can  carry 
on  light  waves  and  electromagnetic  waves,  it  cannot  be  a  perfect  fluid; 
it  has  got  to  be  something  else.  You  cannot  very  well  imagine  vortex 
rings  in  such  an  ether.  So  that  we  are  met  at  every  point  by  some 
objection.  We  have  been  studying  light  for  hundreds  of  years;  we  are 
not  anywhere  near  satisfied  with  the  theory  yet,  and  we  cannot  very 
well  be  expected  to  be  satisfied  with  the  theory  of  Rontgen  rays  in  one 
year. 

Well,  I  think  that  is  all  I  can  say  with  regard  to  the  subject,  and  I 
hope  the  other  gentlemen  who  are  to  carry  on  the  discussion  will  satisfy 
you  on  all  these  points  that  I  have  brought  up  and  left  unanswered. 

[There  followed  a  discussion  by  Professor  Elihu  Thomson,  Professor 
M.  I.  Pupin,  and  others.] 

PROF.  ROWLAND: — I  made  a  few  notes  with  regard  to  what  has  been 
said,  but  they  are  made  in  such  a  way  that  I  do  not  believe  that  I  can 
interpret  them  myself,  especially  as  the  hour  seems  to  be  getting  rather 
late.  One  or  two  remarks,  however,  I  would  like  to  make.  When 
Prof.  Thomson  said  that  he  got  such  a  large  amount  of  rays  from  an 
insulated  piece  of  platinum  by  letting  the  cathode  rays  fall  upon  it, 
he  made  a  sketch.  With  the  exception  of  this  end,  which  was  flat, 
that  is  the  kind  of  thing  that  I  used.  Now,  there  was  absolutely 
no  effect  when  this  was  made  an  anode  and  this  a  cathode,  so  that  all 
the  cathode  rays  were  striking  on  the  platinum.  I  have  the  photo- 
graph; I  got  no  effect  whatever.  Now,  if  Prof.  Thomson  got  an  effect 
in  this  case  and  I  did  not  get  an  effect  in  that  case,  I  have  got  a  case, 
at  least,  where  none  of  these  rays  were  produced  by  the  falling  of  the 
cathode  rays  upon  the  object.  It  doesn't  make  any  difference  how 
many  other  persons  have  something  in  which  they  do  get  an  effect. 
If  I  did  not  get  an  affect,  that  is  one  case,  understand.  That  is  the 
case  where  the  cathode  ray  fell  on  an  object  and  I  got  no  Rontgen  ray. 


THE  RONTGEN  RAY  AND  ITS  RELATION  TO  PHYSICS          585 

If  other  people  got  them  in  other  ways,  why,  there  is  something  else 
coming  in.  I  don't  know  what  it  is. 

PROF.  THOMSON: — I  should  like  to  say  just  there,  Professor,  if  you 
would  allow  me,  that  I  used  exactly  that  arrangement  first,  and  got 
rays  with  the  concave  cathode.  The  anode  at  this  end  and  the  inter- 
posed plate  of  platinum  between,  with  that  wire  extending  outward, 
is  the  standard  form  of  Crookes'  tube — the  first  tube,  in  fact,  that  I 
used.  I  got  not  only  sharp  effects  but  rays. 

THE  CHAIRMAN: — Was  the  platinum  red? 

PROF.  THOMSON: — The  platinum  was  red — yes,  of  course,  and  it  was 
a  vigorous  source  of  rays.  I  got  rays  with  the  same  tube  that  Professor 
Rowland  does  not  get  them. 

PROF.  ROWLAND: — Well,  that  has  nothing  to  do  with  the  point.  The 
point  that  I  raise  is  this,  that  there  was  certainly  no  doubt  that  I  did 
not  get  any,  and  the  cathode  rays  were  falling  from  the  object.  That 
is  the  thing.  Now,  one  thing  that  I  wish  to  remark  is  that  most  people 
draw  a  tube  like  that.  They  don't  say  where  the  wires  go.  Mine 
generally  went  out,  so  that  they  were  very  far  away  from  this  object. 
By  curving  wires  around  in  different  ways  I  can  get  an  inductive  action. 
I  don't  doubt  that  I  could  fix  up  a  tube  so  that  I  could  get  lots  of  rays 
out  of  any  part.  However,  the  time  is  passing,  and  I  will  just  say  one 
word  with  regard  to  the  point  Prof.  Thomson  raised  with  regard  to 
the  fluorescence  over  the  surface  of  the  glass.  He  thought  something 
was  stopped  by  the  glass.  I  must  say  that  Lenard,  when  he  first  experi- 
mented upon  this  subject — and  I  regard  his  experiments  as  quite  as 
valuable  as  Rontgen's,  probably — ,  he  got  several  kinds  of  rays  coming 
out  through  an  aluminium  window.  He  got  rays  which  were  deflected 
by  the  magnet,  as  well  as  others.  He  had  not  separated  them,  how- 
ever. When  the  Lenard  paper  came  to  the  laboratory  I  remarked  to 
my  students:  "  That  is  the  best  discovery  that  has  been  made  in  many 
a  day."  I  immediately  set  somebody  to  work  experimenting.  He  tried 
to  get  some  results  and  would  probably  have  discovered  the  Rontgen 
rays  at  that  time  if  it  had  not  been  that  the  University  of  Chicago 
called  him  off,  and  Johns  Hopkins  University  was  very  poor  and  could 
not  call  him  back,  and  he  had  to  stop  in  the  midst  of  his  work.  They 
always  say  in  Baltimore  that  no  man  in  that  city  should  die  without 
leaving  something  to  Johns  Hopkins.  Now,  Dr.  Pupin  mentioned  a 
means  of  showing  whether  the  rays  were  reflected — a  little  reflector  in 
which  he  had  them  brought  to  a  focus,  as  I  recollect  it.  I  have  read  an 
account  in  which  an  experimenter  did  find  the  rays  were  brought  to  a 


586  HENRY  A.  EOWLAND 

focus,  showing,  provisionally  at  least,  that  there  was  some  regular  reflec- 
tion. But  these  experiments  should  all  be  repeated  many  times  before 
one  actually  believes  them.  We  don't  always  believe  what  we  read. 

Now,  as  to  Helmholtz's  theory  of  the  motion  of  ether  and  so  on — 
well,  as  I  said  before,  what  is  the  motion  of  the  ether?  What  is  motion 
of  the  whole  ether?  You  cannot  move  the  ether  in  the  whole  universe 
all  at  once,  and  if  you  do  not  move  the  ether  in  the  whole  universe 
all  at  once  but  only  move  a  part,  then  it  is  a  wave,  so  it  amounts  to  the 
theory  that  I  gave — an  impulse,  such  as  Stokes  had.  Now,  an  impulse 
such  as  Stokes  had  does  not  go  in  a  straight  line — it  goes  around  cor- 
ners— and  it  does  not  go  in.  a  straight  line  unless  there  are  lots  of 
waves  coming  out.  We  can  readily  prove  that  an  ordinary  molecule, 
vibrating  to  ordinary  light,  must  give  out  a  hundred  thousand  waves 
without  much  diminution  of  amplitude,  or  else  you  cannot  have  the 
sharp  lines  in  the  spectrum  that  we  do.  The  molecule  must  vibrate  a 
long  time — longer  than  any  bell  that  we  can  make.  We  cannot  find  a 
bell  that  will  give  out  a  hundred  thousand  vibrations  without  much 
diminution.  For  ethereal  waves  something  must  vibrate  to  produce 
them.  What  it  is  I  don't  know  that  there  is  any  necessity  for  discuss- 
ing, because  you  can  discuss  it  forever  and  never  get  any  nearer  to  it. 
Something  vibrates.  Now,  the  thing  that  vibrates  we  don't  know.  We 
don't  know  whether  it  is  electricity  or  whether  it  is  mechanical  motion. 
We  know  nothing  about  it.  I  have  often  said  to  my  students,  when  I 
showed  them  the  spectrum  of  some  substance  like  uranium,  in  which 
we  were  taking  photographs  which  would  be  perhaps  ten  feet  long — so 
fine  in  grain  that  you  could  not  put  the  point  of  a  pencil  on  it  without 
finding  a  line.  There  were  thousands  of  lines.  I  said  to  them:  "  A 
molecule  of  matter  is  more  complicated  a  great  deal  than  a  piano. 
Counting  the  overtones  and  everything,  you  would  not  probably  get  up 
anywhere  near  the  number  of  tones  you  get  out  of  a  single  molecule  of 
uranium.  Therefore  it  rather  looks  as  if  the  uranium  molecule  was 
very  complicated."  Of  course,  all  those  spectrum  lines  do  not  indicate 
fundamental  tones — many  are  harmonics.  •  Still  it  is  rather  a  compli- 
cated thing  to  get  a  spectrum  in  which  there  are  many  thousands  of 
lines.  So  when  I  come  to  think  what  a  molecule  is  and  try  to  get  up 
some  theory  of  it,  I  quite  agree  with  Dr.  Pupin  that  we  don't  know  any- 
thing about  it. 


64 

DIFFRACTION  GRATINGS 

[Encyclopcenia  Brltannica,  New  Volumes,  III,  458,  459,  1902] 

The  grating  is  an  optical  instrument  for  the  production  of  the  spec- 
trum ;  it  now  generally  replaces  the  prism  in  a  spectroscope  where  large 
dispersion  is  needed,  or  when  the  ultra-violet  portion  of  the  spectrum 
is  to  be  examined,  or  when  the  spectrum  is  to  be  photographed.  The 
transparent  grating  consists  of  a  plate  of  glass  covered  with  lampblack, 
gold  leaf,  opaque  collodion  or  gelatine,  the  coating  being  scratched 
through  in  parallel  lines  ruled  as  nearly  equidistant  as  possible.  When 
the  lines  are  to  be  ruled  very  close  together,  a  diamond  ruling  directly 
on  glass  is  used.  Other  transparent  materials,  such  as  fluor  spar,  are 
sometimes  substituted  for  glass.  For  certain  researches  on  long  waves 
the  grating  is  made  by  winding  a  very  fine  wire,  l-1000th  inch  in  diam- 
eter, in  the  threads  of  two  fine  screws  placed  parallel  to  each  other, 
soldering  the  wire  to  the  screws  and  then  cutting  it  away  on  one  side 
of  the  screws.  As  the  value  of  a  grating  is  dependent  upon  the  number 
of  lines  ruled,  it  is  very  desirable  to  have  their  number  great.  Glass  is 
so  hard  that  the  diamond  employed  for  the  ruling  wears  away  rapidly; 
and  hence  the  modern  grating  is  generally  a  reflecting  grating,  which 
is  made  by  ruling  on  a  speculum  metal  surface  finely  ground  and  pol- 
ished. On  such  a  surface  it  is  possible  to  rule  100,000  lines  without 
damaging  the  diamond,  although  its  point  even  then  often  wears  away 
or  breaks  down.  The  lines  are  generally  so  close  together  as  15,000  or 
20,000  to  the  inch,  although  it  is  feasible  to  rule  them  even  closer — 
say  40,000  to  50,000  to  the  inch.  There  is  little  advantage,  however, 
in  the  higher  number  and  many  disadvantages. 

The  grating  produces  a  variety  of  spectra  from  a  single  source  of 
light,  and  these  are  designated  as  spectra  of  the  first,  second,  etc.,  order, 
the  numbering  commencing  from  the  central  or  reflected  image  and 
proceeding  in  either  direction  from  it.  The  dispersion  depends  upon 
the  number  of  lines  ruled  in  a  unit  of  length^upon  the  order  of  the 
spectrum,  and  upon  the  angle  at  which  the  grating  is  held  to  the  source 
of  light.  The  defining  power  depends  upon  its  width  and  the  angles 


588  HENKY  A.  EOWLAND 

made  by  the  incident  and  diffracted  rays,  and  is  independent  of  the 
number  of  lines  per  unit  of  length  ruled  on  the  grating.  If  this  num- 
ber is  too  small,  however,  the  different  order  of  the  spectra  will  be  too 
much  mixed  up  with  each  other  for  easy  vision.  A  convenient  number 
is  15,000  to  20,000  lines  to  the  inch,  or  from  6000  to  8000  to  the 
centimetre.  The  defining  power  is  defined  as  the  ratio  of  the  wave- 
length to  the  distance  apart  of  the  two  spectral  lines  which  can  be  just 
seen  separate  in  the  instrument.  Thus  the  sodium  or  D  lines  have 
wave-lengths  which  differ  from  each  other  by  -597  ftp,  and  their  aver- 
age wave-length  is  589-3  pp.  A  spectroscope  to  divide  them  would 
thus  require  a  defining  power  of  988.  The  most  powerful  gratings  have 
defining  powers  from  100,000  to  200,000.  Lord  Eayleigh's  formula  for 
the  defining  power  is 

D  =  Nn. 

When  D  is  the  defining  power,  N  is  the  order  of  the  spectrum,  and  n 
is  the  total  number  of  lines  ruled  on  the  grating.  As  the  defining 
power  increases  with  N,  and  since  we  can  observe  in  a  higher  order  as 
the  number  of  lines  ruled  in  a  unit  of  length  decreases,  it  is  best  to 
express  the  defining  power  in  terms  of  the  width  of  the  grating,  w.  In 
this  case  we  have  for  the  maximum  defining  power  D'  =  20,000  w  for 
small  gratings,  or  D'  =  15,000  w  for  extra  fine  large  gratings,  w  being 
the  width  of  the  gratings  in  centimetres.  It  is  seldom  that  very  large 
gratings  are  perfect  enough  to  have  a  defining  power  of  more  than 
10,000  w,  owing  to  imperfection  of  surface  or  ruling.  The  relative 
brightness  of  the  different  orders  of  spectra  depend  upon  the  shape  of 
the  groove  as  ruled  by  the  diamond.  No  two  gratings  are  ever  alike 
in  this  respect,  but  exhibit  an  infinite  variety  of  distributions  of  bright- 
ness. Copies  of  glass  gratings  can  be  made  by  photography,  contact 
prints  being  taken  on  collodiochloride  of  silver  or  other  dry  plates. 
Eeflecting  gratings  can  be  copied  by  pouring  collodion  or  gelatine  over 
the  grating  and  stripping  off  the  films  thus  formed.  The  latter  warps, 
however,  and  destroys  the  definition  to  a  great  extent.  The  grating 
always  produces  a  brighter  spectrum  in  the  violet  than  a  prism.  In 
the  green  the  reflecting  speculum  metal  grating  may  be  brighter  than 
a  prism  spectroscope  of  five  prisms,  and  for  higher  dispersion  surpasses 
the  prism  spectroscope  both  in  definition  and  brightness  in  all  portions 
of  the  spectrum. 

To  produce  the  pure  spectrum  from  flat  gratings,  two  telescopes  are 
generally  used,  as  in  Fig.  1. 


DIFFRACTION  GRATINGS 


589 


The  telescopes  are  fixed,  and  the  grating  is  turned  on  its  axis  to  pass 
to  different  portions  of  the  spectrum.  As  the  glass  of  the  telescopes 
absorbs  the  ultra-violet  light,  this  portion  of  the  spectrum  is  cut  off 


FIG.  1.  — Method  of  using  Flat  Grating.     A,  source  of  light;  £,  slit;   C,<7,  two  tel- 
escopes, movable  or  fixed;  Z>,  grating,  movable  about  its  centre;  E,  eye-piece. 

entirely,  unless  quartz  lenses  are  used.  The  concave  grating  avoids 
this  trouble,  and  produces  a  spectrum  without  the  aid  of  lenses,  the 
lines  being  ruled  on  a  concave  surface  instead  of  on  a  flat  one.  Such  a 


•5<»u-ee  o 


FIG.  2.  — Method  of  using  Concave  Grating.     A,  source  of  light;  B,  slit;  D,  grating 
mounted  in  beam  C,  movable  along  the  ways  E,  E;  F,  camera-box  or  eye-piece. 

grating,  properly  mounted,  produces  what  has  been  called  a  normal 
spectrum,  and  is  specially  adapted  to  photographic  purposes  (Fig.  2). 


590  HENRY  A.  EOWLAND 

A  special  form  of  grating  of  great  defining  power  has  been  invented 
by  Professor  Michelson  of  the  University  of  Chicago,  called  the 
'  echelon'  spectroscope  (see  SPECTROSCOPY).  It  is,  however,  of  very 
limited  application. 

See  an  article  on  '  Gratings  in  Theory  and  Practice '  in  Astronomy 
and  Astro-Physics,  XII,  p.  129,  1893. 

(H.  A.  E.) 


ADDRESSES 


A  PLEA  FOR  PURE  SCIENCE  l 

ADDRESS  AS  VICE-PRESIDENT  OF    SECTION    B    OP    THE    AMERICAN    ASSOCIATION    FOR  THE 
ADVANCEMENT    OF    SCIENCE,    MINNEAPOLIS,    MINNESOTA,    A0GUST    15,    1883 

[Proceedings  of  the  American  Association  for  the  Advancement  of  Science,  XXXII,  105-126, 
1883  ;  Science,  II,  242-250,  1883 ;  Journal  of  Franklin  Institute,  CXVI,  279-299,  1883] 

The  question  is  sometimes  asked  us  as  to  the  time  of  year  we  like 
the  best.  To  my  mind,  the  spring  is  the  most  delightful;  for  Nature 
then  recovers  from  the  apathy  of  winter,  and  stirs  herself  to  renewed 
life.  The  leaves  grow,  and  the  buds  open,  with  a  suggestion  of  vigor 
delightful  to  behold;  and  we  revel  in  this  ever-renewed  life.  But  this 
cannot  always  last.  The  leaves  reach  their  limit;  the  buds  open  to  the 
full  and  pass  away.  Then  we  begin  to  ask  ourselves  whether  all  this 
display  has  been  in  vain,  or  whether  it  has  led  to  a  bountiful  harvest. 

So  this  magnificent  country  of  ours  has  rivalled  the  vigor  of  spring 
in  its  growth.  Forests  have  been  leveled,  and  cities  built  and  a  large  and 
powerful  nation  has  been  created  on  the  face  of  the  earth.  We  are  proud 
of  our  advancement.  We  are  proud  of  such  cities  as  this,  founded  in  a 
day  upon  a  spot  over  which  but  a  few  years  since,  the  red  man  hunted 
the  buffalo.  But  we  must  remember  that  this  is  only  the  spring  of 
our  country.  Our  glance  must  not  be  backward;  for,  however  beautiful 
leaves  and  blossoms  are,  and  however  marvelous  their  rapid  increase, 
they  are  but  leaves  and  blossoms  after  all.  Rather  should  we  look 
forward  to  discover  what  will  be  the  outcome  of  all  this  and  what  the 
chance  of  harvest.  For  if  we  do  this  in  time,  we  may  discover  the  worm 
which  threatens  the  ripe  fruit,  or  the  barren  spot  where  the  harvest  is 
withering  for  want  of  water. 

I  am  required  to  address  the  so-called  physical  section  of  this  asso- 

1  In  using  the  word  "  science,"  I  refer  to  physical  science,  as  I  know  nothing  of 
natural  science.     Probably  my  remarks  will,  however,  apply  to  both,  but  I  do  not 
know. 
38 


594  HENRY  A.  EOWLAND 

elation.  Fain  would  I  speak  pleasant  words  to  you  on  this  subject; 
fain  would  I  recount  to  you  the  progress  made  in  this  subject  by  my 
countrymen,  and  their  noble  efforts  to  understand  the  order  of  the 
universe.  But  I  go  out  to  gather  the  grain  ripe  to  the  harvest,  and  I 
find  only  tares.  Here  and  there  a  noble  head  of  grain  rises  above  the 
weeds;  but  so  few  are  they,  that  I  find  the  majority  of  my  countrymen 
know  them  not,  but  think  that  they  have  a  waving  harvest,  while  it  is 
only  one  of  weeds  after  all.  American  science  is  a  thing  of  the  future, 
and  not  of  the  present  or  past;  and  the  proper  course  of  one  in  my 
position  is  to  consider  what  must  be  done  to  create  a  science  of  physics 
in  this  country,  rather  than  to  call  telegraphs,  electric  lights,  and  such 
conveniences,  by  the  name  of  science.  I  do  not  wish  to  underrate  the 
value  of  all  these  things;  the  progress  of  the  world  depends  on  them, 
and  he  is  to  be  honored  who  cultivates  them  successfully.  So  also  the 
cook  who  invents  a  new  and  palatable  dish  for  the  table  benefits  the 
world  to  a  certain  degree;  yet  we  do  not  dignify  him  by  the  name  of  a 
chemist.  And  yet  it  is  not  an  uncommon  thing,  especially  in  American 
newspapers,  to  have  the  applications  of  science  confounded  with  pure 
science;  and  some  obscure  American  who  steals  the  ideas  of  some  great 
mind  of  the  past,  and  enriches  himself  by  the  application  of  the  same 
to  domestic  uses,  is  often  lauded  above  the  great  originator  of  the  idea, 
who  might  have  worked  out  hundreds  of  such  applications,  had  his  mind 
possessed  the  necessary  element  of  vulgarity.  I  have  often  been  asked, 
which  was  the  more  important  to  the  world,  pure  or  applied  science. 
To  have  the  applications  of  a  science,  the  science  itself  must  exist. 
Should  we  stop  its  progress,  and  attend  only  to  its  applications,  we 
should  soon  degenerate  into  a  people  like  the  Chinese,  who  have  made 
no  progress  for  generations,  because  they  have  been  satisfied  with  the 
applications  of  science,  and  have  never  sought  for  reasons  in  what  they 
have  done.  The  reasons  constitute  pure  science.  They  have  known 
the  application  of  gunpowder  for  centuries;  and  yet  the  reasons  for  its 
peculiar  action,  if  sought  in  the  proper  manner,  would  have  developed 
the  science  of  chemistry,  and  even  of  physics,  with  all  their  numerous 
applications.  By  contenting  themselves  with  the  fact  that  gunpowder 
will  explode,  and  seeking  no  farther,  they  have  fallen  behind  in  the 
progress  of  the  world;  and  we  now  regard  this  oldest  and  most  numerous 
of  nations  as  only  barbarians,  and  yet  our  own  country  is  in  this  same 
state.  But  we  have  done  better,  for  we  have  taken  the  science  of  the 
old  world,  and  applied  it  to  all  our  uses,  accepting  it  like  the  rain  of 
heaven,  without  asking  whence  it  came,  or  even  acknowledging  the 


A  PLEA  FOR  PUEE  SCIENCE  595 

debt  of  gratitude  we  owe  to  the  great  and  unselfish  workers  who  have 
given  it  to  us;  and,  like  the  rain  of  heaven,  this  pure  science  has  fallen 
upon  our  country,  and  made  it  great  and  rich  and  strong. 

To  a  civilized  nation  of  the  present  day,  the  applications  of  science 
are  a  necessity,  and  our  country  has  hitherto  succeeded  in  this  line 
only  for  the  reason  that  there  are  certain  countries  in  the  world  where 
pure  science  has  been  and  is  cultivated,  and  where  the  study  of  nature 
is  considered  a  noble  pursuit;  but  such  countries  are  rare,  and  those  who 
wish  to  pursue  pure  science  in  our  own  country  must  be  prepared  to 
face  public  opinion  in  a  manner  which  requires  much  moral  courage. 
They  must  be  prepared  to  be  looked  down  upon  by  every  successful 
inventor  whose  shallow  mind  imagines  that  the  only  pursuit  of  man- 
kind is  wealth,  and  that  he  who  obtains  most  has  best  succeeded  in  this 
world.  Everybody  can  comprehend  a  million  of  money;  but  how  few 
can  comprehend  any  advance  in  scientific  theory,  especially  in  its  more 
abstruse  portions!  And  this,  I  believe,  is  one  of  the  causes  of  the  small 
number  of  persons  who  have  ever  devoted  themselves  to  work  of  the 
higher  order  in  any  human  pursuit.  Man  is  a  gregarious  animal,  and 
depends  very  much,  for  his  happiness,  on  the  sympathy  of  those  around 
him;  and  it  is  rare  to  find  one  with  the  courage  to  pursue  his  own  ideas 
in  spite  of  his  surroundings.  In  times  past,  men  were  more  isolated 
than  at  present,  and  each  came  in  contact  with  a  fewer  number  of 
people.  Hence  that  time  constitutes  the  period  when  the  great  sculp- 
tures, paintings  and  poems  were  produced.  Each  man's  mind  was  com- 
paratively free  to  follow  its  own  ideals,  and  the  results  were  the  great 
and  unique  works  of  the  ancient  masters.  To-day  the  railroad  and  the 
telegraph,  the  books  and  newspapers,  have  united  each  individual  man 
with  the  rest  of  the  world;  instead  of  his  mind  being  an  individual,  a 
thing  apart  by  itself,  and  unique,  it  has  become  so  influenced  by  the 
outer  world,  and  so  dependent  upon  it,  that  it  has  lost  its  originality  to 
a  great  extent.  The  man  who  in  times  past  would  naturally  have  been 
in  the  lowest  depths  of  poverty,  mentally  and  physically,  to-day  meas- 
ures tape  behind  a  counter,  and  with  lordly  air  advises  the  naturally 
born  genius  how  he  may  best  bring  his  outward  appearance  down  to  a 
level  with  his  own.  A  new  idea  he  never  had,  but  he  can  at  least  cover 
his  mental  nakedness  with  ideas  imbibed  from  others.  So  the  genius 
of  the  past  soon  perceives  that  his  higher  ideas  are  too  high  to  be 
appreciated  by  the  world;  his  mind  is  clipped  down  to  the  standard 
form;  every  natural  offshoot  upwards  is  repressed,  until  the  man  is  no 
higher  than  his  fellows.  Hence  the  world,  through  the  abundance  of 


,596  HENRY  A.  EOWLAND 

its  intercourse,  is  reduced  to  a  level.  What  was  formerly  a  grand  and 
magnificent  landscape,  with  mountains  ascending  above  the  clouds,  and 
depths  whose  gloom  we  cannot  now  appreciate,  has  become  serene  and 
peaceful.  The  depths  have  been  filled,  and  the  heights  levelled,  and 
the  wavy  harvests  and  smoky  factories  cover  the  landscape. 

As  far  as  the  average  man  is  concerned,  the  change  is  for  the  better. 
The  average  life  of  man  is  far  pleasanter,  and  his  mental  condition 
better,  than  before.  But  we  miss  the  vigor  imparted  by  the  mountains, 
"We  are  tired  of  mediocrity,  the  curse  of  our  country;  we  are  tired  of 
seeing  our  artists  reduced  to  hirelings,  and  imploring  Congress  to  protect 
them  against  foreign  competition;  we  are  tired  of  seeing  our  country- 
men take  their  science  from  abroad,  and  boast  that  they  here  convert 
it  into  wealth;  we  are  tired  of  seeing  our  professors  degrading  their 
chairs  by  the  pursuit  of  applied  science  instead  of  pure  science,  or  sit- 
ting inactive  while  the  whole  world  is  open  to  investigation;  lingering 
by  the  wayside  while  the  problem  of  the  universe  remains  unsolved.  We 
wish  for  something  higher  and  nobler  in  this  country  of  mediocrity,  for  a 
mountain  to  relieve  the  landscape  of  its  monotony.  We  are  surrounded 
with  mysteries,  and  have  been  created  with  minds  to  enjoy  and  reason 
to  aid  in  the  unfolding  of  such  mysteries.  Nature  calls  to  us  to  study 
her,  and  our  better  feelings  urge  us  in  the  same  direction. 

For  generations  there  have  been  some  few  students  of  science  who 
have  esteemed  the  study  of  nature  the  most  noble  of  pursuits.  Some 
have  been  wealthy,  and  some  poor;  but  they  have  all  had  one  thing  in 
common, — the  love  of  nature  and  its  laws.  To  these  few  men  the  world 
owes  all  the  progress  due  to  applied  science,  and  yet  very  few  ever 
received  any  payment  in  this  world  for  their  labors. 

Faraday,  the  great  discoverer  of  the  principle  on  which  all  machines 
for  electric  lighting,  electric  railways,  and  the  transmission  of  power, 
must  rest,  died  a  poor  man,  although  others  and  the  whole  world  have 
been  enriched  by  his  discoveries;  and  such  must  be  the  fate  of  the 
followers  in  his  footsteps  for  some  time  to  come. 

But  there  will  be  those  in  the  future  who  will  study  nature  from 
pure  love,  and  for  them  higher  prizes  than  any  yet  obtained  are  waiting. 
We  have  but  yet  commenced  our  pursuit  of  science,  and  stand  upon  the 
threshold  wondering  what  there  is  within.  We  explain  the  motion  of 
the  planets  by  the  law  of  gravitation;  but  who  will  explain  how  two 
bodies,  millions  of  miles  apart,  tend  to  go  toward  each  other  with  a 
certain  force?  We  now  weigh  and  measure  electricity  and  electric  cur- 
rents with  as  much  ease  as  ordinary  matter,  yet  have  we  made  any 


A  PLEA  FOR  PURE  SCIENCE  597 

approach  to  an  explanation  of  the  phenomenon  of  electricity?  Light  is 
an  undulatory  motion,,  and  yet  do  we  know  what  it  is  that  undulates? 
Heat  is  motion,  yet  do  we  know  what  it  is  that  moves?  Ordinary  matter 
is  a  common  substance,  and  yet  who  shall  fathom  the  mystery  of  its 
internal  constitution? 

There  is  room  for  all  in  the  work,  and  the  race  has  but  commenced. 
The  problems  are  not  to  be  solved  in  a  moment,  but  need  the  best  work 
of  the  best  minds,  for  an  indefinite  time. 

Shall  our  country  be  contented  to  stand  by,  while  other  countries  lead 
in  the  race?  Shall  we  always  grovel  in  the  dust,  and  pick  up  the  crumbs 
which  fall  from  the  rich  man's  table,  considering  ourselves  richer  than 
he  because  we  have  more  crumbs,  while  we  forget  that  he  has  the  cake, 
which  is  the  source  of  all  crumbs?  Shall  we  be  swine,  to  whom  the 
corn  and  husks  are  of  more  value  than  the  pearls?  If  I  read  aright  the 
signs  of  the  times,  I  think  we  shall  not  always  be  contented  with  our 
inferior  position.  From  looking  down  we  have  almost  become  blind, 
but  may  recover.  In  a  new  country,  the  necessities  of  life  must  be 
attended  to  first.  The  curse  of  Adam  is  upon  us  all,  and  we  must  earn 
our  bread. 

But  it  is  the  mission  of  applied  science  to  render  this  easier  for  the 
whole  world.  There  is  a  story  which  I  once  read,  which  will  illustrate 
the  true  position  of  applied  science  in  the  world.  A  boy,  more  fond 
of  reading  than  of  work,  was  employed,  in  the  early  days  of  the  steam- 
engine,  to  turn  the  valve  at  every  stroke.  Necessity  was  the  mother  of 
invention  in  his  case:  his  reading  was  disturbed  by  his  work,  and  he 
soon  discovered  that  he  might  become  free  from  his  work  by  so  tying 
the  valve  to  some  movable  portion  of  the  engine,  as  to  make  it  move  its 
own  valve.  So  I  consider  that  the  true  pursuit  of  mankind  is  intellec- 
tual. The  scientific  study  of  nature  in  all  its  branches,  of  mathematics, 
of  mankind  in  its  past  and  present,  the  pursuit  of  art,  and  the  cultiva- 
tion of  all  that  is  great  and  noble  in  the  world, — these  are  the  highest 
occupation  of  mankind.  Commerce,  the  applications  of  science,  the 
accumulation  of  wealth,  are  necessities  which  are  a  curse  to  those  with 
high  ideals,  but  a  blessing  to  that  portion  of  the  world  which  has  neither 
the  ability  nor  the  taste  for  higher  pursuits. 

As  the  applications  of  science  multiply,  living  becomes  easier,  the 
wealth  necessary  for  the  purchase  of  apparatus  can  be  obtained,  and 
the  pursuit  of  other  things  besides  the  necessities  of  life  becomes 
possible. 

But  the  moral  qualities  must  also  be  cultivated  in  proportion  to  the 


598  HENRY  A.  ROWLAND 

wealth  of  the  country,  before  much  can  be  done  in  pure  science.  The 
successful  sculptor  or  painter  naturally  attains  to  wealth  through  the 
legitimate  work  of  his  profession.  The  novelist,  the  poet,  the  musician, 
all  have  wealth  before  them  as  the  end  of  a  successful  career.  But  the 
scientist  and  the  mathematician  have  no  such  incentive  to  work:  they 
must  earn  their  living  by  other  pursuits,  usually  teaching,  and  only 
devote  their  surplus  time  to  the  true  pursuit  of  their  science.  And 
frequently,  by  the  small  salary  which  they  receive,  by  the  lack  of  instru- 
mental and  literary  facilities,  by  the  mental  atmosphere  in  which  they 
exist,  and,  most  of  all,  by  their  low  ideals  of  life,  they  are  led  to  devote 
their  surplus  time  to  applied  science  or  to  other  means  of  increasing 
their  fortune.  How  shall  we,  then,  honor  the  few,  the  very  few,  who,  in 
spite  of  all  difficulties,  have  kept  their  eyes  fixed  on  the  goal,  and  have 
steadily  worked  for  pure  science,  giving  to  the  world  a  most  precious 
donation,  which  has  borne  fruit  in  our  greater  knowledge  of  the 
universe  and  in  the  applications  to  our  physical  life  which  have  enriched 
thousands  and  benefited  each  one  of  us?  There  are  also  those  who  have 
every  facility  for  the  pursuit  of  science,  who  have  an  ample  salary  and 
every  appliance  for  work,  yet  who  devote  themselves  to  commercial  work, 
to  testifying  in  courts  of  law,  and  to  any  other  work  to  increase  their 
present  large  income.  Such  men  would  be  respectable  if  they  gave  up 
the  name  of  professor,  and  took  that  of  consulting  chemist  or  physicist. 
And  such  men  are  needed  in  the  community.  But  for  a  man  to  occupy 
the  professor's  chair  in  a  prominent  college,  and,  by  his  energy  and 
ability  in  the  commercial  applications  of  his  science,  stand  before  the 
local  community  as  a  newspaper  exponent  of  his  science,  is  a  disgrace 
both  to  him  and  his  college.  It  is  the  death-blow  to  science  in  that 
region.  Call  him  by  his  proper  name,  and  he  becomes  at  once  a  useful 
member  of  the  community.  Put  in  his  place  a  man  who  shall  by  pre- 
cept and  example  cultivate  his  science,  and  how  different  is  the  result! 
Young  men,  looking  forward  into  the  world  for  something  to  do,  see 
before  them  this  high  and  noble  life,  and  they  see  that  there  is  some- 
thing more  honorable  than  the  accumulation  of  wealth.  They  are  thus 
led  to  devote  their  lives  to  similar  pursuits,  and  they  honor  the  professor 
who  has  drawn  them  to  something  higher  than  they  might  otherwise 
have  aspired  to  reach. 

I  do  not  wish  to  be  misunderstood  in  this  matter.  It  is  no  disgrace 
to  make  money  by  an  invention,  or  otherwise,  or  to  do  commercial 
scientific  work  under  some  circumstances;  but  let  pure  science  be  the 
aim  of  those  in  the  chairs  of  professors,  and  so  prominently  the  aim  that 


A  PLEA  FOR  PURE  SCIENCE  599 

there  can  be  no  mistake.  If  our  aim  in  life  is  wealth,  let  us  honestly 
engage  in  commercial  pursuits,  and  compete  with  others  for  its  posses- 
sion; but  if  we  choose  a  life  which  we  consider  higher,  let  us  live  up  to 
it,  taking  wealth  or  poverty  as  it  may  chance  to  come  to  us,  but  letting 
neither  turn  us  aside  from  our  pursuit. 

The  work  of  teaching  may  absorb  the  energies  of  many;  and,  indeed, 
this  is  the  excuse  given  by  most  for  not  doing  any  scientific  work.  But 
there  is  an  old  saying,  that  where  there  is  a  will  there  is  a  way.  Few 
professors  do  as  much  teaching  or  lecturing  as  the  German  professors, 
who  are  also  noted  for  their  elaborate  papers  in  the  scientific  journals. 
I  myself  have  been  burdened  down  with  work,  and  know  what  it  is;  and 
yet  I  here  assert  that  all  can  find  time  for  scientific  research  if  they 
desire  it.  But  here,  again,  that  curse  of  our  country,  mediocrity,  is 
upon  us.  Our  colleges  and  universities  seldom  call  for  first-class  men 
of  reputation,  and  I  have  even  heard  the  trustee  of  a  well-known  college 
assert  that  no  professor  should  engage  in  research  because  of  the  time 
wasted.  I  was  glad  to  see.  soon  after,  by  the  call  of  a  prominent  scientist 
to  that  college,  that  the  majority  of  the  trustees  did  not  agree  with  him. 

That  teaching  is  important  goes  without  saying.  A  successful  teacher 
is  to  be  respected:  but  if  he  does  not  lead  his  scholars  to  that  which  is 
highest,  is  he  not  blameworthy?  We  are,  then,  to  look  to  the  colleges 
and  universities  of  the  land  for  most  of  the  work  in  pure  science  which 
is  done.  Let  us  therefore  examine  these  latter,  and  see  what  the  pros- 
pect is. 

One,  whom  perhaps  we  may  here  style  a  practical  follower  of  Euskin, 
has  stated  that  while  in  this  country  he  was  variously  designated  by  the 
title  of  captain,  colonel,  and  professor.  The  story  may  or  may  not  be 
true,  but  we  all  know  enough  of  the  customs  of  our  countrymen  not  to 
dispute  it  on  general  principles.  All  men  are  born  equal:  some  men 
title  of  captain,  colonel,  and  professor.  The  story  may  or  may  not  be 
The  logic  is  conclusive;  and  the  same  kind  of  logic  seems  to  have  been 
applied  to  our  schools,  colleges,  and  universities.  I  have  before  me  the 
report  of  the  commissioner  of  education  for  1880.  According  to  that 
report,  there  were  389/  or  say,  in  round  numbers,  400  institutions,  call- 
ing themselves  colleges  or  universities,  in  our  country!  We  may  well 
exclaim  that  ours  is  a  great  country,  having  more  than  the  whole  world 
beside.  The  fact  is  sufficient.  The  whole  earth  could  hardly  support 
such  a  number  of  first-class  institutions.  The  curse  of  mediocrity  must 

J364  reported  on,  and  25  not  reported. 


600  HENEY  A.  EOWLAND 

be  upon  them,  to  swarm  in  such  numbers.  They  must  be  a  cloud  of 
mosquitoes,  instead  of  eagles  as  they  profess;  and  this  becomes  evident 
on  further  analysis.  About  one-third  aspire  to  the  name  of  university; 
and  I  note  one  called  by  that  name  which  has  two  professors  and 
eighteen  students,  and  another  having  three  teachers  and  twelve  stu- 
dents! These  instances  are  not  unique,  for  the  number  of  small  insti- 
tutions and  schools  which  call  themselves  universities  is  very  great.  It 
is  difficult  to  decide  from  the  statistics  alone  the  exact  standing  of  these 
institutions.  The  extremes  are  easy  to  manage.  "Who  can  doubt 
that  an  institution  with  over  eight  hundred  students,  and  a  faculty  of 
seventy  is  of  a  higher  grade  than  those  above  cited  having  ten  or  twenty 
students  and  two  or  three  in  the  faculty?  Yet  this  is  not  always  true; 
for  I  note  one  institution  with  over  five  hundred  students  which  is 
known  to  me  personally  as  of  the  grade  of  a  high  school.  The  statistics 
are  more  or  less  defective,  and  it  would  much  weaken  the  force  of  my 
remarks  if  I  went  too  much  into  detail.  I  append  the  following  tables, 
however,  of  330  so-called  colleges  and  universities: 

218  had  from  0  to  100  students. 
88  had  from  100  to  200  students. 
12  had  from  200  to  300  students. 

6  had  from  300  to  500  students. 

6  had  over  500  students. 

Of  322  so-called  colleges  and  universities: 

206  had  0  to  10  in  the  faculty. 
99  had  10  to  20  in  the  faculty. 
17  had  20  or  over  in  the  faculty. 

If  the  statistics  were  forthcoming, — and  possibly  they  may  exist, — 
we  might  also  get  an  idea  of  the  standing  of  these  institutions  and  their 
approach  to  the  true  university  idea,  by  the  average  age  of  the  scholars. 
Possibly  also  the  ratio  of  number  of  scholars  to  teachers  might  be  of 
some  help.  All  these  methods  give  an  approximation  to  the  present 
standing  of  the  institutions.  But  there  is  another  method  of  attacking 
the  problem,  which  is  very  exact,  yet  it  only  gives  us  the  possibilities  in 
the  case  of  the  institutions.  I  refer  to  the  wealth  of  the  institution. 
In  estimating  the  wealth,  I  have  not  included  the  value  of  grounds  and 
buildings,  for  this  is  of  little  importance,  either  to  the  present  or  future 
standing  of  the  institution,  as  good  work  can  be  done  in  a  hovel  as  in  a 


A  PLEA  FOR  PURE  SCIENCE  601 

• 

palace.     I  have  taken  the  productive  funds  of  the  institution  as  the 
basis  of  estimate.     I  find: 

234  have  below  $500,000. 

8  have  between  $500,000  and  $1,000,000. 
8  have  over  $1,000,000. 

There  is  no  fact  more  firmly  established,  all  over  the  world,  than  that 
the  higher  education  can  never  be  made  to  pay  for  itself.  Usually  the 
cost  to  a  college,  of  educating  a  young  man,  very  much  exceeds  what 
he  pays  for  it,  and  is  often  three  or  four  times  as  much.  The  higher 
the  education,  the  greater  this  proportion  will  be;  and  a  university  of 
the  highest  class  should  anticipate  only  a  small  accession  to  its  income 
from  the  fees  of  students.  Hence  the  test  I  have  applied  must  give  a 
true  representation  of  the  possibilities  in  every  case.  According  to  the 
figures,  only  sixteen  colleges  and  universities  have  $500,000  or  over  of 
invested  funds,  and  only  one-half  of  these  have  $1,000,000  and  over. 
Now,  even  the  latter  sum  is  a  very  small  endowment  for  a  college;  and 
to  call  any  institution  a  university  which  has  less  than  $1,000,000  is  to 
render  it  absurd  in  the  face  of  the  world.  And  yet  more  than  100  of 
our  institutions,  many  of  them  very  respectable  colleges,  have  abused 
the  word  "university"  in  this  manner.  It  is  to  be  hoped  that  the 
endowment  of  the  more  respectable  of  these  institutions  may  be  in- 
creased, as  many  of  them  deserve  it;  and  their  unfortunate  appellation 
has  probably  been  repented  of  long  since. 

But  what  shall  we  think  of  a  community  that  gives  the  charter  of 
a  university  to  an  institution  with  a  total  of  $20,000  endowment,  two 
so-called  professors,  and  eighteen  students!  or  another  with  three 
professors,  twelve  students,  and  a  total  of  $27,000  endowment,  mostly 
invested  in  buildings!  And  yet  there  are  very  many  similar  institu- 
tions; there  being  sixteen  with  three  professors  or  less,  and  very  many 
indeed  with  only  four  or  five. 

Such  facts  as  these  could  only  exist  in  a  democratic  country,  where 
pride  is  taken  in  reducing  everything  to  a  level.  And  I  may  also  say. 
that  it  can  only  exist  in  the  early  days  of  such  a  democracy;  for  an 
intelligent  public  will  soon  perceive  that  calling  a  thing  by  a  wrong 
name  does  not  change  its  character,  and  that  truth,  above  all  things, 
should  be  taught  to  the  youth  of  the  nation. 

It  may  be  urged,  that  all  these  institutions  are  doing  good  work  in 
education;  and  that  many  young  men  are  thus  taught,  who  could  not 
afford  to  go  to  a  true  college  or  university.  But  I  do  not  object  to  the 


602  HENRY  A.  ROWLAND 

• 

education., — though  I  have  no  doubt  an  investigation  would  disclose 
equal  absurdities  here, — for  it  is  aside  from  my  object.  But  I  do  object 
to  lowering  the  ideals  of  the  youth  of  the  country.  Let  them  know  that 
they  are  attending  a  school,  and  not  a  university;  and  let  them  know 
that  above  them  comes  the  college,  and  above  that  the  university.  Let 
them  be  taught  that  they  are  only  half  educated,  and  that  there  are 
persons  in  the  world  by  whose  side  they  are  but  atoms.  In  other  words, 
let  them  be  taught  the  truth. 

It  may  be  that  some  small  institutions  are  of  high  grade,  especially 
those  which  are  new;  but  who  can  doubt  that  more  than  two-thirds  of 
our  institutions  calling  themselves  colleges  and  universities  are  un- 
worthy of  the  name?  Each  one  of  these  institutions  has  so-called  pro- 
fessors, but  it  is  evident  that  they  can  be  only  of  the  grade  of  teachers. 
Why  should  they  not  be  so  called?  The  position  of  teacher  is  an 
honored  one,  but  is  not  made  more  honorable  by  the  assumption  of  a 
false  title.  Furthermore,  the  multiplication  of  the  title,  and  the  ease 
with  which  it  can  be  obtained,  render  it  scarcely  worth  striving  for. 
When  the  man  of  energy,  ability,  and  perhaps  genius  is  rewarded  by 
the  same  title  and  emoluments  as  the  commonplace  man  with  the 
modicum  of  knowledge,  who  takes  to  teaching,  not  because  of  any  apti- 
tude for  his  work,  but  possibly  because  he  has  not  the  energy  to  com- 
pete with  his  fellow-men  in  business,  then  I  say  one  of  the  inducements 
for  the  first-class  men  to  become  professors  is  gone. 

When  work  and  ability  are  required  for  the  position,  and  when  the 
professor  is  expected  to  keep  up  with  the  progress  of  his  subject,  and 
to  do  all  in  his  power  to  advance  it,  and  when  he  is  selected  for  these 
reasons,  then  the  position  will  be  worth  working  for,  and  the  successful 
competitor  will  be  honored  accordingly.  The  chivalric  spirit  which 
prompted  Faraday  to  devote  his  life  to  the  study  of  nature  may  actuate 
a  few  noble  men  to  give  their  lives  to  scientific  work;  but  if  we  wish  to 
cultivate  this  highest  class  of  men  in  science,  we  must  open  a  career 
for  them  worthy  of  their  efforts. 

Jenny  Lind,  with  her  beautiful  voice,  would  have  cultivated  it  to 
some  extent  in  her  native  village:  yet  who  would  expect  her  to  travel 
over  the  world,  and  give  concerts  for  nothing?  and  how  would  she  have 
been  able  to  do  so  if  she  had  wished?  And  so  the  scientific  man,  what- 
ever his  natural  talents,  must  have  instruments  and  a  library,  and  a 
suitable  and  respectable  salary  to  live  upon,  before  he  is  able  to  exert 
himself  to  his  full  capacity.  This  is  true  of  advance  in  all  the  higher 
departments  of  human  learning,  and  yet  something  more  is  necessary. 


A  PLEA  FOR  PUEE  SCIENCE  603 

It  is  not  those  in  this  country  who  receive  the  largest  salary,  and  have 
positions  in  the  richest  colleges,  who  have  advanced  their  subject  the 
most:  men  receiving  the  highest  salaries,  and  occupying  the  professor's 
chair,  are  to-day  doing  absolutely  nothing  in  pure  science,  but  are  striv- 
ing by  the  commercial  applications  of  their  science  to  increase  their 
already  large  salary.  Such  pursuits,  as  I  have  said  before,  are  honorable 
in  their  proper  place;  but  the  duty  of  a  professor  is  to  advance  his  science, 
and  to  set  an  example  of  pure  and  true  devotion  to  it  which  shall  demon- 
strate to  his  students  and  the  world  that  there  is  something  high  and 
noble  worth  living  for.  Money-changers  are  often  respectable  men,  and 
yet  they  were  once  severely  rebuked  for  carrying  on  their  trade  in  the 
court  of  the  temple. 

"Wealth  does  not  constitute  a  university,  buildings  do  not:  it  is  the 
men  who  constitute  its  faculty,  and  the  students  who  learn  from  them. 
It  is  the  last  and  highest  step  which  the  mere  student  takes.  He  goes 
forth  into  the  world,  and  the  height  to  which  he  rises  has  been  influenced 
by  the  ideals  which  he  has  consciously  or  unconsciously  imbibed  in  his 
university.  If  the  professors  under  whom  he  has  studied  have  been 
high  in  their  profession,  and  have  themselves  had  high  ideals;  if  they 
have  considered  the  advance  of  their  particular  subject  their  highest 
work  in  life,  and  are  themselves  honored  for  their  intellect  throughout 
the  world, — the  student  is  drawn  toward  that  which  is  highest,  and 
ever  after  in  life  has  high  ideals.  But  if  the  student  is  taught  by  what 
are  sometimes  called  good  teachers,  and  teachers  only,  who  know  little 
more  than  the  student,  and  who  are  often  surpassed  and  even  despised 
by  him,  no  one  can  doubt  the  lowered  «tone  of  his  mind.  He  finds  that 
by  his  feeble  efforts  he  can  surpass  one  to  whom  a  university  has  given 
its  highest  honor;  and  he  begins  to  think  that  he  himself  is  a  born 
genius,  and  the  incentive  to  work  is  gone.  He  is  great  by  the  side  of 
the  molehill,  and  does  not  know  any  mountain  to  compare  himself  with. 

A  university  should  have  not  only  great  men  in  its  faculty,  but  have 
numerous  minor  professors  and  assistants  of  all  kinds,  and  should 
encourage  the  highest  work,  if  for  no  other  reason  than  to  encourage 
the  student  to  his  highest  efforts. 

But,  assuming  that  the  professor  has  high  ideals,  wealth  such  as  only 
a  large  and  high  university  can  command  is  necessary  to  allow  him  the 
fullest  development. 

And  this  is  specially  so  in  our  science  of  physics.  In  the  early  days 
of  physics  and  chemistry,  many  of  the  fundamental  experiments  could 
be  performed  with  the  simplest  apparatus.  And  so  we  often  find  the 


604  HENKT  A.  KOWLAND 

names  of  Wollaston  and  Faraday  mentioned  as  needing  scarcely  any- 
thing for  their  researches.  Much  can  even  now  be  done  with  the  sim- 
plest apparatus,  and  nobody,  except  the  utterly  incompetent,  need  stop 
for  want  of  it;  but  the  fact  remains,  that  one  can  only  be  free  to  investi- 
gate in  all  departments  of  chemistry  and  physics,  when  he  not  only  has 
a  complete  laboratory  at  his  command,  but  a  fund  to  draw  on  for  the 
expenses  of  each  experiment.  That  simplest  of  the  departments  of 
physics,  namely,  astronomy,  has  now  reached  such  perfection  that 
nobody  can  expect  to  do  much  more  in  it  without  a  perfectly  equipped 
observatory;  and  even  this  would  be  useless  without  an  income  sufficient 
to  employ  a  corps  of  assistants  to  make  the  observations  and  computa- 
tions. But  even  in  this  simplest  of  physical  subjects,  there  is  great 
misunderstanding.  Our  country  has  very  many  excellent  observatories, 
and  yet  little  work  is  done  in  comparison,  because  no  provision  has  been 
made  for  maintaining  the  work  of  the  observatory;  and  the  wealth 
which,  if  concentrated,  might  have  made  one  effective  observatory  which 
would  prove  a  benefit  to  astronomical  science,  when  scattered  among  a 
half-dozen  merely  furnishes  telescopes  for  the  people  in  the  surrounding 
region  to  view  the  moon  with.  And  here  I  strike  the  keynote  of  at  least 
one  need  of  our  country,  if  she  would  stand  well  in  science;  and  the 
following  item  which  I  clip  from  a  newspaper  will  illustrate  the  matter: 
"  The  eccentric  old  Canadian,  Arunah  Huntington,  who  left  $200,000 
to  be  divided  among  the  public  schools  of  Vermont,  has  done  something 
which  will  be  of  little  practical  value  to  the  schools.  Each  district  will 
be  entitled  to  the  insignificant  sum  of  $10,  which  will  not  advance 
much  the  cause  of  education."  • 

Nobody  will  dispute  the  folly  of  such  a  bequest,  or  the  folly  of  filling 
the  country  with  telescopes  to  look  at  the  moon,  and  calling  them 
observatories.  How  much  better  to  concentrate  the  wealth  into  a  few 
parcels,  and  make  first-class  observatories  and  institutions  with  it! 

Is  it  possible  that  any  of  our  four  hundred  colleges  and  universities 
have  love  enough  of  learning  to  unite  with  each  other  and  form  larger 
institutions?  Is  it  possible  that  any  have  such  a  love  of  truth  that  they 
are  willing  to  be  called  by  their  right  name?  I  fear  not;  for  the  spirit 
of  expectation,  which  is  analogous  to  the  spirit  of  gambling,  is  strong  in 
the  American  breast,  and  each  institution  which  now,  except  in  name, 
slumbers  in  obscurity,  expects  in  time  to  bloom  out  into  full  prosperity. 
Although  many  of  them  are  under  religious  influence,  where  truth  is 
inculcated,  and  where  men  are  taught  to  take  a  low  seat  at  the  table 
in  order  that  they  may  be  honored  by  being  called  up  higher,  and  not 


A  PLEA  FOR  PURE  SCIENCE  605 

dishonored  by  being  thrust  down  lower,  yet  these  institutions  have  thrust 
themselves  into  the  highest  seats,  and  cannot  probably  be  dislodged. 

But  would  it  not  be  possible  so  to  change  public  opinion  that  no 
college  could  be  founded  with  a  less  endowment  than  say  $1,000,000, 
or  no  university  with  less  than  three  or  four  times  that  amount.  From 
the  report  of  the  commissioner  of  education,  I  learn  that  such  a  thing 
is  taking  place;  that  the  tendency  towards  large  institutions  is  increas- 
ing, and  that  it  is  principally  in  the  west  and  southwest  that  the  multi- 
plication of  small  institutions  with  big  names  is  to  be  feared  most,  and 
that  the  east  is  almost  ready  for  the  great  coming  university. 

The  total  wealth  of  the  four  hundred  colleges  and  universities  in  1880 
was  about  $40,000,000  in  buildings,  and  $43,000,000  in  productive 
i'unds.  This  would  be  sufficient  for  one  great  university  of  $10,000,000, 
four  of  $5,000,000,  and  twenty-six  colleges  of  $2,000,000  each.  But 
such  an  idea  can  of  course  never  be  carried  out.  Government  appro- 
priations are  out  of  the  question,  because  no  political  trickery  must  be 
allowed  around  the  ideal  institution. 

In  the  year  1880  the  private  bequests  to  all  schools  and  colleges 
amounted  to  about  $5,500,000;  and,  although  there  was  one  bequest  of 
$1,250,000,  yet  the  amount  does  not  appear  to  be  phenomenal.  It 
would  thus  seem  that  the  total  amount  was  about  five  million  dollars  in 
one  year,  of  which  more  than  half  is  given  to  so-called  colleges  and 
universities.  It  would  be  very  difficult  to  regulate  these  bequests  so 
that  they  might  be  concentrated  sufficiently  to  produce  an  immediate 
result.  But  the  figures  show  that  generosity  is  a  prominent  feature  of 
the  American  people,  and  that  the  needs  of  the  country  only  have  to 
be  appreciated  to  have  the  funds  forthcoming.  We  must  make  the 
need  of  research  and  of  pure  science  felt  in  the  country.  "We  must  live 
such  lives  of  pure  devotion  to  our  science,  that  all  shall  see  that  we  ask 
for  money,  not  that  we  may  live  in  indolent  ease  at  the  expense  of 
charity,  but  that  we  may  work  for  that  which  has  advanced  and  will 
advance  the  world  more  than  any  other  subject,  both  intellectually  and 
physically.  We  must  live  such  lives  as  to  neutralize  the  influence  of 
those  who  in  high  places  have  degraded  their  profession,  or  have  given 
themselves  over  to  ease,  and  do  nothing  for  the  science  which  they 
represent.  Let  us  do  what  we  can  with  the  present  means  at  our  dis- 
posal. There  is  not  one  of  us  who  is  situated  in  the  position  best 
adapted  to  bring  out  all  his  powers,  and  to  allow  him  to  do  most  for 
his  science.  All  have  their  difficulties,  and  I  do  not  think  that  circum- 
stances will  ever  radically  change  a  man.  If  a  man  has  the  instinct  of 


HENRY  A.  ROWLAND 

research  in  him,  it  will  always  show  itself  in  some  form.  But  circum- 
stances may  direct  it  into  new  paths,  or  may  foster  it  so  that  what 
would  otherwise  have  died  as  a  bud  now  blossoms  and  ripens  into  the 
perfect  fruit. 

Americans  have  shown  no  lack  of  invention  in  small  things;  and  the 
same  spirit  when  united  to  knowledge  and  love  of  science,  becomes  the 
spirit  of  research.  The  telegraph-operator,  with  his  limited  knowledge 
of  electricity  and  its  laws,  naturally  turns  his  attention  to  the  improve- 
ment of  the  only  electrical  instrument  he  knows  anything  about;  and  his 
researches  would  be  confined  to  the  limited  sphere  of  his  knowledge, 
and  to  the  simple  laws  with  which  he  is  acquainted.  But  as  his  knowl- 
edge increases,  and  the  field  broadens  before  him,  as  he  studies  the 
mathematical  theory  of  the  subject,  and  the  electromagnetic  theory  of 
light  loses  the  dim  haze  due  to  distance,  and  becomes  his  constant  com- 
panion, the  telegraph  instrument  becomes  to  him  a  toy,  and  his  effort 
to  discover  something  new  becomes  research  in  pure  science. 

It  is  useless  to  attempt  to  advance  science  until  one  has  mastered  the 
science:  he  must  step  to  the  front  before  his  blows  can  tell  in  the 
strife.  Furthermore,  I  do  not  believe  anybody  can  be  thorough  in  any 
department  of  science,  without  wishing  to  advance  it.  In  the  study  of 
what  is  known,  in  the  reading  of  the  scientific  journals,  and  the  discus- 
sions therein  contained  of  the  current  scientific  questions,  one  would 
obtain  an  impulse  to  work,  even  though  it  did  not  before  exist;  and  the 
same  spirit  which  prompted  him  to  seek  what  was  already  known  would 
make  him  wish  to  know  the  unknown.  And  I  may  say  that  I  never  met 
a  case  of  thorough  knowledge  in  my  own  science,  except  in  the  case  of 
well-known  investigators.  I  have  met  men  who  talked  well,  and  I  have 
sometimes  asked  myself  why  they  did  not  do  something;  but  further 
knowledge  of  their  character  has  shown  the  superficiality  of  their 
knowledge.  I  am  no  longer  a  believer  in  men  who  could  do  something 
if  they  would,  or  would  do  something  if  they  had  a  chance.  They  are 
impostors.  If  the  spirit  is  there,  it  will  show  itself  in  spite  of  circum- 
stances. 

As  I  remarked  before,  the  investigator  in  pure  science  is  usually  a 
professor.  He  must  teach  as  well  as  investigate.  It  is  a  question  which 
has  been  discussed  in  late  years,  as  to  whether  these  two  functions  had 
better  be  combined  in  the  same  individual,  or  separated.  It  seems  to 
be  the  opinion  of  most,  that  a  certain  amount  of  teaching  is  conducive, 
rather  than  otherwise,  to  the  spirit  of  research.  I  myself  think  that 
this  is  true,  and  I  should  myself  not  like  to  give  up  my  daily  lecture;  but 


A  PLEA  FOR  PURE  SCIENCE  607 

one  must  not  be  overburdened.  I  suppose  that  the  true  solution,  in 
many  cases,  would  be  found  in  the  multiplication  of  assistants,  not  only 
for  the  work  of  teaching  but  of  research.  Some  men  are  gifted  with 
more  ideas  than  they  can  work  out  with  their  own  hands,  and  the  world 
is  losing  much  by  not  supplying  them  with  extra  hands.  Life  is  short: 
old  age  comes  quickly,  and  the  amount  one  pair  of  hands  can  do  is  very 
limited.  What  sort  of  shop  would  that  be,  or  what  sort  of  factory,  where 
one  man  had  to  do  all  the  work  with  his  own  hands?  It  is  a  fact  in 
nature,  which  no  democracy  can  change,  that  men  are  not  equal, — that 
some  have  brains,  and  some  hands;  and  no  idle  talk  about  equality  can 
ever  subvert  the  order  of  the  universe. 

I  know  of  no  institution  in  this  country  where  assistants  are  supplied 
to  aid  directly  in  research;  yet  why  should  it  not  be  so?  Even  the 
absence  of  assistant  professors  and  assistants  of  all  kinds,  to  aid  in 
teaching,  is  very  noticeable,  and  must  be  remedied  before  we  can  expect 
much. 

There  are  many  physical  problems,  especially  those  requiring  exact 
measurements,  which  cannot  be  carried  out  by  one  man,  and  can  only 
be  successfully  attacked  by  the  most  elaborate  apparatus,  and  with  a 
full  corps  of  assistants.  Such  are  Eegnault's  experiments  on  the  funda- 
mental laws  of  gases  and  vapors,  made  thirty  or  forty  years  ago  by  aid 
from  the  French  government,  and  which  are  the  standards  to  this  day. 
Although  these  experiments  were  made  with  a  view  to  the  practical 
calculation  of  the  steam-engine,  yet  they  were  carried  out  in  such  a 
broad  spirit  that  they  have  been  of  the  greatest  theoretical  use.  Again, 
what  would  astronomy  have  done  without  the  endowment  of  observa- 
tories? By  their  means,  that  science  has  become  the  most  perfect  of 
all  branches  of  physics,  as  it  should  be  from  its  simplicity.  There  is  no 
doubt,  in  my  mind,  that  similar  institutions  for  other  branches  of 
physics,  or,  better,  to  include  the  whole  of  physics,  would  be  equally 
successful.  A  large  and  perfectly  equipped  physical  laboratory  with  its 
large  revenues,  its  corps  of  professors  and  assistants,  and  its  machine- 
shop  for  the  construction  of  new  apparatus,  would  be  able  to  advance 
our  science  quite  as  much  as  endowed  observatories  have  advanced 
astronomy.  But  such  a  laboratory  should  not  be  founded  rashly.  The 
value  will  depend  entirely  on  the  physicist  at  its  head,  who  has  to 
devise  the  plan,  and  to  start  it  into  practical  working.  Such  a  man  will 
always  be  rare,  and  cannot  always  be  obtained.  After  one  had  been 
successfully  started,  others  could  follow;  for  imitation  requires  little 
brains. 


608  HENRY  A.  EOWLAND 

One  could  not  be  certain  of  getting  the  proper  man  every  time,  but 
the  means  of  appointment  should  be  most  carefully  studied  so  as  to 
secure  a  good  average.  There  can  be  no  doubt  that  the  appointment 
should  rest  with  a  scientific  body  capable  of  judging  the  highest  work 
of  each  candidate. 

Should  any  popular  element  enter,  the  person  chosen  would  be  of  the 
literary-scientific  order,  or  the  dabbler  on  the  outskirts  who  presents  his 
small  discoveries  in  the  most  theatrical  manner.  What  is  required  is 
a  man  of  depth,  who  has  such  an  insight  into  physical  science  that  he 
can  tell  when  blows  will  best  tell  for  its  advancement. 

Such  a  grand  laboratory  as  I  describe  does  not  exist  in  the  world,  at 
present,  for  the  study  of  physics.  But  no  trouble  has  ever  been  found 
in  obtaining  means  to  endow  astronomical  science.  Everybody  can 
appreciate,  to  some  extent,  the  value  of  an  observatory;  as  astronomy 
is  the  simplest  of  scientific  subjects,  and  has  very  quickly  reached  a 
position  where  elaborate  instruments  and  costly  computations  are  neces- 
sary to  further  advance.  The  whole  domain  of  physics  is  so  wide  that 
workers  have  hitherto  found  enough  to  do.  But  it  cannot  always  be 
so,  and  the  time  has  even  now  arrived  when  such  a  grand  laboratory 
should  be  founded.  Shall  our  country  take  the  lead  in  this  matter,  or 
shall  we  wait  for  foreign  countries  to  go  before?  They  will  be  built  in 
the  future,  but  when  and  how  is  the  question. 

Several  institutions  are  now  putting  up  laboratories  for  physics. 
They  are  mostly  for  teaching,  and  we  can  expect  only  a  comparatively 
small  amount  of  work  from  most  of  them.  But  they  show  progress; 
and,  if  the  progress  be  as  quick  in  this  direction  as  in  others,  we  should 
be  able  to  see  a  great  change  before  the  end  of  our  lives. 

As  stated  before,  men  are  influenced  by  the  sympathy  of  those  with 
whom  they  come  in  contact.  It  is  impossible  to  change  public  opinion 
in  our  favor  immediately;  and,  indeed,  we  must  always  seek  to  lead  it, 
and  not  be  guided  by  it.  For  pure  science  is  the  pioneer  who  must  not 
hover  about  cities  and  civilized  countries,  but  must  strike  into  unknown 
forests,  and  climb  the  hitherto  inaccessible  mountains  which  lead  to 
and  command  a  view  of  the  promised  land, — the  land  which  science 
promises  us  in  the  future;  which  shall  not  only  flow  with  milk  and 
honey,  but  shall  give  us  a  better  and  more  glorious  idea  of  this  wonder- 
ful universe.  We  must  create  a  public  opinion  in  our  favor,  but  it  need 
not  at  first  be  the  general  public.  We  must  be  contented  to  stand  aside, 
and  see  the  honors  of  the  world  for  a  time  given  to  our  inferiors;  and 


A  PLEA  FOR  PURE  SCIENCE  609 

must  be  better  contented  with  the  approval  of  our  own  consciences,  and 
of  the  very  few  who  are  capable  of  judging  our  work,  than  of  the  whole 
world  beside.  Let  us  look  to  the  other  physicists,  not  in  our  own  town, 
not  in  our  own  country,  but  in  the  whole  world,  for  the  words  of  praise 
which  are  to  encourage  us.  or  the  words  of  blame  which  are  to  stimulate 
us  to  renewed  effort.  For  what  to  us  is  the  praise  of  the  ignorant?  Let 
us  join  together  in  the  bonds  of  our  scientific  societies,  and  encourage 
each  other,  as  we  are  now  doing,  in  the  pursuit  of  our  favorite  study; 
knowing  that  the  world  will  some  time  recognize  our  services,  and 
knowing,  also,  that  we  constitute  the  most  important  element  in  human 
progress. 

But  danger  is  also  near,  even  in  our  societies.  When  the  average  tone 
of  the  society  is  low,  when  the  highest  honors  are  given  to  the  mediocre, 
when  third-class  men  are  held  up  as  examples,  and  when  trifling  inven- 
tions are  magnified  into  scientific  discoveries,  then  the  influence  of 
such  societies  is  prejudicial.  A  young  scientist  attending  the  meetings 
of  such  a  society  soon  gets  perverted  ideas.  To  his  mind,  a  molehill  is 
a  mountain,  and  the  mountain  a  molehill.  The  small  inventor  or  the 
local  celebrity  rises  to  a  greater  height,  in  his  mind,  than  the  great 
leader  of  science  in  some  foreign  land.  He  gauges  himself  by  the 
molehill,  and  is  satisfied  with  his  stature;  not  knowing  that  he  is  but 
an  atom  in  comparison  with  the  mountain,  until,  perhaps,  in  old  age, 
when  it  is  too  late.  But,  if  the  size  of  the  mountain  had  been  seen  at 
first,  the  young  scientist  would  at  least  have  been  stimulated  in  his 
endeavor  to  grow. 

We  cannot  all  be  men  of  genius;  but  we  can,  at  least,  point  them  out 
to  those  around  us.  We  may  not  be  able  to  benefit  science  much  our- 
selves; but  we  can  have  high  ideals  on  the  subject,  and  instil  them  into 
those  with  whom  we  come  in  contact.  For  the  good  of  ourselves,  for 
the  good  of  our  country,  for  the  good  to  the  world,  it  is  incumbent  on 
us  to  form  a  true  estimate  of  the  worth  and  standing  of  persons  and 
things,  and  to  set  before  our  own  minds  all  that  is  great  and  good  and 
noble,  all  that  is  most  important  for  scientific  advance,  above  the  mean 
and  low  and  unimportant. 

It  is  very  often  said,  that  a  man  has  a  right  to  his  opinion.  This 
might  be  true  for  a  man  on  a  desert  island,  whose  error  would  influence 
only  himself;  but  when  he  opens  his  lips  to  instruct  others,  or  even 
when  he  signifies  his  opinions  by  his  daily  life,  then  he  is  directly 
responsible  for  all  his  errors  of  judgment  or  fact.  He  has  no  right  to 
39 


G10  HENKY  A.  KOWLAND 

think  a  molehill  as  big  as  a  mountain,  nor  to  teach  it,  any  more  than 
he  has  to  think  the  world  is  flat,  and  teach  that  it  is  so.  The  facts  and 
laws  of  our  science  have  not  equal  importance,  neither  have  the  men 
who  cultivate  the  science  achieved  equal  results.  One  thing  is  greater 
than  another,  and  we  have  no  right  to  neglect  the  order.  Thus  shall 
our  minds  be  guided  aright,  and  our  efforts  be  toward  that  which  is  the 
highest. 

Then  shall  we  see  that  no  physicist  of  the  first  class  has  ever  existed 
in  this  country,  that  we  must  look  to  other  countries  for  our  leaders 
in  that  subject,  and  that  the  few  excellent  workers  in  our  country  must 
receive  many  accessions  from  without  before  they  can  constitute  an 
American  science,  or  do  their  share  in  the  world's  work. 

But  let  me  return  to  the  subject  of  scientific  societies.  Here  Ameri- 
can science  has  its  hardest  problem  to  contend  with.  There  are  very 
many  local  societies  dignified  by  high-sounding  names,  each  having  its 
local  celebrity,  to  whom  the  privilege  of  describing  some  crab  with  an 
extra  claw,  which  he  found  in  his  morning  ramble,  is  inestimable.  And 
there  are  some  academies  of  science,  situated  at  our  seats  of  learning, 
which  are  doing  good  work  in  their  localities.  But  distances  are  so 
great  that  it  is  difficult  to  collect  men  together  at  any  one  point.  The 
American  Association,  which  we  are  now  attending,  is  not  a  scientific 
academy,  and  does  not  profess  to  be  more  than  a  gathering  of  all  who 
are  interested  in  science,  to  read  papers  and  enjoy  social  intercourse. 
The  National  Academy  of  Sciences  contains  eminent  men  from  the 
whole  country,  but  then  it  is  only  for  the  purpose  of  advising  the  gov- 
ernment freely  on  scientific  matters.  It  has  no  building,  it  has  no 
library;  and  it  publishes  nothing  except  the  information  which  it  freely 
gives  to  the  government,  which  does  nothing  for  it  in  return.  It  has 
not  had  much  effect  directly  on  American  science;  but  the  liberality  of 
the  government  in  the  way  of  scientific  expeditions,  publications,  etc., 
is  at  least  partly  due  to  its  influence,  and  in  this  way  it  has  done  much 
good.  But  it  in  no  way  takes  the  place  of  the  great  Eoyal  society,  or 
the  great  academies  of  science  at  Paris,  Berlin,  Vienna,  St.  Petersburg, 
Munich,  and,  indeed,  all  the  European  capitals  and  large  cities.  These, 
by  their  publications,  give  to  the  young  student,  as  well  as  to  the  more 
advanced  physicist,  models  of  all  that  is  considered  excellent;  and  to 
become  a  member  is  one  of  the  highest  honors  to  which  he  can  aspire, 
while  to  write  a  memoir  which  the  academy  considers  worthy  to  be  pub- 
lished in  its  transactions  excites  each  one  to  his  highest  effort. 


A  PLEA  FOR  PURE  SCIENCE  611 

The  American  Academy  of  Sciences  in  Boston  is  perhaps  our  nearest 
representation  of  this  class  of  academies,  but  its  limitation  of  member- 
ship to  the  state  deprives  it  of  a  national  character. 

But  there  is  another  matter  which  influences  the  growth  of  our 
science. 

As  it  is  necessary  for  us  still  to  look  abroad  for  our  highest  inspira- 
tion in  pure  science,  and  as  science  is  not  an  affair  of  one  town  or  one 
country,  but  of  the  whole  world,  it  becomes  us  all  to  read  the  current 
journals  of  science  and  the  great  transactions  of  foreign  societies,  as  well 
as  those  of  our  own  countries.  These  great  transactions  and  journals 
should  be  in  the  library  of  every  institution  of  learning  in  the  country, 
where  science  is  taught.  How  can  teachers  and  professors  be  expected 
to  know  what  has  been  discovered  in  the  past,  or  is  being  discovered 
now,  if  these  are  not  provided?  Has  any  institution  a  right  to  starve 
mentally  the  teachers  whom  it  employs,  or  the  students  who  come  to  it? 
There  can  be  but  one  answer  to  this;  and  an  institution  calling  itself  a 
university,  and  not  having  the  current  scientific  journals  upon  its  table 
or  the  transactions  of  societies  upon  its  library  shelves,  is  certainly  not 
doing  its  best  to  cultivate  all  that  is  best  in  this  world. 

We  call  this  a  free  country,  and  yet  it  is  the  only  one  where  there  is  a 
direct  tax  upon  the  pursuit  of  science.  The  low  state  of  pure  science 
in  our  country  may  possibly  be  attributed  to  the  youth  of  the  country; 
but  a  direct  tax,  to  prevent  the  growth  of  our  country  in  that  subject, 
cannot  be  looked  upon  as  other  than  a  deep  disgrace.  I  refer  to  the 
duty  upon  foreign  books  and  periodicals.  In  our  science,  no  books  above 
elementary  ones  have  ever  been  published,  or  are  likely  to  be  pub- 
lished in  this  country;  and  yet  every  teacher  in  physics  must  have  them, 
not  only  in  the  college  library,  but  on  his  own  shelves,  and  must  pay  the 
government  of  this  country  to  allow  him  to  use  a  portion  of  his  small 
salary  to  buy  that  which  is  to  do  good  to  the  whole  country.  All  free- 
dom of  intercourse  which  is  necessary  to  foster  our  growing  science  is 
thus  broken  off,  and  that  which  might,  in  time,  relieve  our  country  of 
its  mediocrity,  is  nipped  in  the  bud  by  our  government,  which  is  most 
liberal  when  appealed  to  directly  on  scientific  subjects. 

One  would  think  that  books  in  foreign  languages  might  be  admitted 
free;  but  to  please  the  half-dozen  or  so  workmen  who  reprint  German 
books,  not  scientific,  our  free  intercourse  with  that  country  is  cut  off. 
Our  scientific  associations  and  societies  must  make  themselves  heard  in 
this  matter,  and  show  those  in  authority  how  the  matter  stands. 


612  HENKY  A.  ROWLAND 

In  conclusion,  let  me  say  once  more  that  I  do  not  believe  that  our 
country  is  to  remain  long  in  its  present  position.  The  science  of  physics, 
in  whose  applications  our  country  glories,  is  to  arise  among  us,  and  make 
us  respected  by  the  nations  of  the  world.  Such  a  prophecy  may  seem 
rash  with  regard  to  a  nation  which  does  not  yet  do  enough  physical  work 
to  support  a  physical  journal.  But  we  know  the  speed  with  which  we 
advance  in  this  country:  we  see  cities  springing  up  in  a  night,  and  other 
wonders  performed  at  an  unprecedented  rate.  And  now  we  see  physical 
laboratories  being  built,  we  see  a  great  demand  for  thoroughly  trained 
physicists,  who  have  not  shirked  their  mathematics,  both  as  professors 
and  in  so-called  practical  life;  and  perhaps  we  have  the  feeling,  common 
to  all  true  Americans,  that  our  country  is  going  forward  to  a  glorious 
future,  when  we  shall  lead  the  world  in  the  strife  for  intellectual  prizes 
as  we  now  do  in  the  strife  for  wealth. 

But  if  this  is  to  be  so,  we  must  not  aim  low.  The  problems  of  the 
universe  cannot  be  solved  without  labor;  they  cannot  be  attacked  with- 
out the  proper  intellectual  as  well  as  physical  tools;  and  no  physicist 
need  expect  to  go  far  without  his  mathematics.  No  one  expects  a  horse 
to  win  in  a  great  and  long  race  who  has  not  been  properly  trained;  and 
it  would  be  folly  to  attempt  to  win  with  one,  however  pure  his  blood 
and  high  his  pedigree,  without  it.  The  problems  we  solve  are  more  diffi- 
cult than  any  race;  the  highest  intellect  cannot  hope  to  succeed  without 
proper  preparation.  The  great  prizes  are  reserved  for  the  greatest 
efforts  of  the  greatest  intellects,  who  have  kept  their  mental  eye  bright 
and  flesh  hard  by  constant  exercise.  Apparatus  can  be  bought  with 
money,  talents  may  come  to  us  at  birth;  but  our  mental  tools,  our  mathe- 
matics, our  experimental  ability,  our  knowledge  of  what  others  have 
done  before  us,  all  have  to  be  obtained  by  work.  The  time  is  almost 
past,  even  in  our  own  country,  when  third-rate  men  can  find  a  place  as 
teachers,  because  they  are  unfit  for  everything  else.  We  wish  to  see 
brains  and  learning,  combined  with  energy  and  immense  working 
power,  in  the  professor's  chair;  but,  above  all,  we  wish  to  see  that  high 
and  chivalrous  spirit  which  causes  one  to  pursue  his  idea  in  spite  of  all 
difficulties,  to  work  at  the  problems  of  nature  with  the  approval  of  his 
own  conscience,  and  not  of  men  before  him.  Let  him  fit  himself  for 
the  struggle  with  all  the  weapons  which  mathematics  and  the  experi- 
ence of  those  gone  before  him  can  furnish,  and  let  him  enter  the  arena 
with  the  fixed  and  stern  purpose  to  conquer.  Let  him  not  be  contented 
to  stand  back  with  the  crowd  of  mediocrity,  but  let  him  press  forward 
for  a  front  place  in  the  strife. 


613 

The  whole  universe  is  before  us  to  study.  The  greatest  labor  of  the 
greatest  minds  has  only  given  us  a  few  pearls;  and  yet  the  limitless 
ocean,  with  its  hidden  depths  filled  with  diamonds  and  precious  stones, 
is  before  us.  The  problem  of  the  universe  is  yet  unsolved,  and  the  mys- 
tery involved  in  one  single  atom  yet  eludes  us.  The  field  of  research 
only  opens  wider  and  wider  as  we  advance,  and  our  minds  are  lost  in 
wonder  and  astonishment  at  the  grandeur  and  beauty  unfolded  before 
us.  Shall  we  help  in  this  grand  work,  or  not?  Shall  our  country  do 
its  share,  or  shall  it  still  live  in  the  almshouse  of  the  world? 


THE  PHYSICAL  LABOKATOKY  IN  MODEKN  EDUCATION 

ADDRESS    FOR    COMMEMORATION    DAY    OF    THE    JOHNS    HOPKINS    UNIVERSITY, 
FEBRUARY    22,    1886 

[Johns  Hopkins  University  Circulars,  No.  50,  pp.  103-105,  1886] 

From  the  moment  we  are  born  into  this  world  down  to  the  day  when 
we  leave  it,  we  are  called  upon  every  moment  to  exercise  our  judgment 
with  respect  to  matters  pertaining  to  our  welfare.  While  nature  has 
supplied  us  with  instincts  which  take  the  place  of  reason  in  our  infancy, 
and  which  form  the  basis  of  action  in  very  many  persons  through  life, 
yet,  more  and  more  as  the  world  progresses  and  as  we  depart  from  the 
age  of  childhood,  we  are  forced  to  discriminate  between  right  and  wrong, 
between  truth  and  falsehood.  No  longer  can  we  shelter  ourselves  behind 
those  in  authority  over  us,  but  we  must  come  to  the  front  and  each  one 
decide  for  himself  what  to  believe  and  how  to  act  in  the  daily  routine 
and  the  emergencies  of  life.  This  is  not  given  to  us  as  a  duty  which  we 
can  neglect  if  we  please,  but  it  is  that  which  every  man  or  woman,  con- 
sciously or  unconsciously,  must  go  through  with. 

Most  persons  cut  this  Gordian  knot,  which  they  cannot  untangle,  by 
accepting  the  opinions  which  have  been  taught  them  and  which  appear 
correct  to  their  particular  circle  of  friends  and  associates:  others  take 
the  opposite  extreme  and,  with  intellectual  arrogance,  seek  to  build  up 
their  opinions  and  beliefs  from  the  very  foundation,  individually  and 
alone,  without  help  from  others.  Intermediate  between  these  two  ex- 
tremes comes  the  man  with  full  respect  for  the  opinions  of  those  around 
him,  and  yet  with  such  discrimination  that  he  sees  a  chance  of  error 
in  all  and  most  of  all  in  himself.  He  has  a  longing  for  the  truth  and  is 
willing  to  test  himself,  to  test  others  and  to  test  nature  until  he  finds  it. 
He  has  the  courage  of  his  opinions  when  thus  carefully  formed,  and 
is  then,  but  not  till  then,  willing  to  stand  before  the  world  and  proclaim 
what  he  considers  the  truth.  Like  Galileo  and  Copernicus,  he  inaugu- 
rates a  new  era  in  science,  or  like  Luther,  in  the  religious  belief  of  man- 
kind. He  neither  shrinks  within  himself  at  the  thought  of  having  an 
opinion  of  his  own,  nor  yet  believes  it  to  be  the  only  one  worth  consid- 
ering in  the  world;  he  is  neither  crushed  with  intellectual  humility,  nor 
yet  exalted  with  intellectual  pride;  he  sees  that  the  problems  of  nature 
and  society  can  be  solved,  and  yet  he  knows  that  this  can  only  come 


THE  PHYSICAL  LABORATOET  IN  MODERN  EDUCATION         615 

about  by  the  combined  intellect  of  the  world  acting  through  ages  of  time 
and  that  he,  though  his  intellect  were  that  of  Newton,  can,  at  best,  do 
very  little  toward  it.  Knowing  this  he  seeks  all  the  aids  in  his  power 
to  ascertain  the  truth,  and  if  he,  through  either  ambition  or  love  of 
truth,  wishes  to  impress  his  opinions  on  the  world,  he  first  takes  care 
to  have  them  correct.  Above  all,  he  is  willing  to  abstain  from  having 
opinions  on  subjects  of  which  he  knows  nothing. 

It  is  the  province  of  modern  education  to  form  such  a  mind  while  at 
the  same  time  giving  to  it  enough  knowledge  to  have  a  broad  outlook 
over  the  world  of  science,  art  and  letters.  Time  will  not  permit  me  to 
discuss  the  subject  of  education  in  general,  and,  indeed,  I  would  be 
transgressing  the  principles  above  laid  down  if  I  should  attempt  it.  I 
shall  only  call  attention  at  this  present  time  to  the  place  of  the  labo- 
ratory in  modern  education.  I  have  often  had  a  great  desire  to  know 
the  state  of  mind  of  the  more  eminent  of  mankind  before  modern  science 
changed  the  world  to  its  present  condition  and  exercised  its  influence 
on  all  departments  of  knowledge  and  speculation.  But  I  have  failed 
to  picture  to  myself  clearly  such  a  mind  while,  at  the  same  time,  the 
study  of  human  nature,  as  it  exists  at  present,  shows  me  much  that  I 
suppose  to  be  in  common  with  it.  As  far  as  I  can  see,  the  unscientific 
mind  differs  from  the  scientific  in  this,  that  it  is  willing  to  accept  and 
make  statements  of  which  it  has  no  clear  conception  to  begin  with  and 
of  whose  truth  it  is  not  assured.  It  is  an  irresponsible  state  of  mind 
without  clearness  of  conception,  where  the  connection  between  the 
thought  and  its  object  is  of  the  vaguest  description.  It  is  the  state  of 
mind  where  opinions  are  given  and  accepted  without  ever  being  sub- 
jected to  rigid  tests,  and  it  may  have  some  connection  with  that  state  of 
mind  where  everything  has  a  personal  aspect  and  we  are  guided  by 
feelings  rather  than  reason. 

When,  by  education,  we  attempt  to  correct  these  faults,  it  is  neces- 
sary that  we  have  some  standard  of  absolute  truth:  that  we  bring  the 
mind  in  direct  contact  with  it  and  let  it  be  convinced  of  its  errors  again 
and  again.  We  may  state,  like  the  philosophers  who  lived  before  Gali- 
leo, that  large  bodies  fall  faster  than  small  ones,  but  when  we  see  them 
strike  the  ground  together  we  know  that  our  previous  opinion  was  false 
and  we  learn  that  even  the  intellect  of  an  Aristotle  may  be  mistaken. 
Thus  we  are  taught  care  in  the  formation  of  our  opinions  and  find  that 
the  unguided  human  mind  goes  astray  almost  without  fail.  We  must 
correct  it  constantly  and  convince  it  of  error  over  and  over  again  until 
it  discovers  the  proper  method  of  reasoning,  which  will  surely  accord 
with  the  truth  in  whatever  conclusions  it  may  reach.  There  is,  however, 


616  HENRY  A.  ROWLAND 

danger  in  this  process  that  the  mind  may  become  over  cautious  and  thus 
present  a  weakness  when  brought  in  contact  with  an  unscrupulous  per- 
son who  cares  little  for  truth  and  a  great  deal  for  effect.  But  if  we 
believe  in  the  maxim  that  truth  will  prevail  and  consider  it  the  duty 
of  all  educated  men  to  aid  its  progress,  the  kind  of  mind  which  I  describe 
is  the  proper  one  to  foster  by  education.  Let  the  student  be  brought 
face  to  face  with  nature:  let  him  exercise  his  reason  with  respect  to  the 
simplest  physical  phenomenon  and  then,  in  the  laboratory,  put  his  opin- 
ions to  the  test;  the  result  is  invariably  humility,  for  he  finds  that  nature 
has  laws  which  must  be  discovered  by  labor  and  toil  and  not  by  wild 
flights  of  the  imagination  and  scintillations  of  so-called  genius. 

Those  who  have  studied  the  present  state  of  education  in  the  schools 
and  colleges  tell  us  that  most  subjects,  including  the  sciences,  are  taught 
as  an  exercise  to  the  memory.  I  myself  have  witnessed  the  melancholy 
sight  in  a  fashionable  school  for  young  ladies  of  those  who  were  born 
to  be  intellectual  beings  reciting  page  after  page  from  memory,  without 
any  effort  being  made  to  discover  whether  they  understood  the  subject 
or  not.  There  are  even  many  schools,  so-called,  where  the  subject  of 
physics  or  natural  philosophy  itself  is  taught,  without  even  a  class  ex- 
periment to  illustrate  the  subject  and  connect  the  words  with  ideas. 
Words,  mere  words,  are  taught  and  a  state  of  mind  far  different  from 
that  above  described  is  produced.  If  one  were  required  to  find  a  sys- 
tem of  education  which  would  the  most  surely  and  certainly  disgust  the 
student  with  any  subject,  I  can  conceive  of  none  which  would  do  this 
more  quickly  than  this  method,  where  he  is  forced  to  learn  what  he 
does  not  understand.  It  is  said  of  the  Faraday  that  he  never  could 
understand  any  scientific  experiment  thoroughly  until  he  had  not  only 
seen  it  performed  by  others,  but  had  performed  it  himself.  Shall  we 
then  expect  children  and  youth  to  do  what  Faraday  could  not  do?  A 
thousand  times  better  never  teach  the  subject  at  all. 

Tastes  differ,  but  we  may  safely  say  that  every  subject  of  study  which 
is  thoroughly  understood  is  a  pleasure  to  the  student.  The  healthy 
mind  as  well  as  the  healthy  body  craves  exercise,  and  the  school  room 
or  the  lecture  room  should  be  a  source  of  positive  enjoyment  to  those 
who  enter  it.  Above  all.  the  study  of  nature,  from  the  magnificent  uni- 
verse, across  which  light  itself,  at  the  rate  of  186,000  miles  per  second, 
cannot  go  in  less  than  hundreds  of  years,  down  to  the  atom  of  which 
millions  are  required  to  build  up  the  smallest  microscopic  object,  should 
be  the  most  interesting  subject  brought  to  the  notice  of  the  student. 

Some  are  born  blind  to  the  beauties  of  the  world  around  them,  some 


THE  PHYSICAL  LABORATOKY  ix  MODERN  EDUCATION         61? 

have  their  tastes  better  developed  in  other  directions,  and  some  have 
minds  incapable  of  ever  understanding  the  simplest  natural  phenomenon; 
but  there  is  also  a  large  class  of  students  who  have  at  least  ordinary  pow- 
ers and  ordinary  tastes  for  scientific  pursuits:  to  train  the  powers  of 
observation  and  classification  let  them  study  natural  history,  not  only 
from  books,  but  from  prepared  specimens  or  directly  from  nature:  to 
give  care  in  experiment  and  convince  them  that  nature  forgives  no 
error,  let  them  enter  the  chemical  laboratory:  to  train  them  in  exact  and 
logical  powers  of  reasoning,  let  them  study  mathematics:  but  to  com- 
bine all  this  training  in  one  and  exhibit  to  their  minds  the  most  perfect 
and  systematic  method  of  discovering  the  exact  laws  of  nature,  let  them 
study  physics  and  astronomy,  where  observation,  common  sense  and 
mathematics  go  hand  in  hand.  The  object  of  education  is  not  only  to 
produce  a  man  who  Tcnows,  but  one  who  does;  who  makes  his  mark  in 
the  struggle  of  life  and  succeeds  well  in  whatever  he  undertakes:  who 
can  solve  the  problems  of  nature  and  of  humanity  as  they  arise,  and  who, 
when  he  knows  he  is  right,  can  boldly  convince  the  world  of  the  fact. 
Men  of  action  are  needed  as  well  as  men  of  thought. 

There  is  no  doubt  in  my  mind  that  this  is  the  point  in  which  much 
of  our  modern  education  fails.  Why  is  it?  I  answer  that  the  memory 
alone  is  trained  and  the  reason  and  judgment  are  used  merely  to  refer 
matters  to  some  authority  who  is  considered  final,  and  worse  than  all, 
they  are  not  trained  to  apply  their  knowledge  constantly.  To  produce 
men  of  action  they  must  be  trained  in  action.  If  the  languages  be 
studied,  they  must  be  made  to  translate  from  one  language  to  the  other 
until  they  have  perfect  facility  in  the  process.  If  mathematics  be 
studied,  they  must  work  problems,  more  problems  and  problems  again, 
until  they  have  the  use  of  what  they  know.  If  they  study  the  sciences, 
they  must  enter  the  laboratory  and  stand  face  to  face  with  nature;  they 
must  learn  to  test  their  knowledge  constantly  and  thus  see  for  them- 
selves the  sad  results  of  vague  speculation;  they  must  learn  by  direct 
experiment  that  there  is  such  a  thing  in  the  world  as  truth  and  that 
their  own  mind  is  most  liable  to  error.  They  must  try  experiment  after 
experiment  and  work  problem  after  problem  until  they  become  men  of 
action  and  not  of  theory. 

This,  then,  is  the  use  of  the  laboratory  in  general  education,  to  train 
the  mind  in  right  modes  of  thought  by  constantly  bringing  it  in  con- 
tact with  absolute  truth  and  to  give  it  a  pleasant  and  profitable  method 
of  exercise  which  will  call  all  its  powers  of  reason  and  imagination  into 
play.  Its  use  in  the  special  training  of  scientists  needs  no  remark,  for  it 


618  HENKY  A.  EOWLAND 

is  well  known  that  it  is  absolutely  essential.  The  only  question  is 
whether  the  education  of  specialists  in  science  is  worth  undertaking  at 
all,  and  of  these  I  have  only  to  consider  natural  philosophers  or  physi- 
cists. I  might  point  to  the  world  around  me,  to  the  steam  engine,  to 
labor-saving  machinery,  to  the  telegraph,  to  all  those  inventions  which 
make  the  present  age  the  "Age  of  Electricity,"  and  let  that  be  my 
answer.  Nobody  could  gainsay  that  the  answer  would  be  complete,  for 
all  are  benefited  by  these  applications  of  science,  and  he  would  be  con- 
sidered absurd  who  did  not  recognize  their  value.  These  follow  in  the 
train  of  physics,  but  they  are  not  physics;  the  cultivation  of  physics 
brings  them  and  always  will  bring  them,  for  the  selfishness  of  mankind 
can  always  be  relied  upon  to  turn  all  things  to  profit.  But  in  the  edu- 
cation pertaining  to  a  university  we  look  for  other  results.  The  special 
physicist  trained  there  must  be  taught  to  cultivate  his  science  for  its 
own  sake.  He  must  go  forth  into  the  world  with  enthusiasm  for  it  and 
try  to  draw  others  into  an  appreciation  of  it,  doing  his  part  to  convince 
the  world  that  the  study  of  nature  is  one  of  the  most  noble  of  pursuits, 
that  there  are  other  things  worthy  of  the  attention  of  mankind  besides 
the  pursuit  of  wealth.  He  must  push  forward  and  do  what  he  can,  ac- 
cording to  his  ability,  to  further  the"  progress  of  his  science. 

Thus  does  the  university,  from  its  physical  laboratory,  send  forth  into 
the  world  the  trained  physicist  to  advance  his  science  and  to  carry  to 
other  colleges  and  technical  schools  his  enthusiasm  and  knowledge. 
Thus  the  whole  country  is  educated  in  the  subject  and  others  are  taught 
to  devote  their  lives  to  its  pursuit,  while  some  make  the  applications  to 
the  ordinary  pursuits  of  life  that  are  appreciated  by  all. 

But  for  myself,  I  value  in  a  scientific  mind  most  of  all  that  love  of 
truth,  that  care  in  its  pursuit  and  that  humility  of  mind  which  makes 
the  possibility  of  error  always  present  more  than  any  other  quality.  This 
is  the  mind  which  has  built  up  modern  science  to  its  present  perfection, 
which  has  laid  one  stone  upon  the  other  with  such  care  that  it  to-day 
offers  to  the  world  the  most  complete  monument  to  human  reason.  This 
is  the  mind  which  is  destined  to  govern  the  world  in  the  future  and  to 
solve  problems  pertaining  to  politics  and  humanity  as  well  as  to  inani- 
mate nature. 

It  is  the  only  mind  which  appreciates  the  imperfections  of  the  human 
reason  and  is  thus  careful  to  guard  against  them.  It  is  the  only  mind 
that  values  the  truth  as  it  should  be  valued  and  ignores  all  personal 
feeling  in  its  pursuit.  And  this  is  the  mind  the  physical  laboratory  is 
built  to  cultivate. 


ADDRESS   AS   PRESIDENT    OF   THE   ELECTRICAL   CONFER- 
ENCE AT  PHILADELPHIA,  SEPTEMBER  8,  1884 

[Report  of  the  Conference,  pp.  12-28,  Washington,  1886] 

To  the  student  of  science  who  has  a  disposition  to  look  into  the  pages 
of  history,  no  life  has  greater  interest  than  that  of  Archimedes,  and  yet 
there  are  few  men  about  whom  so  little  is  known.  Living  more  than 
two  thousand  years  ago,  the  accounts  of  him  which  have  come  to  us  are 
little  short  of  fabulous,  and  yet  they  are  of  such  a  nature  that  we  can 
say  without  any  doubt  that  he  was  a  genius  such  as  the  world  has  sel- 
dom seen.  To  him  we  owe  some  of  the  fundamental  facts  of  mechanics, 
such  as  the  principle  of  the  lever  and  the  pulley,  and  the  fact  that  a 
body  immersed  in  a  liquid  loses  in  weight  as  much  as  an  equal  volume 
of  the  liquid  weighs.  And  in  military  engineering  his  success  was  so 
great  that  he  prolonged  the  siege  of  Syracuse  by  the  Romans  from  what 
would  probably  have  been  a  few  days  to  three  years.  His  engines  shot 
against  the  enemy  immense  numbers  of  darts  and  huge  stones,  which 
mowed  them  down  in  columns,  and  falling  on  their  ships  destroyed 
them.  He  thrust  out  huge  beams  from  the  walls  over  the  ships  and 
drew  them  into  the  air,  where  they  swung  to  and  fro  to  the  amazement 
and  terror  of  the  Romans  and  were  finally  dropped  and  sunk  to  the  bot- 
tom of  the  sea.  He  is  even  said  to  have  set  them  on  fire  by  means  of 
the  reflected  light  of  the  sun.  But  his  principal  work  was  in  geometry, 
and  of  this  I  only  need  to  quote  the  words  of  Professor  De  Morgan  re- 
ferring to  those  geometrical  works  of  Archimedes  which  have  come 
down  to  us.  "  Here,"  says  Professor  De  Morgan,  "  he  finds  all  that  re- 
lates to  the  surface  and  solidity  of  the  sphere,  cone  and  cylinder  and 
their  segments.  A  modern  work  on  the  differential  calculus  would  not 
give  more  results  than  are  found  here."  As  to  the  quality  of  the  indi- 
vidual, the  impression  which  his  writings  give  us  is  that  of  a  power 
which  has  never  been  surpassed.  No  one  has  a  right  to  say  that  New- 
ton himself,  in  the  place  of  Archimedes,  could  have  done  more. 

Thus  before  the  birth  of  modern  science,  in  the  dim  ages  of  the  past 
when  the  light  of  history  begins  to  fade  and  the  mist  of  legend  to  cover 


620  HENEY  A.  ROWLAND 

our  view,  there  lived  a  man  of  almost  superhuman  intellect  whose  mind 
seemed  equally  adapted  to  either  pure  or  applied  science.  And  yet  Plu- 
tarch says  of  him:  "Archimedes  possessed  so  high  a  spirit,  so  profound 
a.  soul,  and  such  treasures  of  scientific  knowledge,  that,  though  the  in- 
ventions (referring  to  his  military  engines)  had  now  obtained  for  him 
the  renown  of  more  than  human  sagacity,  he  yet  would  not  deign  to 
leave  behind  him  any  commentary  or  writing  on  such  subjects,  but,  re- 
pudiating as  sordid  and  ignoble  the  whole  trade  of  engineering,  and 
every  sort  of  art  that  lends  itself  to  mere  use  and  profit,  he  placed  his 
whole  affection  and  ambition  in  those  purer  speculations  where  there 
can  be  no  reference  to  the  vulgar  needs  of  life;  studies,  the  superiority 
of  which  to  all  others  is  unquestioned,  and  in  which  the  only  doubt  can 
be,  whether  the  beauty  and  grandeur  of  the  subjects  examined,  or  the 
precision  and  cogency  of  the  methods  and  means  of  proof,  most  deserve 
our  admiration." 

Here,  then,  at  the  dawn  of  science  the  question  of  the  relative  value 
of  pure  and  applied  science  had  been  brought  up.  To  the  people  of 
Syracuse,  who  had  to  defend  themselves  against  an  overwhelming  enemy, 
the  military  engines  of  Archimedes  were  of  far  more  interest  than  the 
whole  of  geometry,  for  the  knowledge  of  the  ratio  of  the  solid  contents 
of  a  sphere  and  its  circumscribed  cylinder  cannot  bring  a  dead  man  to 
life  or  restore  wealth  to  a  plundered  city.  And  yet,  from  a  point  of 
view  distant  more  than  two  thousand  years,,  we  are  forced  to  admit  that 
Archimedes  was  right.  Archimedes'  engines  of  destruction  have  passed 
away,  but  the  geometrical  and  mechanical  truths  which  he  discovered 
are  to-day  almost  the  axioms  of  the  mathematician  and  the  worker  in 
physical  science,  and  the  ratio  of  the  circumference  of  a  circle  to  its 
radius  is  to-day  the  most  important  of  our  physical  constants. 

But  this  is  only  a  meager  part  of  the  influence  of  this  man.  The 
truths  which  he  discovered  have  formed  a  part  of  the  education  of  every 
student  of  mathematics  to  the  present  time,  and  have  given  pure  intel- 
lectual enjoyment  to  all.  They  have  helped  to  form  the  minds  of  all 
those  whom  we  consider  great  in  our  science,  and  they  have  done  their 
share  in  that  march  of  progress  which  is  gradually  transforming  the 
world. 

Great  should  be  the  honor  in  which  we  hold  the  intellect  of  Archime- 
des, but  greater  should  be  our  reverence  when  we  approach  that  noble 
spirit  which  could  ignore  all  worldly  considerations  and  prefer  the  truths 
of  geometry  to  the  vast  physical  power  given  him  by  his  other  inven- 
tions, which  were  his  amusements  for  a  moment.  We  now  see  that  he 


ELECTRICAL  CONFERENCE  AT  PHILADELPHIA  621 

was  right,  but  we  cannot  for  a  moment  suppose  that  he  foresaw,  except 
dimly,  any  so-called  practical  advantages  from  his  discoveries.  A  thou- 
sand times  no!  He  preferred  his  geometrical  labors  because  of  a  subtle 
quality  of  his  mind,  an  instinct  toward  that  which  was  highest  and 
noblest  and  a  faith  that  the  pursuit  of  what  is  noble  is  the  surest  road 
to  the  final  happiness  of  the  individual  and  of  the  world.  Our  highest 
moral  qualities  are  of  this  nature,  and  we  despise  as  the  lowest  of  the 
low  one  who  is  honest  because  "honesty  is  the  best  policy,"  but  esteem 
him  whose  instincts  lead  him  to  honesty  whatever  the  consequences. 

So  we  reverence  the  noble  and  lofty  spirit  of  Archimedes,  and  yet  we 
do  not  at  the  present  day  quite  agree  with  his  estimate  of  the  relative 
value  of  his  works.  His  military  inventions  were  far  from  worthy  of 
being  despised,  even  though  the  only  reason  were  that  they  gave  the 
world  three  more  years  of  Archimedes'  life.  The  world  is  not  formed 
of  disembodied  spirits,  but  of  men,  in  whom  there  is  a  wonderful  com- 
bination of  mind  and  matter,  and  a  sound  mind  in  a  sound  body  is  the 
highest  type  of  manhood.  But  we  also  know  that  the  mind  is  hampered 
by  many  considerations  connected  with  the  body.  Archimedes  recog- 
nized this,  and  his  noble  spirit  revolted  at  it.  But  to-day  we  see  that 
no  progress  can  come  from  this  method  of  treatment;  the  body  still  re- 
mains, however  much  we  may  despise  it,  and  the  buzzing  of  a  fly  can 
disturb  the  most  profound  thought  of  the  philosopher. 

We  now  study  the  laws  of  nature  and  seek  thus  to  assist  our  bodies 
in  obeying  the  thoughts  of  our  minds.  Our  railroads  carry  us  hither 
and  thither  on  the  earth  with  somewhat  the  facility  of  spirits,  and  our 
thoughts  pass  with  almost  the  speed  of  light  to  the  uttermost  portion 
of  the  earth.  The  steam  engine  does  our  work,  and  labor-saving  ma- 
chinery takes  the  place  of  our  hands.  With  a  minimum  amount  of  labor 
we  can  to-day  possess  luxuries  unknown  even  to  kings  in  ancient  times, 
and  our  minds  are  free  to  study  the  order  of  nature  or  engage  in  any 
intellectual  pursuit  we  may  desire.  Instead  of  being  the  slaves  of  na- 
ture and  groveling  in  the  dust  before  her  to  find  the  food  which  we 
crave,  we  have  now  assumed  the  command,  and  find  her  a  willing  servant 
to  those  who  know  her  language. 

But  here  we  reach  the  keystone  of  the  problem.  To  command  her  we 
must  know  her  language.  Knowledge,  then,  is  the  price  of  her  service, 
and  she  obeys  not  the  ignorant  or  degraded,  but  grinds  them  into  dust 
beneath  her  heel. 

Knowledge,  then,  is  power,  and  it  is  more  than  power;  it  is  that 
which  the  intellect  most  craves  and  is  the  object  of  many  of  our  highest 


622  HENEY  A.  ROWLAND 

aspirations.  What  truth  is,  is  the  goal  of  intellectual  mankind  in  all 
ages,  and  its  pursuit  leads  not  only  to  intellectual  but  also  to  physical 
satisfaction. 

The  pursuit  of  the  one  leads  to  the  other.,  and  we  shall  see  as  we  pro- 
ceed that  the  only  way  for  the  world  to  progress  in  practical  science  is 
by  the  cultivation  of  the  theoretical  science. 

Pure  science  must  exist  before  its  applications,  and  the  truths  of  pure 
science  are  far  more  reaching  in  their  effects  than  any  of  its  applica- 
tions; and  yet  the  applications  of  science  often  have  a  much  more  im- 
mediate interest  for  the  world  at  large  than  many  discoveries  in  pure 
science,  which  will  finally  revolutionize  it,  both  physically  and  mentally. 
They  both  have  their  importance  and  both  are  at  work  in  causing  that 
intellectual  and  material  progress  in  which  the  world  is  now  pushing 
forward  with  giant  steps.  But  there  is  this  difference — the  names  of  the 
great  inventors  are  seen  in  every  paper  and  their  deeds  are  recounted 
to  the  rising  youth  of  the  country  as  examples  to  be  followed.  And 
yet  the  discoveries  of  the  principles  on  which  their  inventions  are  based 
may  have  died  in  comparative  obscurity,  with  poverty  knocking  at  the 
door.  We  are  in  no  danger  of  forgetting  those  who  have  been  success- 
ful in  those  applications  of  science  which  are  in  daily  use,  and  it  is  use- 
less to  repeat  the  story  of  the  telegraph  or  telephone,  but  it  will  be  of 
more  interest  for  me  to  recall  to  your  minds  a  few  of  the  landmarks  in 
our  science  and  then  to  consider  the  present  state  of  our  science,  with 
a  possible  glance  into  the  future. 

Thus  we  shall  obtain  a  clearer  view  of  how  our  science  has  been  built 
up  and  of  the  means  which  are  necessary  for  its  further  progress.  We 
shall  also  see  the  relations  between  pure  and  applied  science,  and  the 
relative  importance  of  the  two  in  the  progress  of  the  world. 

It  is  impossible  for  one  here  to  discuss  the  reasons  why  the  ancients 
followed  their  science  to  so  short  a  distance  and  the  world  had  to  wait 
more  than  two  thousand  years  before  the  light  of  modern  science  com- 
menced to  shine.  It  must  be  left  to  the  psychologists  and  historians. 
But  this  I  may  say,  modern  progress  is  cumulative.  By  the  study  of 
the  science  of  the  past,  the  minds  of  men  are  trained  for  its  further  ad- 
vance in  the  future,  and  so  when  there  was  no  science  to  study  there 
could  be  but  little  training  of  the  mind  in  the  true  methods  of  thought. 

The  average  intellect  of  mankind  has  improved,  and  what  could  only 
have  been  comprehended  in  past  times  by  a  few  is  to-day  understood 
by  the  majority  of  educated  persons.  And  this  increase  has  been  most 
apparent  in  the  reason  and  moral  sense  of  mankind,  the  two  qualities  of 


ELECTEICAL  CONFERENCE  AT  PHILADELPHIA  623 

the  mind  which  come  most  into  play  in  the  study  of  science.  To  the 
mind  of  the  ancients,  where  the  imagination  ran  riot  without  the  guide 
of  reason  or  a  warning  from  their  moral  sense  to  speak  the  truth,  it  was 
easier  to  attribute  the  attraction  of  rubbed  amber  to  an  inherent  soul 
or  essence,  which,  awakened  by  friction,  went  forth  and  brought  back 
the  small  particles  floating  around,  than  to  examine  and  find  out  the 
truth. 

The  simple  experiment  of  the  amber  remained  without  investigation 
for  2200  years.  Had  the  reasoning  of  many  modern  persons  been  fol- 
lowed, we  should  never  have  had  a  science  of  electricity.  Why  should 
anybody  investigate  this  phenomenon,  this  feeble  force,  which  could 
only  attract  a  few  particles  of  dust?  The  world  could  eat,  drink,  and 
take  its  ease  without  doing  anything  in  the  matter,  and  it  did  so  for 
more  than  "two  thousand  years  of  intellectual,  moral  and  physical  degra- 
dation. Then  the  awakening  came,  and  men  began  to  feel  that  they 
were  reasoning  beings.  They  began  to  see  that  there  were  other  pleas- 
ures in  the  world  besides  animal  pleasures,  and  that  they  had  been  placed 
in  this  wonderful  universe  that  they  might  exalt  their  intelligence  by  its 
proper  study.  No  question  of  gain  entered  into  the  minds  of  these 
early  investigators,  but  they  were  led  by  that  instinct  toward  truth  which 
indicates  the  highest  type  of  man.  And  yet  their  researches  have  trans- 
formed the  world,  not  only  intellectually,  but  physically.  Some  would 
say  that  science  had  been  degraded  by  its  applications,  but  who  that 
looks  over  the  world  at  the  present  time  can  think  so?  There  is  no 
danger  of  this  view  becoming  general;  the  danger  is  in  the  other 
direction,  and  that  science  shall  be  degraded  in  the  estimate  of  the 
world  by  the  idea  that  its  principal  use  is  to  be  applied  to  the  common 
purposes  of  life.  A  thousand  times  no!  Its  use  is  in  the  intellectual 
training  of  mankind  and  the  high  and  noble  pleasure  it  gives  to  those 
who  are  born  to  understand  it;  to  lift  mankind  above  the  level  of  the 
brute  and  to  make  him  appreciate  the  beauties  and  wonders  of  nature; 
to  cause  him  to  stand  in  humiliation  and  awe  before  that  universe 
which  the  intellect  of  ages  has  attempted  to  understand  and  yet  has 
failed;  to  make  even  Newton  say,  "  I  know  not  what  the  world  may 
think  of  my  labors,  but  to  myself  it  seems  to  me  that  I  have  been  but 
as  a  child  playing  on  the  seashore;  now  finding  some  pebble  rather  more 
polished,  and  now  some  shell  rather  more  agreeably  variegated  than 
another,  while  the  immense  ocean  of  truth  extended  itself  unexplored 
before  me." 

But  the  great  moral  law  of  the  universe  here  enters.     If  the  world 


624  HENKY  A.  EOWLAND 

would  only  pursue  those  things  which  are  high  and  right  and  noble  its 
reward  would  not  be  confined  to  the  minds  of  men.  Physical  rewards 
await  it  as  well,  and  disease,  that  principal  cause  of  human  misery, 
would  almost  pass  away  when  the  effect  of  inheritance  from  the  present 
generation  had  passed.  So  the  pursuit  of  pure  science  brings  not  only 
the  rewards  I  have  mentioned,,  but  the  physical  rewards  of  applied 
science  and  the  pursuit  of  applied  science  gives  wealth  which  may  be 
again  employed  to  further  pure  science.  So  the  two  react  on  each  other 
to  produce  that  perfect  whole,  modern  science,  pure  and  applied. 

This  moral  law  of  the  universe  is  well  illustrated  by  the  well-known 
story  of  Solomon: 

"  The  Lord  appeared  to  Solomon  in  a  dream  by  night;  and  God  said, 
Ask  what  I  shall  give  thee. 

"And  Solomon  said,  Thou  hast  made  thy  servant  king  instead  of  David 
my  father,  and  I  am  but  a  little  child;  I  know  not  how  to  go  out  or  come 
in.  Give  therefore  thy  servant  an  understanding  heart  to  judge  thy 
people,  that  I  may  discern  between  good  and  bad;  for  who  is  able  to 
judge  this  thy  so  great  a  people? 

"And  God  said  unto  him,  Because  thou  hast  asked  this  thing,  and  hast 
not  asked  for  thyself  long  life,  neither  hast  asked  riches  for  thyself,  nor 
hast  asked  the  life  of  thine  enemies,  but  hast  asked  for  thyself  under- 
standing to  discern  judgment,  behold,  I  have  done  according  to  thy 
words;  lo,  I  have  given  thee  a  wise  and  an  understanding  heart,  so  that 
there  was  none  like  thee  before  thee,  neither  after  thee  shall  any  arise 
like  unto  thee.  And  I  have  also  given  thee  that  which  thou  hast  not 
asked,  both  riches  and  honor;  so  that  there  shall  not  be  any  among  the 
kings  like  unto  thee  all  thy  days."  / 

So  the  world,  when  it  chose  knowledge  and  truth  above  all  things, 
acquired  not  only  the  treasures  of  pure  theoretical  science,  but  also  the 
wealth  and  riches  and  honor  which  come  from  applied  science  such  as 
the  world  has  never  seen  before  and  could  see  in  no  other  way. 

It  is  to  William  Gilbert,  an  English  physician,  that  we  owe  the  com- 
mencement of  the  modern  science  of  electricity.  His  book  on  the  mag- 
net was  published  in  1600,  and  contained  his  electrical  experiments. 
Thus,  at  this  early  date,  the  similarity  of  electrical  to  magnetic  attrac- 
tion was  recognized.  But  how  slowly  did  the  subject  advance!  The 
difference  between  conductors  and  non-conductors  was  discovered  by 
Gray.  But  not  until  1746,  150  years  after  Gilbert,  was  the  Leyden  jar 
invented.  Then  the  remarkable  nature  of  the  phenomenon  became  ap- 
parent, and  the  world  was  startled  by  it.  The  subtle  spirit  which  went 


ELECTRICAL  CONFERENCE  AT  PHILADELPHIA  625 

forth  from  the  amber,  which  was  so  feeble  as  only  to  attract  dust,  now 
flashed  forth  with  light  and  sound  and  heat,  and  could  cause  the  strength 
of  the  giant  to  vanish.  To  the  world  at  large  there  was  now  something 
worth  looking  into.  But  do  we  think  that  the  spark  from  the  Leyden 
jar  is  more  wonderful  than  the  gentle  attraction  of  the  amber?  By  no 
means,  for,  to  the  scientist,  they  are  both  equally  remarkable,  and  be- 
yond our  powers  of  explanation.  It  is  only  to  the  vulgar  and  unedu- 
cated taste  that  the  tinsel  and  gewgaws  of  an  electric  spark  appeal  more 
strongly  than  the  subtle  spirit  of  the  amber.  Nevertheless,  despicable 
as  the  means,  the  spark  of  the  Leyden  jar  acted  as  a  trumpet  call  to 
Europe  and  even  America  to  come  to  the  study  of  the  wonderful  science 
of  electricity.  At  no  other  time  has  there  been  such  excitement  over 
any  electrical  discovery,  and  electrical  experiments  became  general. 

It  was  only  after  the  discovery  of  the  Leyden  jar  that  the  idea  of  an 
electric  current  occurred  to  mankind,  and  this  current  was  even  trans- 
mitted to  a  distance  by  a  wire  and  a  shock  given  to  a  person  across  the 
Thames,  the  water  forming  the  return  circuit.  And  the  English  ex- 
perimenters even  went  so  far  as  to  form  a  circuit  with  the  two  observ- 
ers two  miles  apart,  using  the  earth  as  the  return  circuit.  Thus  the 
fundamental  fact  which  forms  the  basis  of  the  telegraph  was  early  ob- 
served. 

But  isolated  facts  are  of  little  value  unless  connected  together  by 
something  which  we  call  a  theory,  and  in  this  line  we  owe  much  to 
Franklin,  whose  letters  upon  this  subject  appeared  between  1747  and 
1754.  To  him  we  owe  the  theory  of  positive  and  negative  electricity, 
and  the  fact  that  they  are  always  generated  in  equal  amounts,  a  law 
whose  importance  can  scarcely  be  estimated.  He  investigated  the  Ley- 
den jar,  and  showed  that  the  coatings  had  equal  positive  and  negative 
charges,  and  explained  the  fact  that  the  jar  cannot  be  charged  when 
the  outside  coating  is  insulated.  He  invented  the  charge  and  discharge 
by  cascade  and  showed  that  it  was  the  glass  of  the  jar  and  not  the 
coatings  which  contained  the  charge.  He  discovered  the  property  of 
points  in  discharging  an  electrified  body,  and  the  identity  of  lightning 
with  electricity.  He  also  made  the  first  experiments  upon  atmospheric 
electricity. 

To  Canton  is  due  the  honor  of  giving  the  first  experiments  on  induc- 
tion, but  Franklin  is  the  first  who  gave  the  general  law  of  this  species 
of  action.  Truly  our  country  and  this  city  should  honor  the  memory 
of  this  man. 

But  it  is  not  my  purpose  to  repeat  to  you  in  detail  the  familiar  history 
40 


626  HENRY  A.  EOWLAND 

of  our  science.  Thus  far  no  important  applications  of  electricity  had 
been  discovered;  there  was  nothing  but  pure  science  to  attract  inves- 
tigators, and  thus  the  science  remained  for  many  years  after. 

But  no  science  is  complete  unless  it  is  quantitative  as  well  as  quali- 
tative. It  is  now  very  nearly  one  hundred  years  since  Coulomb  laid 
the  foundation  of  electrostatics  and  Aepinus  and  Cavendish  commenced 
to  lay  the  foundation  of  mathematical  electricity,  and  they  were  fol- 
lowed by  Laplace,  Biot,  Poisson,  and  Murphy. 

The  discoveries  by  Galvani  and  Volta  in  1790  and  1800,  and  by 
Oersted  in  1820,  gave  us  the  galvanic  battery  and  electro-magnetism, 
and  it  was  not  until  the  latter  date  that  any  useful  practical  application 
was  possible.  Then,  so  complete  was  the  science  that  no  factor  of  other 
than  minor  importance  was  necessary  to  transmit  intelligence  from  one 
extremity  of  the  earth  to  the  other. 

By  the  labors  of  the  immortal  Faraday,  electro-magnetic  induction 
was  discovered  and  the  modern  dynamo-electric  machine  became  a  cer- 
tainty. 

To  his  other  labors,  both  experimental  and  theoretical,  the  modern 
science  of  electricity  owes  much,  but  it  is  familiar  to  all.  The  name  of 
Faraday  needs  no  eulogy  from  me,  for  it  stands  where  it  can  never  be 
hidden,  and  the  spark  which  Faraday  first  kindled  now  dazzles  us  at 
every  street  corner.  No  wealth  came  to  him,  though  he  had  only  to 
hold  out  his  hand  for  it.  But  the  holding  out  of  one's  hand  takes  time, 
which  Faraday  could  not  spare  from  his  labors,  and  so  the  wealth  which 
was  rightly  his  went  to  others.  Who  will  follow  in  his  footsteps  and 
live  such  a  life  that  the  thought  of  it  almost  fills  one  with  reverence? 
It  is  not  only  his  intellect  which  we  admire;  it  is  his  moral  qualities 
which  fill  us  with  awe — his  noble  and  unselfish  spirit. 

The  name  of  Faraday  brings  us  down  to  modern  times,  whose  history 
it  is  unnecessary  to  repeat  in  detail,  especially  as  there  are  some  now 
present  who  have  contributed  largely  to  bring  the  science  to  its  present 
perfection. 

One  of  the  principal  features  which  we  remark  in  our  modern  science 
of  electricity  is  the  perfection  of  our  means  of  measuring  both  electrical 
and  magnetic  quantities.  In  this  connection  the  great  names  of  Gauss 
and  Weber  appear,  the  fathers  of  the  modern  absolute  system  of  elec- 
trical and  magnetic  measurement,  and  that  of  Sir  William  Thomson, 
in  no  less  degree  distinguished.  On  the  laws  of  electric  attraction  we 
base  our  electrostatic  system  of  measurement,  and  on  the  magnetic  ac- 
tion of  the  current,  the  great  discovery  of  Oersted,  we  base  our  electro- 


ELECTRICAL  CONFERENCE  AT  PHILADELPHIA  627 

magnetic  system,  and  we  connect  these  two  systems  by  that  great  physi- 
cal constant,  the  ratio  of  electro-magnetic  to  the  electrostatic  system  of 
units. 

What  can  be  simpler  in  theory  than  the  electrostatic  system,  based, 
as  it  is,  on  the  law  that  electric  attraction  varies  inversely  as  the  square 
of  the  distance?  We  only  have  to  know  how  the  electricity  is  dis- 
tributed and  its  attraction  is  known.  Hence  we  must  select  the  simplest 
possible  case,  such  as  two  parallel  disks,  and  to  render  the  problem  cal- 
culable, we  add  a  guard  ring  to  the  movable  disk.  We  then  have  the 
absolute  electrometer  of  Thomson.  This  gives  us  a  measure  of  the 
electric  potential.  Knowing  the  capacity  and  difference  of  potential 
of  the  surface  of  a  condenser,  we  know  its  charge.  But  all  these  quan- 
tities, the  calculation  of  the  electrometer  and  the  capacity  of  the  con- 
denser, depend  upon  the  mathematical  theory  of  electric  distribution. 
Are  we  able  to  calculate  the  capacity  of  condensers  of  all  forms?  I  am 
sorry  to  say  we  are  not.  The  modern  method  of  treatment  is  due  to 
George  Green,  an  English  investigator,  whose  name  should  be  held  in 
honor  by  all  electricians.  But  this  method  is  what  is  called  an  inverse 
one.  It  is  not  a  method  by  which  we  can  calculate  the  distribution 
on  any  body  at  random,  but  the  shape  of  the  body  and  the  electrical 
distribution  on  it  are  both  found  at  once  by  a  species,  as  it  were,  of 
exploration  and  discovery.  So  that  we  cannot  make  our  electrometers 
and  condensers  of  any  shape  and  then  calculate  them,  but  we  are  forced 
to  make  them  of  some  simple  geometrical  form  whose  solution  is 
known.  We  fit  our  apparatus  to  the  mathematics  rather  than  the  mathe- 
matics to  the  apparatus. 

But  when  we  have  satisfied  all  the  conditions  we  measure  out  our 
static  charges  as  easily  as  a  quantity  of  matter.  The  manufacturer  sells 
the  oxygen  and  hydrogen  in  iron  cylinders  and  determines  the  amount 
by  the  product  of  the  capacity  of  the  cylinders  by  the  pressure.  Were 
there  any  buyers  of  electricity  we  might  sell  them  a  Leyden  jar  full  and 
determine  the  amount  by  the  product  of  the  capacity  of  the  jar  by  the 
electric  potential.  According  to  this  analogy,  then,  the  electricity  is 
similar  to  matter  and  the  potential  fluid  pressure,  while  the  word  ca- 
pacity has  a  similar  meaning  in  both. 

In  the  electro-magnetic  method  of  electrical  measurement  we  make 
use  of  the  magnetic  action  of  the  current,  either  on  a  neighboring  mag- 
net or  another  current  or  portion  of  the  same  current.  The  laws  of  the 
action  of  a  current  on  a  magnet  were  discovered  by  Biot  and  Savart, 
and  of  two  currents  on  each  other  by  Ampere,  and  the  results  applied  to 


628  HENKY  A.  ROWLAND 

practical  measurement  to-day  give  us  galvanometers  of  all  kinds  and 
the  electro-dynamometer  of  Weber.  By  the  galvanometer  we  can  meas- 
ure the  quantity  of  electricity  passing  at  any  moment,  but  by  the  elec- 
tro-dynamometer we  measure  the  integral  square  of  the  current,  a 
quantity  on  which  the  heating  of  the  circuit  and  the  energy  expended 
depend. 

Thus  the  electro-dynamometer  measures  the  energy  from  an  alternat- 
ing current  dynamo-electric  machine  as  easily  as  from  one  giving  a  con- 
tinuous current,  but  to  know  this  energy  we  must  know  something  else 
besides  the  integral  square  of  the  current,  and  this  is  either  the  resist- 
ance of  the  circuit  or  the  electromotive  force.  But  the  measurement  of 
electromotive  force  depends  on  a  resistance.  The  question  then  comes 
up  as  to  what  unit  of  resistance  is  the  proper  one.  Here  we  have  to 
refer  to  the  mathematical  theory  of  the  subject,  and  the  great  law  of  the 
conservation  of  energy  tells  us  that  what  is  known  as  the  absolute  unit 
of  electrical  resistance  is  the  proper  one  for  use  in  this  case.  Hence 
the  great  practical  use  of  determining  this  unit.  The  experiments  of 
Kirchhoff,  Weber,  Kohlrausch,  and  the  British  Association  found  a 
value  from  1  to  3  per  cent  too  large. 

Many  years  ago  I  myself  experimented  on  the  subject,  and  obtained 
a  result  about  4  per  cent  too  high.  Recently  Lord  Rayleigh  has  taken 
up  the  matter  and  made  a  series  of  experiments  of  unparalleled  accu- 
racy in  this  line.  The  International  Commission,  determined  on  by  the 
Electrical  Congress  in  Paris  in  1881,  met  in  April  of  this  year  at  Paris, 
and  has  now  given  us  a  legal  ohm  defined  as  being  the  resistance  of  a 
column  of  mercury  106  centimetres  long  and  1  millimetre  in  section  at 
0°  C.  The  length  best  satisfying  the  experiments  is  about  106-25,  but 
it  was  considered  best  to  use  the  round  number.  The  experiments 
which  I  have  been  making  under  an  appropriation  from  the  Government 
are  now  barely  completed,  but  they  will  probably  agree  very  well  with 
the  latter  figure.  Hence,  we  can  say  that  we  now  know  this  unit  of 
resistance  to  one  part  in  one  thousand,  at  least.  And  so  we  are  in  a  posi- 
tion to  measure  the  energy  of  a  current  to  the  same  degree  of  accuracy, 
as  far  as  this  quantity  is  concerned. 

But  to  measure  a  current  by  the  tangent  galvanometer  one  requires 
to  know  the  intensity  of  the  earth's  magnetism,  a  quantity  difficult  to 
determine  and  constantly  varying  with  time  and  place.  The  electro- 
dynamometer,  when  made  with  care,  is  excellent,  but  a  good  one  is  im- 
mensely expensive.  Our  methods,  then,  of  current  measurement  are 
bad,  unless  carried  out  in  a  completely  equipped  physical  laboratory. 


ELECTRICAL  CONFERENCE  AT  PHILADELPHIA  629 

With  a  practical  standard  of  electromotive  force,  such  as  a  Clark's 
standard  cell  or  a  thermo-electric  battery,  this  difficulty  partially  van- 
ishes. Better,  perhaps,  we  might  make  simple  electro-dynamometers 
with  constants  determined  by  comparisons  with  a  more  costly  instru- 
ment. 

But  where  shall  these  standards  be  kept?  Evidently  the  Govern- 
ment, which  decides  on  our  standards  of  weights  and  measures,  should 
take  in  charge  the  electrical  standards,  and  possibly  also  the  thermo- 
metric  standards.  The  formation  of  such  a  Bureau  of  Physical  Stand- 
ards will  be  brought  to  the  attention  of  this  Conference. 

Having  given  certain  standards  then,  the  measurement  of  currents 
and  current  energy  becomes  easy.  The  amount  of  heat  generated  in  a 
wire  of  known  resistance  by  a  known  current  is  also  easily  found  from 
the  absolute  system  of  electrical  measurement. 

Besides  the  two  so-called  absolute  systems  of  measurement  of  elec- 
tricity and  electric  currents,  we  have  also  one  based  on  the  chemical 
action  of  the  current  whose  laws  were  discovered  by  Faraday.  Know- 
ing the  electro-chemical  equivalent  of  some  substance,  we  are  able  to 
measure  the  time  integral  of  the  current  or  the  total  quantity  of  the 
current  which  has  passed. 

The  absolute  measurement  of  magnetism  is  equally  simple  with  that 
of  electricity,  and  it  is  a  common  observation  to  find  the  earth's  magnetic 
force.  But  Faraday  has  put  in  our  hands  a  very  simple  method  of  meas- 
uring a  magnetic  field,  and  to-day  all  are  familiar  with  his  beautiful 
laws  with  respect  to  magnetic  lines  of  force.  We  know  the  laws  of 
electro-magnetism,  and  just  how  many  lines  of  force  (better  induction) 
can  pass  through  a  piece  of  iron  of  given  cross-section,  and  what  is  their 
relative  resistance  when  passing  through  air  or  iron.  In  fact,  we  have 
all  that  is  necessary  for  a  complete  theory  of  the  dynamo-electric  ma- 
chine, and  consequently  we  find  that  the  latter  agrees  perfectly  with 
theory,  and  no  fact  has  been  observed  with  reference  to  it  which  could 
not  have  been  foreseen  from  theory  by  a  person  of  proper  intelligence. 

This  part  of  electrical  science,  the  measurement  of  electrical  and  mag- 
netic quantities,  is  thus  in  a  very  forward  state,  based,  as  it  is,  on  the 
mathematical  theory  of  the  subject.  But,  in  reality,  this  forms  but  a 
very  small  portion  of  our  science.  Shall  we  be  contented  with  a  simple 
measurement  of  that  of  which  we  know  nothing?  I  think  nobody  would 
care  to  stop  at  this  point,  although  he  might  be  forced  to  do  so.  The 
mind  of  man  is  of  a  nobler  cast,  and  seeks  knowledge  for  itself  alone. 
We  are  not  so  base  as  to  be  honest  because  "  Honesty  is  the  best  policy," 


630  HENRY  A.  KOWLAND 

neither  are  we  so  ignoble  as  to  seek  knowledge  because  "  Knowledge  is 
power  " — two  sayings  which  are  certainly  true,  but  low  and  sordid  in 
their  tone. 

We  have,  then,  the  beautiful  fabric  of  mathematical  electricity  given 
to  the  world  by  Poisson,  Green,  Helmholtz,  Thomson,  Maxwell,  and 
others  whose  names  are  immortal.  No  hypothesis  as  to  the  nature  of 
electricity  rests  at  its  base.  Starting  from  the  most  simple  laws  of 
electricity  and  magnetism,  it  rises  from  a  stable  foundation  and  rears 
its  form  high  in  the  air,  never  to  be  overturned,  whatever  the  fate  of 
the  so-called  electric  fluid  or  the  ultimate  theory  of  magnetism.  On  the 
simple  fact  that  there  is  no  electric  force  inside  a  closed  conductor,  it  is 
proved  that  the  electric  attraction  and  repulsion  varies  inversely  as  the 
square  of  the  distance.  The  fact  is  sufficient  to  give  us  the  whole  theory 
of  electrostatic  distribution  on  conductors. 

From  the  simple  fact  that  we  can  break  a  magnet  up  into  parts  which 
are  similar  to  each  other,  and  that  these  parts  attract  and  repel  each 
other  in  a  certain  manner,  we  derive  many  important  facts  with  regard 
to  magnetism. 

From  the  magnetic  action  of  the  current  we  find,  by  an  application  of 
the  great  law  of  conservation  of  energy,  all  the  laws  of  induced  cur- 
rents, either  from  magnets  or  other  currents.  By  an  almost  superhu- 
man effort  of  the  intellect  we  detach  our  electric  currents  from  matter, 
and  suppose  them  to  take  place  in  the  ether  of  space,  and  we  have  the 
grand  electro-magnetic  theory  of  light  given  to  us  by  Maxwell. 

But  the  subject  is  too  vast  to  be  treated  in  a  moment.  Suffice  it  to 
say  that  no  person  at  the  present  day  has  the  right  to  express  an  opin- 
ion on  any  theoretical  question  connected  with  electricity  without  a 
knowledge  of  its  mathematics. 

This  study  has  led  us  to  alter  our  ideas  on  many  questions.  What 
is  the  mechanism  of  electri'c  or  magnetic  attraction?  Faraday  has 
given  us  his  idea  of  lines  of  force,  and  has  made  them  play  an  important 
part  in  the  theory  of  magnetic  induction.  When  treated  mathemati- 
cally, Maxwell  has  shown  that  all  electric  and  magnetic  attractions  can 
be  explained  by  a  tension  along  the  lines  of  force  and  pressure  at  right 
angles  to  them — an  idea  due  to  Faraday. 

The  mathematical  theory  of  these  lines  shows  that  all  electrostatic 
forces  between  either  conductors  or  non-conductors  can  be  explained  in 
this  manner.  As  the  laws  of  magnetic  attraction  are  the  same  in  every 
way  as  electrostatic  attraction,  if  we  should  do  away  with  electric  con- 
duction, it  follows  that  magnetic  attraction  is  to  be  explained  in  exactly 


ELECTRICAL  CONFERENCE  AT  PHILADELPHIA  631 

the  same  manner.  In  obtaining  this  result  Maxwell  calculated  the 
forces  acting  on  the  medium  at  every  point,  and  compares  these  with 
imaginary  stresses  in  a  medium  at  the  given  point.  Hence,  the  energy 
stored  up  can  be  represented  either  as  due  to  the  mutual  attraction  of 
the  electricity  at  a  distance,  or  to  the  stresses  in  the  medium  at  every 
point,  and  thus,  as  Thomson  has  shown,  by  a  volume  integral  of  the 
square  of  the  force  at  every  point.  Hence,  we  are  at  liberty  to  deny 
the  existence  of  all  action  at  a  distance,  and  attribute  it  to  the  inter- 
vening medium,  which,  to  be  logical,  we  must  assume  to  be  continuous 
and  not  molecular  in  constitution. 

Thomson  has  pointed  out  that  magnetism  must  be  of  the  nature  of  ro- 
tation, such  as  possibly  vortex  motion  in  a  fluid,  and  Maxwell  has  done 
something  toward  making  a  mechanical  model  of  such  a  medium.  Thom- 
son's wonderful  address  at  Montreal  has  also  given  us  much  to  think  of 
in  the  same  direction. 

But  here  we  have  reached  the  limit  of  our  science,  and  even  that  serv- 
ant of  our  reason,  imagination,  fails  us.  We  are  yet  unable  to  picture 
to  ourselves  what  takes  place  in  a  medium  subject  to  electrostatic  ac- 
tion. We  are  face  to  face  with  the  great  problem  of  nature,  and  the 
questions,  What  is  matter?  What  is  electricity?  evoke  no  answer  from 
the  wisest  among  us.  Our  mathematics  has  guided  us  safely  up  to  a 
certain  point  and  will  guide  us  still  further;  science  will  advance  and 
we  shall  know  more.  But,  for  the  present,  this  is  the  limit  which  we 
have  yet  attained  in  this  direction.  However,  the  idea  of  a  medium  is 
still  serviceable  in  other  portions  of  our  science. 

We  have  seen  that  the  medium  explains  the  electrical  and  magnetic 
attraction  of  bodies  at  rest.  The  question  then  comes  up  as  to  what 
happens  in  the  medium  when  these  bodies  move.  Are  the  imaginary 
stresses  in  the  medium  transmitted  from  place  to  place  instantaneously 
or  do  they  require  time?  Mathematics  in  the  hands  of  the  immortal 
Maxwell  has  answered  this  question,  and  we  now  know  that  any  mag- 
netic or  electric  distrubance  is  propagated  through  space  with  a  velocity 
equal  to  the  ratio  of  the  electro-magnetic  to  the  electrostatic  unit  of 
electricity.  This  great  physical  constant  has  now  been  found  by  experi- 
ment to  be  equal  to  the  velocity  of  light,  and  thus  has  arisen  that  great 
modern  theory,  Maxwell's  electro-magnetic  theory  of  light.  Indeed,  at 
the  present  day,  so  perfectly  does  this  theory  agree  with  experiment  that 
we  can  almost  regard  it  as  a  certainty.  The  velocity  of  light  and  the 
ratio  of  the  units  agree  far  within  the  limits  of  experimental  error.  The 
fact  that  bodies  having  a  true  (not  electrolytic)  electric  conduction  are 


632  HENRY  A.  KOWLAND 

always  more  or  less  opaque,  the  refraction  and  dispersion  of  light,  dou- 
ble refraction,  and  diffraction,  all  are  explained  on  this  theory  with  an 
ease  and  simplicity  wanting  in  all  other  theories;  and,  lastly,  an  elec- 
tro-magnetic phenomenon  has  been  discovered,  which,  when  applied  to 
this  theory  of  light,  explains  the  rotation  of  the  plane  of  polarization 
produced  by  a  magnet.  There  is  no  fact  in  nature  seriously  in  disagree- 
ment with  this  theory,  and  it  serves  to  connect  two  of  our  most  impor- 
tant branches  of  physics,  light  and  electricity. 

But  some  physicists  say  that  it  is  not  a  true  theory,  because  it  is  not 
mechanical,  the  object  of  these  physicists  being  to  reduce  every  phe^ 
nomenon  of  nature  to  matter  and  motion.  Whether  this  is  necessary  or 
not  I  leave  to  the  philosophers.  But  it  is  to  be  noted  that  the  old  me- 
chanical theory  that  light  is  a  vibration  in  a  medium  having  the  prop- 
erties of  an  elastic  solid  is  not  entirely  at  variance  with  the  new  theory. 
The  medium  we  call  ether.  The  electro-magnetic  theory  says  that 
the  waves  of  light  are  waves  of  electric  displacement,  while  the  old 
theory  says  they  are  waves  of  ether.  Make  electricity  and  the  ether 
equal  to  each  other  and  the  two  theories  become  one.  We  have  arrived 
at  that  hazy  and  unsatisfactory  theory  of  Edlund  that  ether  and  elec- 
tricity are  one,  except  that  by  this  theory  electricity  is  presented  to  us 
as  an  elastic  solid! 

But  the  ground  trembles  beneath  us,  and  we  shall  soon  be  plunged  in 
the  mire  of  vague  speculation  if  we  do  not  draw  back. 

Among  the  other  questions  which  depend  for  their  solution  on  the 
presence  of  a  medium  may  be  mentioned  the  mutual  action  of  two  elec- 
trified bodies  moving  in  space.  It  has  been  found  that  electricity  car- 
ried through  space  on  a  charged  body  has  exactly  the  same  magnetic 
effect  on  a  stationary  magnetic  needle  as  if  it  had  been  conducted. 

But  when  electrified  bodies  move  uniformly  forward  in  space,  we  can 
conceive  of  no  mutual  effect  from  such  motion  unless  it  is  relative  to  a 
medium,  for  we  cannot  even  conceive  of  absolute  motion. 

Assuming  the  medium  to  exist,  we  then  know  that  a  positively  and  a 
negatively  charged  body  flying  through  space  with  the  velocity  of  light 
would  have  their  electric  attraction  just  balanced  by  their  magnetic  re- 
pulsion, and  so  would  exert  no  force  on  each  other. 

But  it  is  a  most  wonderful  fact  that  we  have  never  been  able  to  dis- 
cover anything  on  the  earth  by  which  our  motion  through  a  medium 
can  be  directly  proved.  Carried,  as  we  suppose,  by  the  earth  with  im- 
mense velocity  through  regions  of  space  filled  with  ether,  we  have  never 
yet  been  able  to  prove  any  direct  influence  from  this  ethereal  wind. 


ELECTRICAL  CONFERENCE  AT  PHILADELPHIA  633 

The  assumption  of  a  medium  allows  us  to  solve  in  some  cases  that 
problem  so  long  under  discussion  by  electricians — namely,  the  true  ve- 
locity of  an  electric  current.  We  now  know  that  the  term  velocity 
hardly  applies  to  this  case,  and  that  the  current  arrives  at  different 
points  so  gradually  that  we  know  not  when  to  say  it  has  arrived.  But 
there  is  certainly  a  minimum  time  when  even  an  infinitesimal  current 
can  reach  a  distant  point.  Suppose  two  wires  stretched  in  space  with 
their  ends  near  together  at  one  end  and  a  Leyden  jar  be  discharged  from 
one  to  the  other  at  the  near  end.  The  minimum  possible  time  of  obtain- 
ing a  spark  at  the  distant  end  will  evidently  be  the  time  required  by 
light  to  pass  from  the  Leyden  jar  to  the  distant  point,  not  around  the 
wire,  but  in  a  straight  line.  In  this  case  the  greatest  maximum  velocity 
is  thus  twice  that  of  light  reckoned  around  the  wire,  and  may  be  any 
amount  greater  when  we  bend  the  wire.  For  all  ordinary  distances  this 
velocity  may  be  considered  infinite,  and  the  retardation  to  depend 
only  on  the  electrostatic  capacity  and  magnetic  self-induction  of  the 
wire.  Treated  in  this  way,  we  have  Thomson's  mathematical  theory 
of  the  propagation  of  an  electric  wave  along  a  telegraph  wire  or  cable, 
a  theory  of  great  practical  use  in  telegraphy  and  telephony.  But  until 
the  action  in  the  external  medium  is  also  taken  into  account,  it  can  only 
be  considered  an  approximation.  For  we  can  never  move  a  magnet, 
discharge  a  Leyden  jar,  or  complete  the  circuit  of  a  battery,  without 
causing  a  wave  of  electro-magnetic  disturbance  in  the  ether,  and  every 
signal  which  is  sent  along  a  telegraph  line  is  accompanied  by  a  wave  in 
the  ether,  which  travels  outward  into  space  with  the  velocity  of  light. 
Truly  the  idea  of  a  medium  is  to-day  the  keystone  of  electrical  theory, 
but  we  can  hardly  suppose  that  it  has  even  yet  attained  a  fraction  of 
the  importance  to  which  it  is  destined  to  rise. 

Let  me  now  call  your  attention  to  one  of  the  most  wonderful  facts 
connected  with  electrical  science.  When  we  are  dealing  with  the  elec- 
trostatic action  of  electricity,  we  find  that  it  is  the  so-called  electric  fluid 
which  attracts  the  opposite.  Not  only  do  we  observe  the  attraction  of 
bodies  oppositely  charged,  but  the  electricity  itself  on  the  two  bodies  is 
displaced  by  its  mutual  action.  But  when  we  come  to  investigate  the 
mutual  attraction  or  repulsion  of  electric  currents  on  each  other,  we  find 
an  entirely  different  law.  In  this  case  the  conductors  carrying  the  cur- 
rents attract  or  repel  each  other,  but  the  currents  within  those  con- 
ductors have  no  influence  of  attraction  or  repulsion  to  displace  them- 
selves within  the  body  of  the  conductor.  In  other  words,  the  current 
is  not  displaced  by  the  action  of  a  neighboring  magnet,  but  flows  on 
calmly  as  if  it  were  not  present. 


634  HENEY  A.  KOWLAND 

This  to  me  is  one  of  the  most  wonderful  facts  in  electrical  science,  and 
lies  at  the  foundation  of  our  science.  It  cannot  be  ignored  in  any  fur- 
ther progress  we  may  make  in  electrical  theory,  but  points  out  a  radical 
difference  between  electrostatic  and  electro-magnetic  action. 

I  have  said  there  is  no  action  of  a  magnet  in  displacing  an  electric 
current,  and  have  thus  stated  the  broad  general  fact,  and  which  is  per- 
fectly true  in  some  metals.  But  in  others  there  is  a  small  action  which 
changes  in  direction  with  the  material.  The  elements  of  the  electric 
current  within  the  material  are  rotated  around  the  lines  of  magnetic 
force,  sometimes  in  one  direction  and  sometimes  in  the  other,  according 
to  the  material.  But  the  action  is,  in  all  cases,  very  weak.  When  ap- 
plied to  the  electro-magnetic  theory  of  light,  this  action  leads  to  the 
magnetic  rotation  of  the  plane  of  polarization  of  light.  As  to  the  ex- 
planation of  both  these  actions,  Thomson  has  remarked  in  the  case  of 
light,  from  dynamical  considerations,  the  rotation  can  only  come  from  a 
true  rotation  of  something  in  the  magnetic  field,  and  leads  us  to  think  of 
all  magnetic  action  as  of  the  nature  of  vortex  motion  in  a  fluid.  But 
here  our  theory  ends  for  the  present.  We  have  obtained  a  clew,  but  it 
is  not  yet  worked  up. 

I  have  now  taken  a  rapid  glance  at  some  of  the  modern  advances  of 
electrical  science,  and  we  have  not  yet  had  to  give  up  the  old  idea  that 
electricity  is  liquid.  To  the  profound  thinker  this  idea  is  very  vague, 
and  there  are  some  facts  at  variance  with  it,  but  it  is  still  useful.  We 
often  hear  persons  say  that  this  old  idea  is  gone,  and  that  electricity  is 
"  force,"  whatever  they  may  mean  by  that.  But  let  us  see.  The  work 
or  energy  of  an  electric  current  between  any  two  points  is  the  quantity 
of  electricity  passed  multiplied  by  the  potential;  this  work  goes  to 
heating  the  wire.  Let  a  curient  of  water  be  passing  in  a  pipe,  and  the 
quantity  of  water  multiplied  by  the  difference  of  pressure  between  two 
points  gives  us  the  work  which  has  been  done  in  the  intervening  space, 
and  which  has  produced  heat.  The  analogy  is  complete.  No  electricity 
has  been  destroyed  in  the  one  case,  or  water  in  the  other,  but  the  work 
has  come  from  the  fall  of  potential  in  the  one  case,  and  the  fall  of 
pressure  in  the  other;  the  resultant  is  the  same  in  both — heat.  Again, 
we  can  obtain  work  from  the  mutual  attraction  and  repulsion  of  elec- 
trified bodies,  and  the  work  in  this  case  always  comes  from  the  change 
of  potential  between  the  bodies  while  the  electric  charges  remain  undis- 
turbed in  quantity.  Electricity,  then,  is  not  energy,  but  is  more  of  the 
nature  of  matter. 

So  far  for  electricity  in  the  state  of  rest  or  steady  flow.     But  when  it 


ELECTRICAL  CONFERENCE  AT  PHILADELPHIA  635 

changes  from  rest  to  motion,  all  known  liquids  have  a  property  known 
as  inertia;  furthermore,  they  have  weight.  But  the  electric  fluid  has 
neither  inertia  nor  weight  as  far  as  we  have  yet  experimented,  and  in 
this  respect  differs  from  all  known  matter.  Furthermore,  we  have  never 
yet  been  able  to  separate  electricity  from  ordinary  matter.  When  we 
pass  electricity  through  a  vacuum,  the  resistance  becomes  less  and  less, 
and  one  may  have  hopes  of  finally  having  an  electric  current  through  a 
vacuum.  But,  as  the  exhaustion  proceeds,  we  observe  that  the  resist- 
ance begins  to  increase  until  it  reaches  such  a  point  that  no  discharge 
can  take  place.  Electricity  cannot  exist,  then,  without  matter,  a  fact 
fatal  to  the  idea  of  a  fluid,  however  useful  that  may  be.  We  have  but 
one  conclusion  from  this,  and  that  is  that  electricity  is  a  property  of 
matter.  Do  with  it  what  we  may,  it  can  never  be  separated  from  matter, 
and  when  we  have  an  electrical  separation  the  lines  of  force  must  always 
begin  and  end  in  matter. 

The  theory  of  matter,  then,  includes  electricity  and  magnetism,  and 
hence  light;  it  includes  gravitation,  heat,  and  chemical  action;  it  forms 
the  great  problem  of  the  universe.  When  we  know  what  matter  is, 
then  the  theories  of  light  and  heat  will  also  be  perfect;  then  and  only 
then,  shall  we  know  what  is  electricity  and  what  is  magnetism. 

It  is  the  problem  of  the  universe  which  looms  up  before  us  and  before 
which  we  stand  in  awe.  The  intellect  of  the  greatest  among  us  appears 
but  feeble  and  we  all,  like  Newton,  appear  but  as  children  on  the  sea- 
shore. But  how  few  of  us  find  the  shells  which  Newton  did.  and  how 
few  of  us  try.  The  problem  is  vast  and  the  means  for  its  solution  must 
be  of  corresponding  magnitude.  Our  progress  so  far  has  been  but  small. 
AY  hen  we  push  our  inquiry  in  any  direction  we  soon  reach  a  limit;  the 
region  of  the  unknown  is  infinitely  greater  than  the  known,  and  there 
is  no  fear  of  there  not  being  work  for  the  whole  world  for  centuries  to 
come.  As  to  the  practical  applications  which  await  us,  the  telegraph, 
the  telephone,  and  electric  lighting  are  but  child's  play  to  what  the 
world  will  see  in  the  future. 

But  what  is  necessary  to  attain  these  results?  We  have  seen  how  the 
feeble  spirit,  which  was  waked  up  by  friction  in  the  amber  and  went  forth 
to  draw  in  light  bodies,  has  grown  until  it  now  dazzles  the  world  by  its 
brilliancy,  and  carries  our  thoughts  from  one  extremity  of  the  world  to 
the  other.  It  is  the  genius  of  Aladdin's  lamp  which,  when  thoroughly 
roused,  goes  forth  into  the  world  to  do  us  service,  and  returns  bearing 
us  wealth  and  honor  and  riches.  But  it  can  never  be  the  servant  of  an 
ignorant  or  lazy  world.  Like  the  genius  of  Aladdin's  lamp  it  appeared 


636  HENRY  A.  ROWLAND 

to  the  world  when  the  amber  was  rubbed,  but  the  world  knew  not  the 
language  in  which  to  give  it  orders,  and  was  too  lazy  to  learn  it.  The 
spirit  of  the  amber  appeared  before  them  to  receive  its  orders,  but  was 
only  gazed  at  in  silly  wonder,  and  retired  in  disgust.  They  had  but  to 
order  it  and  it  would  have  gone  to  the  uttermost  parts  of  the  earth  with 
'almost  the  velocity  of  light  to  do  their  bidding.  But  in  their  ignorance 
they  knew  not  its  language.  For  two  thousand  years  they  did  not  study 
it,  and  when  they  then  began  to  do  so  it  took  them  two  hundred  and  fifty 
years  to  learn  the  language  sufficiently  to  make  a  messenger  of  it.  And 
even  now  we  are  but  children  studying  its  ABC.  It  is  knowledge, 
more  knowledge,  that  we  want. 

I  have  briefly  recounted  the  advances  which  we  have  now  made  in 
one  science,  and,  however  beautiful  it  may  appear,  we  have  soon  reached 
the  limit  of  the  known,  and  have  stood  in  wonder  before  the  vast  un- 
known. For  very  much  of  our  science  we  see  no  practical  applications, 
but  we  value  it  no  less  on  that  account.  We  study  it  because  we  have 
been  gifted  with  minds  whose  exercise  delights  us,  and  because  it  seems 
to  us  one  of  the  highest  and  noblest  of  employments.  And  we  know  by 
the  history  of  the  past  that  the  progress  of  the  world  depends  on  our 
pursuit,  and  that  practical  applications,  such  as  the  world  has  never  even 
conceived  of,  await  us.  It  is  necessary  that  some  should  go  before  to 
clear  the  way  for  the  world's  advance. 

This  is  the  work  of  the  pure  scientist;  to  him  the  problem  of  the  uni- 
verse is  worth  devoting  his  life,  and  he  looks  upon  wealth  as  only  add- 
ing to  his  means  of  research.  He  hopes  not  to  solve  the  problem  him- 
self, but  is  contented  if  he  may  add  some  small  portion  to  human  knowl- 
edge; if  he  may  but  do  his  part  in  the  march  of  human  progress.  He 
looks  not  for  practical  applications,  but  he  knows  full  well  that  his  most 
abstruse  discoveries  will  finally  be  made  useful  to  mankind  at  large,  and 
so  troubles  himself  no  further  about  it. 

The  science  which  he  creates  is  studied  by  others.  Their  minds  are 
educated  by  it  and  their  hearts  entranced  by  its  beauties.  And  some 
are  led  to  devote  their  lives  to  its  further  advancement.  But  the  whole 
world  benefits  by  it  intellectually.  The  wayward  spirit  of  the  amber 
has  vanished  forever,  and  prosaic,  law-abiding  electricity  has  taken  its 
place  even  in  the  estimation  of  the  most  ignorant.  The  world  has  ad- 
vanced, and  in  great  part  from  the  study  of  science. 

Then  comes  the  practical  man,  who  sees  that  other  benefits  can  be 
reaped  besides  those  of  pure  intellectual  enjoyment.  While  the  inves- 
tigator toils  to  understand  the  problem  of  the  universe,  the  practical 


ELECTKICAL  CONFERENCE  AT  PHILADELPHIA  637 

man  seeks  to  make  a  servant  of  our  knowledge.  He  seeks  to  increase 
the  power  of  our  bodies  and  to  make  the  bonds  by  which  the  mind  is 
united  to  it  less  irksome.  It  is  he  that  increases  the  wealth  of  the  world, 
and  thus  allows  those  so  disposed  to  cultivate  their  tastes  and  to  elevate 
themselves  above  the  savages.  The  progress  of  the  world  depends  upon 
his  inventions. 

Let  not,  then,  the  devotee  of  pure  science  despise  practical  science, 
nor  the  inventor  look  upon  the  scientific  discoverer  as  a  mere  visionary 
person.  They  are  both  necessary  to  the  world's  progress  and  they  are 
necessary  to  each  other. 

To-day  our  country,  by  its  liberal  patent  laws,  encourages  applied 
science.  We  point  to  our  inventions  with  pride,  and  our  machinery  in 
many  of  the  arts  is  not  surpassed.  But  in  the  cultivation  of  the  pure 
sciences  we  are  but  children  in  the  eyes  of  the  world.  Our  country  has 
now  attained  wealth,  and  this  wealth  should  partly  go  in  this  direction. 
We  have  attained  an  honorable  position  in  applied  science,  and  now  let 
us  give  back  to  the  world  what  we  have  received  in  the  shape  of  pure 
science.  Thus  shall  we  no  longer  be  dependent,  but  shall  earn  our  own 
science  as  well  as  inventions. 

Let  physical  laboratories  arise;  let  men  of  genius  be  placed  at  their 
head,  and,  best  of  all,  let  them  be  encouraged  to  pursue  their  work  by 
the  sympathy  of  those  around  them.  Let  the  professors  be  given  a 
liberal  salary,  so  that  men  of  talent  may  be  contented.  Let  technical 
schools  also  be  founded,  and  let  them  train  men  to  carry  forward  the 
great  work  of  applied  science. 

Let  them  not  be  machines  to  grind  out  graduates  by  the  thousand, 
irrespective  of  quality.  But  let  each  one  be  trained  in  theoretical 
science,  leaving  most  of  his  practical  science  to  be  learned  afterward, 
avoiding,  however,  overtraining.  Life  is  too  short  for  one  man  to  know 
everything,  but  it  is  not  too  short  to  know  more  than  is  taught  in  most 
of  our  technical  schools.  It  is  not  telegraph  operators,  but  electrical 
engineers  that  the  future  demands. 

Such  a  day  has  almost  come  to  our  country  and  we  welcome  its  ap- 
proach. 

Then,  and  not  till  then,  should  our  country  be  proud  and  point  with 
satisfaction  to  her  discoveries  in  science,  pure  and  applied,  while  she 
has  knowledge  enough  to  stand  in  humiliation  before  that  great  undis- 
covered ocean  of  truth  on  whose  shores  Newton  thought  he  had  but 
played. 


THE    ELECTEICAL    AND    MAGNETIC    DISCOVERIES  OF 

FARADAY 

ADDRESS    AT    THE    OPENING    OF    THE    ELECTRICAL    CLUB    HOUSE    OF 
NEW    YORK    CITY,  1888 

[Electrical  Review,  New  York,  Feb.  4,  1888] 

In  the  progress  of  all  sciences  there  are  epochs  when  men,  thoroughly 
fitted  by  nature,  if  not  by  education  also,  for  the  most  successful  study 
and  advancement  of  their  science,  are  born  into  the  world,  and  by  their 
natural  talent,  perseverance  and  love  of  their  science,  give  it  an  impetus 
which  stamps  their  name  forever  on  its  history.  But,  however  great 
they  may  be,  we  know  enough  of  the  nature  of  scientific  progress  to  be 
sure  that  there  never  was  one  of  such  greatness  as  to  be  absolutely  neces- 
sary to  human  progress.  The  world  would  never  have  stood  still  on 
account  of  the  absence  of  any  name  from  its  annals,  and  even  the  place 
of  the  immortal  Newton  would  sooner  or  later  have  been  filled  by  others, 
and  all  the  discoveries  of  his  "  Principia  "  have  been  known  to  us  now, 
even  had  he  never  existed. 

Discoveries,  then,  have  their  origin  not  only  in  the  presence  of  men 
of  exceptional  genius  in  the  world,  but  in  a  true  and  overwhelming 
progress  of  science  which  marches  forward  to  the  understanding  of  the 
universe,  irrespective  of  the  efforts  of  any  single  individual  to  promote 
or  retard  it.  It  is  a  great  fact,  whose  explanation  we  find  in  the  craving 
of  mankind  for  knowledge  of  nature  and  power  over  her. 

As  men  of  genius  are  born,  they  find  the  discoveries  of  those  who 
have  gone  before  them  awaiting  them.  They  join  in  the  good  work, 
and  add  their  efforts  toward  the  advancement  of  knowledge.  But  in  all 
cases  they  start  at  the  point  where  those  who  have  gone  before  them 
have  left  off;  if  their  work  is  good  they  continue  it;  if  it  is  bad  they 
replace  it  by  better,  that  the  structure  of  science  may  be  reared  on  solid 
foundations,  and  grow  surely  and  steadily  toward  a  perfect  whole. 

To  understand,  then,  the  place  of  any  man  like  Faraday  in  the  history 
of  science,  we  must  also  understand  the  state  of  that  science  at  the  time 
when  he  did  his  work. 

Michael  Faraday,  the  son  of  a  smith,  was  born  in  1791,  and  was  ap- 
prenticed to  a  bookseller  and  bookbinder  in  1804.  He  educated  himself 
by  reading,  and  became  the  assistant  of  the  great  chemist,  Sir  Humphry 


ELECTRICAL  AND  MAGNETIC  DISCOVEKIES  OF  FARADAY        639 

Ihivy,  when  he  was  twenty-two  years  old.  His  attention  was  first  given 
to  chemistry,  but  was  finally  attracted  to  electricity  by  the  discovery  of 
electro-magnetism  by  Oersted,  in  1820.  At  this  period  the  subject  of 
electrostatics  was  very  far  advanced  even  as  compared  with  modern 
limes. 

More  than  200  years  before,  Gilbert  had  commenced  the  study  of 
electricity,  and  divided  bodies  into  electrics  and  non-electrics,  accord- 
ing as  they  produced  or  did  not  produce  electricity  by  friction.  Nearly 
100  years  before,  Stephen  Gray  had  discovered  the  difference  between 
conductors  and  non-conductors,  and  had  shown  the  means  of  carrying 
electrical  effects  to  a  distance  of  several  hundred  feet  by  means  of  a  con- 
ducting thread  or  wire  suspended  by  non-conducting  threads  of  silk. 
Otto  von  Guericke,  du  Fay  and  Wilke  had  shown  that  there  were  two 
kinds  of  electricity — resinous  and  vitreous.  The  Leyden  jar  had  been 
discovered  by  the  Dutch  philosophers.  Franklin  had  written  his  cele- 
brated series  of  letters  on  electricity,  explaining  the  phenomenon  of  the 
Leyden  jar  and  induction  as  clearly  as  we  can  do  it  at  present,  giving 
his  theory  of  positive  and  negative  electricity  to  the  world,  and  demon- 
strating in  the  most  perfect  manner  the  electrical  nature  of  thunder 
and  lightning. 

Aepinus  and  Cavendish  had  applied  mathematics  to  the  subject,  and 
the  latter  had  discovered  the  law  of  inverse  squares,  and  made  for  himself 
a  series  of  graduated  condensers,  by  which  he  measured  the  capacity  of 
differently  shaped  bodies.  They  had  been  followed  by  Laplace,  Pois- 
son  and  Biot  in  mathematical  electricity.  Coulomb  had  introduced  Jiis 
torsion  balance,  the  first  accurate  instrument  for  electrical  measure- 
ment. 

Galvani  and  Volta  had  shown  how  to  produce  a  current  of  electricity 
by  the  galvanic  battery.  The  chemical  action  of  electricity  had  long 
been  known,  and  had  been  forcibly  brought  before  the  world  by  the 
immortal  experiments  of  Davy  only  a  short  time  before,  and  Ritter  had 
discovered  polarization  and  1he  storage  battery. 

But,  although  many  persons  had  suspected  that  there  was  some  con- 
nection between  electricity  and  magnetism  it  was  not  until  Oersted,  in 
1820,  discovered  the  nature  of  this  connection,  and  Ampere  had  given 
the  laws  of  the  attraction  of  currents,  that  the  science  of  electro-mag- 
netism became  a  subject  of  investigation.  This  new  discovery  aroused 
the  attention  of  the  scientific  world  to  another  field  of  research,  and 
especially  awakened  in  Faraday  that  sublime  curiosity  with  respect  to  its 
laws,  which  finally  led  him  to  his  first  discovery  in  this  subject. 


640  HENRY  A.  ROWLAND 

The  new  fact  of  electro-magnetism  interested  him.  Soon  he  found 
that  the  turning  of  the  needle,  as  found  by  Oersted,  could  be  accounted 
for  by  the  attempt  of  the  north  pole  tp  revolve  around  the  wire  in  one 
direction  and  the  south  pole  in  the  other.  Not  content  with  demon- 
strating the  theory,  he  invented  some  pieces  of  apparatus  by  which 
this  revolution  could  be  realized,  and  every  collection  of  physical  appar- 
atus now  has  them.  The  little  wires  or  magnets  hanging  in  the  cups  of 
mercury  are  familiar  to  all,  and  form  the  first  notable  instance  of  a 
continuous  rotary  motion  produced  by  the  electric  current;  it  was  the 
first  form  of  electro-magnetic  motor  so  common  in  our  day.  But  we 
can  not  call  this  a  great  discovery,  as  the  principles  were  very  apparent. 

Eight  or  nine  years  now  passed  before  Faraday  gave  anything  of 
importance  to  the  world  in  the  subject  of  electricity  and  magnetism. 

Seebeck  discovered  thermo-electricity.  Ohm  discovered  the  law  con- 
necting electro-motive  force,  resistance  and  current,  and  the  whole 
scientific  world  was  alert  to  discover  new  facts.  Faraday  brooded  on 
the  subject:  the  electric  current  produced  magnetism,  why  should  not 
magnetism  produce  an  electric  current?  At  the  present  age  of  the 
world  we  could  answer  this  question  at  once,  by  aid  of  the  great  law  of 
the  conservation  of  energy.  But  fifty-seven  years  ago  it  was  unknown, 
except  in  a  very  vague  manner;  the  foreshadowing  of  this  great  law 
soon  came  into  the  mind  of  Faraday,  but  at  this  period  he  could  only 
grope  blindly  in  the  dark.  He  knew  that  a  piece  of  soft  iron  became 
magnetic  in  the  presence  of  a  magnet,  and  that  a  conductor  was  electri- 
fied by  induction  when  near  a  charged  body.  Reasoning  by  analogy, 
why  should  not  a  conducting  circuit  have  a  current  generated  in  it  in 
the  presence  of  a  wire  carrying  a  current?  This  was  Faraday's  reason- 
ing, and  he  proceeded  to  test  it  by  experiment.  Winding  two  wires 
side  by  side,  on  a  cylinder  of  wood,  he  passed  strong  currents  of  elec- 
tricity through  one  of  them,  and  attached  the  other  at  its  two  ends 
to  a  galvanometer.Kttf'he  slightest  permanent  deflection  was  observed, 
and  many  a  man  would  have  pronounced  the  experiment  a  failure. 
But  Faraday  was  not  of  that  nature;  he  tried  again  and  again,  and 
while  bending  over  the  galvanometer  in  a  vain  effort  to  see  a  slight 
permanent  deflection,  he  noticed  a  little  jerk  of  the  needle,  almost  too 
small  to  be  noticed.  His  attention  was  arrested  by  this  curious  action, 
and  he  proceeded  to  investigate  it. 

He  found  that  this  slight  movement  of  the  needle  was  in  one  direc- 
tion on  making  the  current,  and  the  opposite  direction  on  breaking  it. 
He  substituted  a  helix,  enclosing  an  unmagnetized  needle  for  the  gal- 


ELECTRICAL  AND  MAGNETIC  DISCOVERIES  OF  FARADAY        641 

vanometer,  and  he  found  that  it  was  magnetized  by  this  electrical  wave, 
at  the  moment  of  making  or  breaking  the  main  circuit. 

But  Faraday  was  not  content  until  he  had  discovered  all  the  laws 
of  this  new  action;  he  placed  two  wires  on  boards,  so  that,  when  near 
together,  they  were  parallel  to  each  other.  He  now  found  that  the 
action  took  place,  not  only  when  the  current  was  interrupted,  but  also 
when  one  wire  was  moved  with  respect  to  the  other. 

So  far,  the  new  effect  had  only  been  obtained  near  an  electric  current. 
But  Faraday  did  not  forget  the  connection  between  electricity  and 
magnetism,  but  now  proceeded  to  give  a  new  aspect  to  his  discovery. 

For  this  purpose  he  chose  a  ring  of  wrought  iron  on  which  he  wound 
two  coils  of  wire  which  he  attached  to  a  battery,  and  to  a  galvanometer, 
as  before.  From  the  presence  of  the  iron,  however,  he  obtained  an 
immensely  greater  effect  than  at  first,  so  that,  instead  of  an  almost 
microscopical  deflection,  the  needle  of  the  galvanometer  whirled  around 
three  or  four  times,  and  on  attaching  two  points  of  charcoal  to  the  ends 
of  the  secondary  wire,  he  observed  a  minute  spark  between  them  on 
completing  the  main  current.  The  same  increased  effects  occurred  on 
placing  bars  of  iron  in  straight  coils  of  wire,  and  Faraday  had  now 
proved  that  the  new  effect  was  dependent  on  the  magnetic  action  of 
the  current. 

He  now  made  one  step  further,  and  showed  that  these  induced  cur- 
rents could  be  obtained  from  permanent  magnets  without  the  aid  of 
other  currents,  by  the  simple  motion  of  a  wire  near  a  magnet,  and  that 
they  were  specially  intense  when  the  wire  was  wound  on  a  soft  iron 
cylinder,  which  was  then  moved  near  the  poles  of  a  magnet.  Not  con- 
tent with  observing  these  currents  by  a  galvanometer,  he  obtained  a 
powerful  permanent  magnet  and  allowed  his  bar  of  iron,  wound  with  the 
coil,  to  come  in  contact  with  the  poles,  the  circuit  being  broken  at  the 
same  instant.  A  spark  was  observed  at  this  broken  junction  every  time 
the  bar  came  down  on  the  poles.  Tyndall  tells  a  very  curious  story  of 
this  experiment  which  we  can  well  recall.  Faraday  was  attending  a 
meeting  of  the  British  Association  in  Oxford,  in  1832,  and  was  re- 
quested to  show  some  of  his  wonderful  results  to  the  scientists  there 
gathered.  While  he  was  thus  occupied  a  dignitary  of  the  University 
entered  and  inquired  what  was  going  on.  Prof.  Daniell,  who  was 
standing  near,  explained  the  matter  in  popular  language.  The  Dean 
listened  with  attention,  and  looked  earnestly  at  the  brilliant  spark,  but 
a  moment  afterwards  he  assumed  a  serious  countenance,  and  shook  his 
head:  "  I  am  sorry  for  it,"  said  he,  as  he  walked  away;  "  I  am  sorry  for 
41 


642  HENRY  A.  KOWLAND 

it;  indeed  I  am  sorry  for  it;  it  is  putting  new  arms  into  the  hands  of  the 
incendiary."  This  occurred  a  short  time  after  the  papers  had  been 
filled  with  the  doings  of  the  hayrick  burners. 

Now,  after  more  than  fifty  years,  the  spark  of  Faraday  blazes  at  every 
street  corner,  but  it  has  never  been  found  more  efficient  than  an  ordinary 
lucifer  match  in  the  burning  of  hayricks. 

Faraday's  attention  was  now  called  to  the  explanation  of  a  curious 
action  discovered  by  Arago,  who  found  that  a  rotating  disk  of  copper 
carried  a  magnetic  needle  with  it  when  the  latter  was  suspended  over 
it.  The  explanation  had  never  been  obtained,  but  Faraday  now  saw 
that  it  was  but  an  instance  of  his  newly  discovered  action.  In  order 
to  show  that  currents  were  induced  in  the  revolving  plate,  he  mounted 
it  between  the  poles  of  a  magnet  and  connected  the  centre  with  one 
pole  of  a  galvanometer;  on  pressing  a  wire  from  the  other  pole  to  the 
edge,  Faraday  obtained  a  continuous  current  of  electricity.  This  was 
the  first  continuous  current  dynamo  ever  constructed. 

But  he  rested  not  until  he  had  obtained  the  laws  of  induced  currents 
and  expressed  them  in  such  simple  language  that  they  have  ever  since 
been  the  admiration  of  the  scientific  world. 

In  giving  the  law  of  the  production  of  these  induced  currents,  Fara- 
day for  the  first  time  made  use  of  his  famous  "  lines  of  force,"  although 
he  here  calls  them  magnetic  curves. 

He  showed  that  a  wire  must  cut  these  lines  in  order  to  have  a  current 
induced  in  it.  In  order  to  account  for  the  induction  in  neighboring 
wires  on  making  and  breaking  an  electric  current,  he  pictured  in  his 
mind  the  lines  of  force  moving.  The  current  could  only  start  gradually 
after  contact  was  made,  and  while  it  was  increasing  the  lines  of  force 
always  closed  on  themselves  in  rings,  were  expanding  outwards  cutting 
any  wires  near  it,  and  inducing  currents  in  them.  When  the  current 
was  broken,  the  lines  contracted  and  produced  contrary  induced  cur- 
rents. 

In  after  years  he  made  his  law  quantitative,  and  proved  that  the 
integral  induced  current  was  in  proportion  to  the  number  of  lines  of 
force  cut  by  the  wire. 

In  his  papers  of  1831-2  I  find  these  lines  always  called  magnetic 
curves,  and  his  laws  of  induced  currents  are  given  in  terms  of  these 
curves.  This  idea  of  lines  of  force  was  ever  after  one  of  the  principal 
points  around  which  the  mind  of  Faraday  revolved.  He  applied  it  to 
electrical  action  as  well  as  to  magnetic,  and  we  see  him  in  after  years 
striving  to  do  away  with  action  at  a  distance,  and  substitute  for  it  a 
medium  filled  with  these  lines  of  force. 


ELECTRICAL  AND  MAGNETIC  DISCOVERIES  OF  FARADAY        643 

The  medium  subjected  to  electrical  or  magnetic  forces  is,  according 
to  Faraday's  idea,  polarized  in  the  direction  of  these  lines  of  force,  so 
that  each  particle  only  has  to  act  upon  the  one  next  to  it  in  order  that 
the  force  may  be  transmitted  to  any  distance.  In  Faraday's  mind  these 
lines  had  not  only  an  imaginary  existence  as  being  the  direction  in 
which  the  north  pole  of  a  needle  or  an  electrified  particle  tended  to 
move  in  space,  but  also  a  real  existence.  He  imagined  them  as  elastic 
bands  repelling  each  other  laterally,  and  binding  the  north  and  south 
poles  of  a  magnet,  or  the  positive  and  negative  electricities,  together. 

It  was  only  in  after  years  that  he  discovered  all  the  properties  of  these 
lines,  and  I  shall  therefore  return  to  them  again. 

Guided  by  these  lines  of  force,  he  investigated  the  subject  of  in- 
duced electric  currents  in  so  complete  a  manner  that  nothing  of  funda- 
mental importance  has  ever  been  added  to  the  subject.  True,  to-day 
we  understand  the  subject  much  better  than  Faraday  ever  did.  The 
mathematical  researches  of  Helmholtz,  Thomson,  Maxwell  and  others 
have  thrown  a  flood  of  light  upon  the  induction  of  electric  currents, 
and  the  law  of  the  conservation  of  energy  gives  us  means  of  proving  all 
its  laws,  and  indeed  of  showing  that  magneto-electric  induction  is  the 
consequence  of  the  magnetic  action  of  the  current  as  discovered  by 
Oersted. 

But  fifty  years  ago  this  law  of  the  conservation  of  energy  was  too 
little  known  to  be  used  in  this  way.  It  required  the  support  of  just 
such  experiments  as  those  of  Faraday  to  bring  into  existence  and  to 
prove  it.  Hence,  Faraday  had  but  little  to  guide  him  to  the  discovery, 
except  that  subtle  reasoning  of  a  man  of  genius  which  almost  amounts 
to  instinct. 

The  difference  of  common  and  voltaic  electricity  next  engaged  his 
attention.  A  Leyden  jar  highly  charged  might  have  large  sparks  and  a 
loud  sound;  it  might  ignite  alcohol  and  produce  a  strong  shock  when 
passed  through  the  human  body,  but  it  was  almost  incapable  of  decom- 
posing water,  and  could  scarcely  affect  a  magnetic  needle.  The  voltaic 
battery,  on  the  other  hand,  could  produce  the  latter  effects,  but  not  the 
former. 

How  did  these  two  kinds  of  electricity  differ? 

Faraday  answered  this  by  producing  all  the  effects  with  one  kind  of 
electricity  that  could  be  obtained  from  the  other.  He  showed  that  the 
difference  was  caused  by  there  being  great  tension,  or,  as  we  call  it, 
potential  in  one  case,  with  very  little  quantity,  while  in  the  other  there 
was  great  quantity  with  low  tension.  By  charging  Leyden  jar  batteries 


644  HENRY  A.  ROWLAND 

of  different  sizes  with  the  same  number  of  turns  of  his  machine,  and 
discharging  them  through  a  galvanometer,  he  proved  that  the  sudden 
deflection  of  the  instrument  depended  on  the  quantity,  and  not  the 
tension,  of  the  electricity.  He  then  arranged  a  little  voltaic  hattery  out 
of  zinc  and  platinum  wires,  so  that,  when  joined  to  the  galvanometer  for 
three  seconds,  it  gave  the  same  swing  to  the  needle  as  the  Leyden  jar 
battery  charged  with  thirty  turns  of  his  machine.  By  this  means  he 
was  able  to  estimate  that  a  small  battery  which  decomposed  a  grain  of 
water,  furnished  as  much  electricity  as  800,000  discharges  of  his  large 
Leyden  battery,  and  would  form  a  powerful  stroke  of  lightning,  if  dis- 
charged at  once. 

The  investigation  gives  us  the  first  rough  idea  of  the  magnitude  of  the 
quantities  involved  in  frictional  and  voltaic  electricity,  and  it  may  be 
considered  as  the  first  rough  approximation  to  the  ratio  of  the  electro- 
magnetic to  the  electrostatic  units  of  electricity. 

But  Faraday  was  a  chemist.  His  associations  with  Davy  had  made 
him  familiar  from  the  first  with  the  chemical  action  of  the  battery,  and 
it  is  but  natural  that  his  attention  should  be  directed  to  its  investiga- 
tion. In  the  progress  of  these  researches  he  noted  the  curious  fact  that 
all  bodies  which  could  be  decomposed  by  electricity  when  a  fluid,  could 
neither  conduct  the  current  nor  be  decomposed  by  it  when  they  were 
solidified  by  the  cold.  The  conduction  and  decomposition  went  to- 
gether. Rising  from  this  to  a  general  law,  he  finally  proved,  by  im- ' 
mense  labor,  that,  for  a  given  quantity  of  electricity,  whatever  the  de- 
composing conductor  may  be,  the  amount  of  chemical  action  is  the 
same.  The  current,  the  size  of  the  electrodes  and  the  strength  of  the 
solution  might  vary,  but  the  amount  decomposed  by  a  given  quantity  of 
electricity  remained  the  same.  Furthermore,  the  amount  of  different 
substances  separated  was  in  proportion  to  their  chemical  equivalents. 
Hence,  the  voltameter  for  measuring  the  electric  currents  which,  in 
the  form  of  the  silver  voltameter,  is  to-day  one  of  our  most  accurate  in- 
struments. 

As  I  have  mentioned  before,  the  leading  idea  in  Faraday's  mind  was 
the  replacing  of  all  action  at  a  distance  by  curved  lines  of  force  which 
had  a  definite  physical  existence.  So,  in  attacking  this  subject  of  elec- 
trolysis, he  very  quickly  showed  that  Davy's  idea  that  the  poles  sepa- 
rated an  electrolyte,  by  actually  attracting  its  components,  was  false, 
and  that  the  theory,  according  to  which  decomposition  and  reeompo- 
sition  took  place  throughout  the  whole  course  of  the  current  in  the  elec- 
trolyte, was  correct. 


ELECTRICAL  AND  MAGNETIC  DISCOVERIES  OF  FARADAY        645 

Faraday  now  took  up  an  analogous  subject — the  source  of  the  elec- 
tricity in  the  voltaic  battery.  He  showed  that  the  current  from  the 
battery  was  proportional  to  the  amount  of  zinc  dissolved,  and  that  the 
direction  of  the  current  depended  on  the  direction  of  the  chomical 
action. 

The  theory  of  Volta,  that  the  contact  of  two  metals  was  the  source  of 
electricity,  was  thus  effectually  disposed  of,  so  that  even  the  recent  at- 
tempt to  revive  that  ancient  theory  could  only  have  met  with  the  disas- 
ter which  befell  it. 

It  is  impossible  for  me,  in  a  few  minutes,  to  give  account  of  all  that 
Faraday  did  on  these  subjects  of  electrolysis  and  the  theory  of  the  voltaic 
battery.  His  work  is  a  perfect  mine  of  results — not  haphazard  and  dis- 
connected, but  each  designed  to  elucidate  some  point  in  theory  or  dem- 
onstrate some  law,  and  his  name  must  forever  be  associated  with  this 
subject.  His  law  of  the  definite  chemical  action  of  the  current  will 
always  form  an  enduring  monument  to  his  fame. 

Every  discovery  that  Faraday  made  only  served  as  a  guide  to  him  in 
making  fresh  ones. 

We  have  seen  that  Faraday  found  that  when  an  electrolyte  was  in  the 
solid  state  it  no  longer  conducted  the  current.  To  most  observers  this 
would  only  have  been  an  interesting,  but  disconnected,  fact.  But  the 
far-sighted  mind  of  Faraday  perceived  in  this  an  explanation  of  no  less 
a  subject  than  that  of  electric  induction.  As  in  the  electrolyte,  he  con- 
ceived the  particles  to  be  arranged  in  certain  directions,  decomposing 
and  recomposing  along  lines  in  the  direction  of  the  electric  currents,  so 
in  the  solidified  electrolyte  there  was  some  arrangement  along  the  lines 
in  which  the  current  wished  to  pass,  that  is,  of  electric  force.  Hence  his 
theory  of  the  nature  of  electric  induction  and  of  electric  force.  It  was 
not  action  at  a  distance,  but  the  action  of  contiguous  particles  on  each 
other.  As  in  magnetism,  so  in  electricity,  the  action  was  carried  to  a 
distance  by  a  medium. 

Not  content  with  merely  giving  the  theory,  he  proceeded  to  prove 
it.  If  it  were  true,  then  the  nature  of  the  medium  should  affect  the 
amount  of  the  induction.  We  all  know  his  beautiful  apparatus  for  test- 
ing this — the  two  globular  Leyden  jars  which  could  be  filled  with 
air,  glass,  oil  of  turpentine,  gases,  etc.,  how  he  divided  the  charge  of 
one  between  the  two  and  measured  it  on  a  Coulomb  electrometer,  and 
thus  discovered  that  his  inference  was  correct,  that  each  substance  had 
a  specific  inductive  capacity,  and  that  the  charge  of  a  condenser  de- 
pended not  only  on  the  area  of  the  surface  and  the  thickness  of  the 


646  HENRY  A.  ROWLAND 

dielectric,  but  also  on  the  nature  of  the  latter,  air  or  vacuum  producing 
the  least  condensing  effect,  and  glass,  sulphur,  etc.,  a  greater  one. 

To  complete  his  mental  vision  of  an  electrified  system,  it  was  neces- 
sary for  him  to  test  in  a  very  complete  manner  the  idea  that  positive 
and  negative  electricities  are  generated  in  equal  quantities.  To  accom- 
plish this,  he  erected  a  room  of  twelve  feet  on  a  side  out  of  a  frame- 
work covered  with  tinfoil,  and  the  whole  insulated.  By  generating 
electricity  inside  of  it,  he  was  able  to  prove  in  a  more  complete  manner 
than  had  been  done  before  that  we  never  generate  positive  electricity  or 
negative  electricity  by  itself,  but  always  in  equal  quantities  together. 
Every  complete  electrostatic  system  contains  equal  quantities  of  posi- 
tive and  negative  electricity,  which  are  separated  by  a  dielectric,  through 
which  they  are  connected  by  the  lines  of  electric  induction,  whose  ten- 
sion produced  electric  attraction. 

To-day,  when  the  mathematics  of  Maxwell  have  added  clearness  to  the 
subject,  we  see  every  electrostatic  system  made  up  of  minute  and  equal 
portions  of  positive  and  negative  electricity,  connected  together  by 
tubes  of  induction  as  by  elastic  bands,  these  tubes  repelling  each  other 
laterally,  so  as  to  be  held  in  position,  we  know  that  the  attraction  of  all 
electrified  bodies  is  accounted  for  by  such  a  system,  which  was  roughly 
conceived  by  Faraday,  but  in  which  the  positions  and  form  of  every  lino 
can  now  be  calculated. 

It  is  impossible,  on  the  present  occasion,  to  follow  Faraday  through 
all  his  researches  on  the  different  forms  of  electric  discharge,  and  his 
continued  researches  on  electrolysis;  but  I  will  pass  immediately  to  two 
of  his  greatest  discoveries,  the  action  of  magnetism  on  light  and  diamag- 
netism.  In  his  researches  on  optical  glass  he  had  discovered  a  variety  of 
heavy  glass,  called  silicated  borate  of  lead.  On  placing  this  between 
the  poles  of  a  magnet,  and  looking  through  it  along  the  lines  of  force, 
he  found  that  the  plane  of  polarization  was  rotated. 

Using  other  substances,  he  found  that  most  of  them  had  some  effect 
of  this  kind  in  the  magnetic  field.  The  laws  of  the  magnetic  rotation 
he  found  very  different  from  those  of  the  ordinary  rotation  of  turpen- 
tine or  sugar,  and  altogether  it  forms  a  most  interesting  and  important 
experiment  when  considering  the  theory  of  magnetism. 

Not  content  with  discovering  this  law  with  his  piece  of  optical  glass, 
he  now  sought  to  discover  whether  there  was  any  force  of  attraction 
or  repulsion  between  it  and  the  magnet.  Hanging  it  up  between  the 
poles,  he  discovered  that  as  iron  was  attracted  by  a  magnet,  so  the  heavy 
glass  was  repelled.  He  called  this  property  diamagnetism,  and  showed 


ELECTKICAL  AND  MAGNETIC  DISCOVERIES  OF  FARADAY        647 

that  all  bodies  were  acted  upon  by  magnetism  and  could  be  classified  as 
magnetic  or  diamagnetic.  Magnetism  now  had  a  universal  significance 
as  applying  to  all  bodies.  It  was  universal  in  its  action,  and  all  bodies 
responded  to  it  to  some  extent  at  least.  Even  gases  were  acted  on  by  it, 
and  the  oxygen  of  the  air  was  found  quite  strongly  magnetic. 

Quickly  his  mind  seized  another  idea.  , 

As  the  intense  magnetism  of  iron,  nickel  and  cobalt  was  destroyed  by 
heat,  might  it  not  b€  possible  that  all  bodies  should  become  magnetic 
when  cold?  He  carefully  tried  the  experiment,  but  never  was  able  to 
find  any  effect  with  the  means  of  producing  cold  at  his  command. 

In  reading  Faraday's  papers  we  are  surprised  at  the  clearness  with 
which  his  laws  are  expressed.  Although  he  naturally  wished  to  bring 
his  lines  of  force  into  use  in  this  case  of  diamagnetism,  yet  we  now  find 
him  making  no  use  of  them.  His  law  says  that  magnetic  substances  in 
the  field  of  a  magnet  tend  to  the  stronger  part  of  the  field,  and  the  dia- 
magnetic to  the  weaker,  irrespective  of  the  direction  of  the  lines  of 
force. 

Bismuth  he  found  the  most  strongly  diamagnetic  of  all  bodies.  In 
using  a  crystal  of  this  substance  instead  of  a  bar,  he  found  that  it 
would  set  itself  in  a  magnetic  field,  even  if  this  was  uniform.  On  using 
other  substances  he  proved  the  general  law  that  all  crystals  possessed 
this  property  and  he  called  it  magne-crystallic  force. 

The  researches  on  diamagnetism  and  magne-crystallic  force  occupied 
Faraday's  time  for  five  years,  from  1845  to  1850,  and  he  was  now  in  the 
sixtieth  year  of  his  age.  No  more  great  discoveries  fell  to  his  lot,  but 
his  mind  turned  more  and  more  to  brooding  over  the  consequences  of 
his  past  discoveries  and  following  out  their  results. 

The  idea  of  lines  of  force  was  still  on  his  mind,  and  the  discovery  of 
diamagnetism  had  now  given  him  a  further  insight  into  their  nature. 
He  saw  that  the  magnetic  and  diamagnetic  nature  of  bodies  could  be 
explained  by  considering  them  as  good  or  bad  conductors  of  these  lines 
of  force.  Iron  was  a  good  conductor  and  bismuth  a  bad  one.  When 
soft  iron  was  placed  in  a  magnetic  field,  the  lines  of  force,  or,  as  we  now 
more  exactly  term  them,  the  lines  of  induction,  were  more  easily  con- 
ducted by  it  than  by  the  air,  and  they  were  deflected  toward  and  through 
it;  but  a  piece  of  bismuth  was  a  poorer  conductor  and  these  lines  of 
force  tended  to  pass  around  it  rather  than  through  it.  By  surrounding 
a  weak  magnetic  body  by  a  strong  magnetic  fluid  he  found  that  it  pos- 
sessed all  the  properties  of  a  diamagnetic  one.  Pursuing  the  subject, 
he  showed  how  the  lines  of  induction  were  distributed  around  and  within 


648  HENRY  A.  KOWLAND 

a  magnet,  and  how  we  are  able  to  measure  them  by  the  induced  current 
in  moving  wires.  The  method  of  exploring  the  magnetic  field  is  the  only 
exact  method  which  has  ever  been  devised  for  use  in  such  cases  as  the 
field  of  modern  dynamo-electric  machines,  or  in  most  of  the  problems 
of  modern  electrical  engineering.  He  also  proved  that  the  lines  of  in- 
duction are  always  closed  circuits,  whether  they  are  due  to  permanent 
magnets  or  electric  currents,  thus  forever  destroying  our  hope  of  obtain- 
ing a  continuous  current  by  induction  without  the  use  of  a  commutator. 

When  a  soft  iron  bar  was  approached  to  the  magnet,  it  drew  the  lines 
in  upon  itself;  they  proceeded  down  the  bar  until  they  were  forced  into 
the  badly  conducting  air  and  the  number  which  went  further  down  the 
bar  to  those  which  passed  out  into  the  air  at  any  point  was  in  proportion 
to  the  conductivity  of  the  two.  A  steel  magnet  was,  in  his  eyes,  like  a 
voltaic  pile  in  water.  As  the  current  of  electricity  was  forced  forward 
by  the  electromotive  force  of  the  pile  and  diffused  itself  in  currents 
through  the  water,  so  the  lines  of  magnetic  induction  were  formed  by 
the  coercive  power  of  the  steel.  It  is  now  known  to  be  a  fact  that  the 
distribution  of  magnetism  on  a  steel  magnet,  or  indeed  in  any  case,  can 
be  calculated  by  these  principles  Faraday  laid  down.  The  idea  of  a  mag- 
netic circuit  is  familiar  now  to  all  electrical  engineers. 

To  Faraday's  eye,  a  magnet  not  only  consisted  of  a  piece  of  steel  or 
loadstone  which  is  apparent  to  our  ordinary  vision,  but  included  all  the 
space  around  which  was  filled  with  lines  of  force;  it  was  bounded  only  by 
the  limits  of  the  universe.  The  steel  served  merely  to  bind  together 
the  ring-like  lines  of  induction  which  passed  from  the  magnet  to  every 
point  of  space. 

Faraday  was  not  a  mathematician,  and  could  not  thus  follow  out  the 
consequences  of  his  great  ideas.  This  has  been  done  for  him  by  the  im- 
mortal Maxwell.  He  has  taken  up  the  idea  that  electrical  and  mag- 
netic forces  only  proceed  to  a  distance  by  aid  of  the  intervening  particles 
of  matter,  or  ether,  as  the  case  may  be,  and  has  given  it  a  mathematical 
basis. 

To-day  a  body  charged  with  electricity,  a  magnet  or  a  wire  carrying 
an  electrical  current,  all  are  incomplete  without  the  space  around  them. 

When  we  attach  a  battery  to  a  wire  and  the  current  apparently  flows 
through  it  as  if  it  were  a  current  of  water,  Faraday's  idea  shows  us  that 
we  are  only  looking  at  the  matter  superficially;  around  that  wire  and 
permeating  space  in  every  part  are  lines  of  magnetic  force,  and  lines  of 
electrostatic  force.  At  the  moment  of  joining  the  battery  to  the  wire 
this  whole  complicated  system  of  lines  of  force  must  be  formed.  At  the 


ELECTRICAL  AXD  MAGNETIC  DISCOVERIES  OF  FARADAY       649 

moment  of  breaking  circuit,  the  system  must  vanish,  and  we  obtain  the 
energy  stored  up  in  this  space  surrounding  the  wire  in  the  bright  spark 
known  as  the  extra  current. 

What  a  flood  of  light  this  throws  on  many  experiments  such  as  those 
of  Wheatstone,  on  the  velocity  of  electricity.  With  his  wire  arranged 
in  parallel  loops  around  an  ordinary  room,  he  discharged  a  Leyden  jar 
through  it,  and  assumed  that  the  electricity  passed  through  the  whole 
wire  before  a  spark  could  form  at  the  distant  end.  But  we  know  that 
whole  room  was  instantly  filled  with  moving  lines  of  magnetic  force, 
which  induced  currents  in  every  wire  they  crossed,  and  hence  what 
Wheatstone  measured  was  merely  the  current  induced  from  one  wire 
or  those  near  it. 

Thomson  and  Maxwell  have  shown  that  the  medium  around  a  wire 
carrying  an  electric  current  is  in  motion,  and  that  the  vortex  filaments 
form  Faraday's  lines  of  magnetic  force;  for  Faraday's  discovery  of  the 
magnetic  rotation  of  the  plane  of  polarization  of  light  can  be  explained 
in  no  other  way. 

Thus  the  discoveries  of  Faraday  have  been  engrafted  on  our  science, 
and  form  one  of  its  most  essential  features.  They  are  among  the  foun- 
dation stones  of  the  edifice  of  our  science. 

We  know  far  more  than  the  electricians  of  that  day,  in  the  details  of 
the  subject,  and  mathematics  has  given  us  a  broad  view  of  electricity 
and  magnetism,  such  as  never  before  was  obtained.  In  its  practical  use 
and  measurement  we  have  made  immense  strides  in  devising  methods 
and  instruments,  and  we  now  carry  out  our  experiments  on  a  scale  which 
Faraday  could  not  attempt,  seeing  that  subject,  which  has  hitherto  been 
best  adapted  to  the  contemplation  of  a  few  philosophers,  has  become 
of  use  to  all,  and  electricity  bids  fair  to  become  our  most  important 
servant. 

The  spark,  which  Faraday  more  than  fifty  years  ago  observed  in  a 
darkened  room,  now  blazes  out  almost  with  the  power  of  the  sun,  but  it 
is  still  the  spark  of  Faraday.  Though  it  is  a  thousand  times  as  large,  it 
is  still  made  on  the  principles  which  Faraday  laid  down,  and  nothing 
except  mechanical  details  has  ever  been  added  to  its  process. 

How  suitable,  then,  that  we  should  remember  his  name  on  this 
occasion,  since  his  discoveries  have  served  as  the  basis  of  all  progress 
in  electrical  engineering.  Had  Faraday  not  lived  we  should  not  have 
been  here  to-night.  True,  as  I  have  shown  before,  the  progress  of  science 
could  only  have  been  delayed  by  the  absence  of  any  one  man,  but  how 
long,  in  this  case,  we  cannot  tell.  We  can  only  receive  with  gratitude 


650  HENRY  A.  ROWLAND 

what  Faraday  has  given  freely  to  us,  and  speak  his  name  with  the  rever- 
ence due,  not  only  to  his  intellectual  eminence,  but  to  his  character. 
Too  noble  to  leave  science  for  the  wealth  held  out  to  him,  he  persevered 
in  it  to  the  end,  and  gave  to  the  world  the  fruits  of  his  labor  in  his 
'  Experimental  Researches  in  Electricity.' 

He  never  obtained  from  the  world  the  material  reward  for  his  labor, 
but  died  a  poor  man,  who  had  enriched  the  world. 

We  stand  at  an  important  epoch  in  the  history  of  our  science.  We 
have  gone  far  enough  into  its  practical  applications  to  see  some  dis- 
tance into  the  future.  The  arc  light,  which  Davy  brought  into  promi- 
nence at  the  beginning  of  this  century,  fed  by  the  machines  of  Faraday, 
blazes  throughout  the  night  in  all  cities  of  the  world.  The  incandescent 
light,  known  long  to  scientists,  has  been  improved  and  bids  fair  to  rival 
gas  in  cheapness,  as  it  surpasses  it  in  beauty.  The  secondary  battery 
discovered  by  Ritter  eighty  years  or  more  ago,  improved  by  Plante  and 
Faure  in  recent  times,  still  struggles  to  fill  the  place  assigned  to  it,  to  be 
replaced  by  one  before  long  which  shall  not  waste  fifty  per  cent  of  the 
power  given  to  it,  and  weigh  tons  for  a  few  foot-pounds  of  energy  stored 
up.  We  see  it  in  its  new  form  replacing  the  laboring  horses  in  the 
streets,  and  serving  in  many  cases  where  small  power  is  needed.  But  the 
transmission  of  energy  seems  to  me  to  open  one  of  the  widest  fields,  and 
the  time  is  not  very  distant  when  a  few  large  engines  will  replace  the 
numerous  small  ones  in  our  cities;  when  also  the  power  of  waterfalls  may 
be  made  available  at  a  distance. 

The  principle  of  the  telephone  also  is  destined  to  bear  unseen  fruit. 

There  is  work  for  all,  the  practical  and  theoretical  man  alike. 

The  philosopher,  studying  the  problems  of  the  universe,  deems  himself 
rewarded  by  some  new  fact  discovered,  some  new  law  demonstrated.  To 
him  the  universe  is  a  problem  to  solve,  and  his  motto  is,  "  Science  is 
knowledge." 

He  sees  before  him  the  time  when  man's  insight  into  nature  shall  be 
vastly  increased,  and  esteems  the  science  of  to-day  as  but  an  atom  to 
what  we  shall  know  in  the  future.  While  not  despising  the  wealth,  he 
seldom  has  time  for  its  accumulation,  as  he  considers  other  things  of 
vastly  more  importance;  the  truth  is  what  he  seeks;  the  truth  as  to  this 
wonderful  universe  in  which  we  live.  What  is  matter?  what  is  electric- 
ity, what  is  the  medium  which  transmits  light  from  one  point  to  an- 
other, how  comes  it  that  the  earth,  is  magnetic?  These  are  some  of  the 
problems  he  is  trying  to  solve.  He  knows  that  one  man  can  do  but  little 
toward  it,  even  though  he  should  surpass  what  Faraday  has  done,  but 


ELECTRICAL  AND  MAGNETIC  DISCOVERIES  OF  FARADAY        651 

he  trusts  to  the  combined  efforts  of  mankind,  shown  in  the  steady  prog- 
ress of  science,  to  finally  arrive  at  a  solution. 

The  devotee  of  applied  science,  the  so-called  practical  man,  looks 
upon  the  forces  of  nature  as  his  servants,  and  strives  to  become  their 
master.  The  world  must  move,  its  work  must  be  accomplished.  We 
are  not  satisfied  to  live  as  our  fathers  have  done,  and  we  must  have 
luxuries  unknown  to  them.  Our  thoughts  must  fly  to  the  farthest  parts 
of  the  earth  in  an  instant,  at  our  bidding,  and  we  must  pass  from  point 
to  point  on  the  wings  of  the  wind,  for  flesh  and  blood  is  too  slow  for  us. 
To  accomplish  this,  the  engineer  harnesses  the  forces  of  nature  and 
compels  them  to  work  for  him.  He  takes  the  discoveries  of  the  phil- 
osopher and  uses  them  for  the  practical  needs  of  daily  life.  His  motto 
is,  "  Science  is  power."  As  he  ministers  more  directly  to  the  present 
generation  of  mankind  than  to  the  generations  to  come,  as  does  the  phil- 
osopher, so  he  often  reaps  his  reward  in  the  present,  and  retains  some 
of  that  wealth  which  his  inventions  bring  into  the  world.  For  the 
source  of  the  wealth  of  the  world  is  labor,  and  the  labor  of  the  forces 
of  nature,  in  our  behalf,  surpasses  very  many  fold  that  of  human  flesh 
and  blood.  He  who  adds  but  the  slightest  to  our  power  over  these 
forces  enriches  the  world,  and  is  entitled  to  its  practical,  as  well  as  its 
sentimental  gratitude,  be  he  philosopher  or  engineer.  The  great  ques- 
tion which  we  should  ask  ourselves  is  how  our  science  can  best  be  fur- 
thered. The  philosopher  must  precede  the  engineer.  To  have  the  ap- 
plications of  electricity,  there  must  be  a  science  of  electricity.  This 
science  cannot  depend  for  its  existence  on  practical  men  whose  minds 
are  engrossed  with  other  than  theoretical  problems.  It  nuist  exist  in 
minds  like  Faraday,  which  are  specially  adapted  to  its  reception  and 
advancement — men  who  are  willing  to  devote  their  lives  to  it,  and  who 
have  the  ability  to  further  it.  We  cannot  create  such  men,  but  we  can 
give  them  our  practical  as  well  as  our  sentimental  sympathy,  when 
found.  The  philosopher  is  made  of  flesh  and  blood  as  well  as  other 
men.  He  must  live  and  have  his  tastes  gratified  as  well  as  others. 
His  place  in  the  world  as  at  present  constituted  is  usually  that  of  a  pro- 
fessor in  our  universities  and  colleges.  Are  only  men  like  Faraday 
chosen  for  these  positions?  Of  the  four  hundred  or  more,  how  many 
choose  their  professors  on  account  of  their  eminence  in  theoretical 
science?  Are  there  a  dozen?  I  doubt  it.  Furthermore,  what  facilities 
and  encouragement  would  they  have  in  these  institutions  to  do  work? 
Too  far  away  from  each  other  to  be  a  mutual  help,  they  have  but  an 
incomplete  scientific  life.  Faraday  could  not  have  been  himself  in 


652  HEXEY  A.  ROWLAND 

Africa  and  would  have  languished  in  our  own  country.  In  London,  in 
contact  with  the  science  of  Europe  and  encouraged  by  its  atmosphere, 
with  the  Royal  Society  at  which  to  announce  his  discoveries  and  the 
Royal  Institution  in  which  to  make  them,  Faraday,  in  spite  of  poor 
education,  was  stimulated  to  his  best  efforts.  Alone  in  one  of  our  iso- 
lated colleges,  cut  off  from  intercourse  with  the  rest  of  the  world  by  a 
so-called  protective  duty  on  his  very  life,  books,  with  no  journal  spe- 
cially devoted  to  theoretic  physics,  and  no  society  like  the  Royal  Society, 
who  can  say  whether  his  discoveries  would  have  been  made  or  not?  The 
endowment  of  research  seems  to  me  to  offer  the  best  means  out  of  the 
difficulty.  Let  professorships  be  endowed  and  funds  to  pay  the  expenses 
of  apparatus  and  assistants  be  formed  in  our  universities,  with  the  under- 
standing that  the  research  is  to  be  the  principal  work;  work,  while  teach- 
ing is  not  to  be  neglected.  The  result  will  be  the  formation  of  a  scien- 
tific atmosphere  in  which  men  like  Faraday  can  live  and  labor,  and  the 
dry  bones  of  the  pedagogue  be  replaced  by  the  fire  and  life  of  the  orig- 
inal investigator.  And  let  not  practical  science  be  neglected.  Let  us 
have  scientific  schools  of  the  highest  grade,  where  modern  science  is 
taught,  so  that  fifty  years  shall  not  again  pass,  as  it  has  done,  before  a 
discovery  like  that  of  Faraday  is  utilized. 

Furthermore,  let  us  have  scientific  societies  and  clubs  like  the  pres- 
ent, where  men  of  like  tastes  can  meet  and  interchange  ideas. 

Thus  we  meet  together  to-night,  electricians  all,  practical  and  theo- 
retical, at  a  time  in  the  history  of  our  science  and  of  the  world  which 
will  in  future  be  called  the  beginning  of  the  age  of  electricity. 

The  feeble  attraction  of  the  amber  has  become  a  mighty  force,  which 
is  destined  to  make  itself  felt,  and  it  is  to  be  hoped  that  our  mutual  in- 
tercourse in  this  Club  may  aid  us  all  in  our  efforts  to  make  an  impress 
on  its  future  history. 


ADDRESS  BEFORE  THE  AMERICAN  INSTITUTE  OF  ELECTRICAL  ENGINEERS, 
NEW  YORK,  MAY  22,   1889 

[Transactions  of  the  American  Institute  of  Electrical  Engineers,  VI,  342-357,  1889] 

As,  a  short  time  since,  I  stood  in  a  library  of  scientific  books  and 
glanced  around  me  at  the  works  of  the  great  masters  in  physics,  my  mind 
wandered  back  to  the  time  when  the  apparatus  for  a  complete  course 
of  lectures  on  the  subject  of  electricity  consisted  of  a  piece  of  amber 
and  a  few  light  bodies  to  be  attracted  by  it.  From  that  time  until 
now,  when  we  stand  in  a  magnificent  laboratory  with  elaborate  and 
costly  apparatus  in  great  part  devoted  to  its  study,  how  greatly  has  the 
world  changed  and  how  our  science  of  electricity  has  expanded  both  in 
theory  and  practice  until,  in  the  one  case,  it  threatens  to  include  within 
itself  nearly  the  whole  of  physics,  and  in  the  other  to  make  this  the  age 
of  electricity. 

Were  I  to  trace  the  history  of  the  views  of  physicists  with  respect 
to  electric  currents  it  would  include  the  whole  history  of  electricity. 
The  date  when  the  conception  of  an  electric  current  was  possible  was 
when  Stephen  Gray,  about  170  years  ago,  first  divided  bodies  into  con- 
ductors and  non-conductors,  and  showed  that  the  first  possessed  the 
property  of  transmitting  electrical  attractions  to  a  distance.  But  it 
was  only  when  the  Leyden  jar  was  discovered  that  the  idea  of  a  current 
became  very  definite.  The  notion  that  electricity  was  a  subtle  fluid 
which  could  flow  along  metal  wires  as  water  flows  along  a  tube,  was 
then  prevalent,  and,  indeed,  remains  in  force  to-day  among  all  ex- 
cept the  leaders  in  scientific  thought.  It  is  not  my  intention  to  depre- 
ciate this  notion,  which  has  served  and  still  serves  a  very  important  pur- 
pose in  science.  But,  for  many  years,  it  has  been  recognized  that  it  in- 
cludes only  a  very  small  portion  of  the  truth  and  that  the  mechanism  by 
which  energy  is  transmitted  from  one  point  of  space  to  another  by  means 
of  an  electric  current  is  a  very  complicated  one. 

Here  for  instance,  on  the  table  before  me  are  two  rubber  tubes  filled 
with  water,  in  one  of  which  the  water  is  in  motion,  in  the  other  at  rest. 
It  is  impossible,  by  any  means  now  known  to  us,  to  find  out,  without 
moving  the  tubes,  which  one  has  the  current  of  water  flowing  in  it  and 


654  HENRY  A.  EOWLAND 

which  has  the  water  at  rest.  Again,  I  have  here  two  wires,  alike  in  all 
respects,  except  that  one  has  a  current  of  electricity  flowing  in  it  and 
the  other  has  not.  But  in  this  case  I  have  only  to  bring  a  magnetic 
needle  near  the  two  to  find  out  in  which  one  the  current  is  flowing.  On 
our  ordinary  sense  the  passage  of  the  current  has  little  effect;  the  air 
around  it  does  not  turn  green  or  the  wire  change  in  appearance.  But 
we  have  only  to  change  our  medium  from  air  to  one  containing  magnetic 
particles  to  perceive  the  commotion  which  the  presence  of  a  current 
may  cause.  Thus  this  other  wire  passes  through  the  air  near  a  large 
number  of  small  suspended  magnets,  and,  as  I  pass  the  current  through 
it,  every  magnet  is  affected  and  tends  to  turn  at  right  angles  to  the  wire 
and  even  to  move  toward  it  and  wrap  itself  around  it.  If  we  suppose 
the  number  of  these  magnets  to  become  very  great  and  their  size  small, 
or  if  we  imagine  a  medium,  every  atom  of  which  is  a  magnet,  we  see  that 
no  wire  carrying  a  current  of  electricity  can  pass  through  it  without 
creating  the  greatest  commotion.  Possibly  this  is  a  feeble  picture  of 
what  takes  place  in  a  mass  of  iron  near  an  electric  current. 

Again,  coil  the  wire  around  a  piece  of  glass,  or  indeed,  almost  any 
transparent  substance,  and  pass  a  strong  current  through  the  wire. 
With  our  naked  eye  alone  we  can  see  no  effect  whatever,  as  the  glass  is 
apparently  unaltered  by  the  presence  of  the  current;  but,  examined  in 
the  proper  way,  by  means  of  polarized  light,  we  see  that  the  structure  of 
the  glass  has  been  altered  throughout  in  a  manner  which  can  only  be 
explained  by  the  rotation  of  something  within  the  glass  many  millions 
of  times  every  second. 

Once  more,  bring  a  wire  in  which  no  current  exists  nearer  and  nearer 
to  the  one  carrying  the  current,  and  we  shall  find  that  its  motion  in  such 
a  neighborhood  causes  or  tends  to  cause  an  electric  current  in  it.  Or,  if 
we  move  a  large  solid  mass  of  metal  in  the  neighborhood  of  such  a  cur- 
rent we  find  a  peculiar  resistance  unfelt  before,  and  if  we  force  it  into 
motion,  we  shall  perceive  that  it  becomes  warmer  and  warmer  as  if  there 
was  great  friction  in  moving  the  metal  through  space. 

Thus,  by  these  tests,  we  find  that  the  region  around  an  electric  cur- 
rent has  very  peculiar  properties  which  it  did  not  have  before,  and 
which,  although  stronger  in  the  neighborhood  of  the  current,  still  ex- 
tend to  indefinite  distances  in  all  directions,  becoming  weaker  as  the 
distances  increase. 

How  great,  then,  the  difference  between  a  current  of  water  and  a  cur- 
rent of  electricity.  The  action  of  the  former  is  confined  to  the  interior 
of  the  tube,  while  that  of  the  latter  extends  to  great  distances  on  all 


MODERN  VIEWS  WITH  EESPECT  TO  ELECTRIC  CURRENTS       655 

sides,  the  whole  of  space  being  agitated  by  the  formation  of  an  electric 
current  in  any  part.  To  show  this  agitation,  I  have  here  two  large 
frames  with  coils  of  wire  around  them.  They  hang  face  to  face  about 
6  feet  apart.  Through  one  I  discharge  this  Leyden  jar,  and  immediately 
you  see  a  spark  at  a  break  in  the  wire  of  the  other  coil,  and  yet  there  is 
no  apparent  connection  between  the  two.  I  can  carry  the  coils  50  feet 
or  more  apart,  and  yet  by  suitable  means  I  can  observe  the  disturbances 
due  to  the  current  in  the  first  coil. 

The  question  is  forced  upon  us  as  to  how  this  action  takes  place.  How 
is  it  possible  to  transmit  so  much  power  to  such  a  distance  across  appar- 
ently unoccupied  space?  According  to  our  modern  theory  of  physics 
there  must  be  some  medium  engaged  in  this  transmission.  We  know 
that  it  is  not  the  air,  because  the  same  effects  ta,ke  place  in  a  vacuum, 
and,  therefore,  we  must  fall  back  on  that  medium  which  transmits  light 
and  which  we  have  named  the  ether.  That  medium  which  is  supposed 
to  extend  unaltered  throughout  the  whole  of  space,  whose  existence  is 
very  certain  but  whose  properties  we  have  yet  but  vaguely  conceived. 

I  cannot,  in  the  course  of  one  short  hour,  give  even  an  idea  of  the 
process  by  which  the  minds  of  physicists  have  been  led  to  this  conclusion 
or  the  means  by  which  we  have  finally  completely  identified  the  ether 
which  transmits  light  with  the  medium  which  transmits  electrical  and 
magnetic  disturbances.  The  great  genius  who  first  identified  the  two  is 
Maxwell,  whose  electro-magnetic  theory  of  light  is  the  centre  around 
which  much  scientific  thought  is  to-day  revolving,  and  which  we  regard 
as  one  of  the  greatest  steps  by  which  we  advance  nearer  to  the  under- 
standing of  matter  and  its  laws.  It  is  this  great  discovery  of  Maxwell 
which  allows  me,  at  the  present  time,  to  attempt  to  explain  to  you  the 
wonderful  events  which  happen  everywhere  in  space  when  one  estab- 
lishes an  electric  current  in  any  other  portion. 

In  the  first  place,  we  discover  that  the  disturbance  does  not  take  place 
in  all  portions  of  space  at  once,  but  proceeds  outwards  from  the  centre 
of  the  disturbance  with  a  velocity  exactly  equal  to  the  velocity  of  light. 
So  that,  when  I  touch  these  wires  together  so  as  to  complete  the  circuit 
of  yonder  battery,  I  start  a  wave  of  ethereal  disturbance  which  passes 
outwards  with  a  velocity  of  185,000  miles  per  second,  thus  reaching  the 
sun  in  about  eight  minutes,  and  continues  to  pass  onwards  forever  or 
until  it  reaches  the  bounds  of  the  universe.  And  yet  none  of  our  senses 
inform  us  of  what  has  taken  place  unless  we  sharpen  them  by  the  use  of 
suitable  instruments.  Thus,  in  the  case  of  these  two  coils  of  wire,  sus- 
pended near  each  other,  which  we  have  already  used,  when  the  wave 


656  HENRY  A.  EOWLAND 

from  the  primary  disturbance  reaches  the  second  coil,  we  perceive  the 
disturbance  by  means  of  the  spark  formed  at  the  break  of  the  coil. 
Should  I  move  the  coils  further  apart,  the  spark  in  the  second  coil  would 
be  somewhat  delayed,  but  the  distance  of  185,000  miles  would  be  neces- 
sary before  this  delay  could  amount  to  as  much  as  one  second.  Hence 
the  effects  we  observe  on  the  earth  take  place  so  nearly  instantaneously 
that  the  interval  of  time  is  very  difficult  to  measure,  amounting,  in  the 
present  case,  to  only  TT(nnj-1-{mro.  of  a  second. 

It  is  impossible  for  me  to  prove  the  existence  of  this  interval,  but  I 
can  at  least  show  you  that  waves  have  something  to  do  with  the  action 
here  observed.  For  instance,  I  have  here  two  tuning  forks  mounted  on 
sounding  boxes  and  tuned  to  exact  unison.  I  sound  one  and  then  stop 
its  vibrations  with  my  hand,  instantly  you  hear  that  the  other  is.  in  vibra- 
tion, caused  by  the  waves  of  sound  in  the  air  between  the  two.  When, 
however,  I  destroyed  the  unison  by  fixing  this  piece  of  wax  on  one  of  the 
forks,  the  action  ceases. 

Now,  this  combination  of  a  coil  of  wire  and  a  Leyden  jar  is  a  vibrating 
system  for  electricity  and  its  time  of  vibration  is  about  10,000,000 
times  a  second.  This  second  system  is  the  same  as  the  first,  and  there- 
fore its  time  of  vibration  is  the  same.  You  see  how  well  the  experiment 
works  now  because  the  two  are  in  unison.  But  let  me  take  away  this 
second  Leyden  jar,  thus  destroying  the  unison,  and  you  see  that  the 
sparks  instantly  cease.  Eeplacing  it,  the  sparks  reappear.  Adding  an- 
other on  one  side  and  they  disappear  again,  only  to  reappear  when  the 
system  is  made  symmetrical  by  placing  two  on  each  side. 

This  experiment  and  that  of  the  tuning  forks  have  an  exact  analogy 
to  one  another.  In  each  we  have  two  vibrating  systems  connected  by  a 
medium  capable  of  transmitting  vibrations,  and  they  both  come  under 
the  head  of  what  we  know  as  sympathetic  vibrations.  In  the  one  case, 
we  have  two  mechanical  tuning  forks  connected  by  the  air;  in  the  other, 
two  pieces  of  apparatus  which  we  might  call  electrical  tuning  forks,  con- 
nected by  the  luminiferous  ether.  The  vibrations  in  one  case  can  be 
seen  by  the  eye  or  heard  by  the  ear,  but  in  the  other  case  they  can  only 
be  perceived  when  we  destroy  them  by  making  them  produce  a  spark. 
The  fact  that  we  are  able  to  increase  the  effect  by  proper  tuning  dem- 
onstrates that  vibrations  are  concerned  in  the  phenomenon.  This  can, 
however,  be  separately  demonstrated  by  examining  the  spark  by  means 
of  a  revolving  mirror,  when  Ave  find  that  it  is  made  up  of  many  succes- 
sive sparks  corresponding  to  the  successive  backward  and  forward  move- 
ments of  the  current. 


MODERN    VIEWS    WITH    RESPECT   TO    ELECTRIC    CURRENTS          657 

The  fact  of  the  oscillatory  character  of  the  Leyden  jar  discharge  was 
first  demonstrated  by  our  own  countryman,  Henry,  in  1832,  but  he  pur- 
sued the  subject  only  a  short  distance,  and  it  remained  for  Sir  William 
Thomson  to  give  the  mathematical  theory  and  prove  the  laws  according 
to  which  the  phenomenon  takes  place. 

Thus,  in  the  case  of  a  charged  Leyden  jar  whose  inner  and  outer  coat- 
ings have  been  suddenly  joined  by  a  wire,  the  electricity  flows  back  and 
forth  along  the  wire  until  all  the  energy  originally  stored  up  in  the  jar 
has  expended  itself  in  heating  the  wire  or  the  air  where  the  spark  takes 
place  and  in  generating  waves  of  disturbance  in  the  ether  which  move 
outward  into  space  with  the  velocity  of  light.  These  ethereal  waves  we 
have  demonstrated  by  letting  them  fall  on  this  coil  of  wire  and  causing 
the  electrical  disturbance  to  manifest  itself  by  electric  sparks. 

I  have  here  another  more  powerful  arrangement  for  producing  electro- 
magnetic waves  of  very  long  wave-length,  each  one  being  about  500 
miles  long.  It  consists  of  a  coil,  within  which  is  a  bundle  of  iron  wires. 
On  passing  a  powerful  alternating  current  through  the  coil,  the  iron 
wires  are  rapidly  magnetized  and  demagnetized,  and  send  forth  into 
space  a  system  of  electro-magnetic  waves  at  the  rate  of  360  in  a  second. 

Here,  also,  I  have  another  piece  of  apparatus  [a  lamp]  for  sending 
out  the  same  kind  of  electro-magnetic  waves;  on  applying  a  match,  we 
start  it  into  action.  But  the  last  apparatus  is  tuned  to  so  high  a  pitch 
that  the  waves  are  only  so^00  inch  long,  and  55,000,000,000,000  are 
given  out  in  one  second.  These  short  waves  are  known  by  the  name  of 
light  and  radiant  heat,  though  the  name  radiation  is  more  exact.  Plac- 
ing any  body  near  the  lamp  so  that  the  radiation  can  fall  on  it,  we  ob- 
serve that  when  the  body  absorbs  the  rays  it  is  heated  by  them;  the 
well-known  property  of  so-called  radiant  heat  and  light.  Is  it  not  pos- 
sible for  us  to  get  some  substance  to  absorb  the  long  waves  of  disturb- 
ance, and  so  obtain  a  heating  effect?  I  have  here  such  a  substance  in 
the  shape  of  a  sheet  of  copper,  which  I  fasten  on  the  face  of  a  thermo- 
pile, and  I  hold  it  where  the  waves  are  the  strongest  [near  the  coil  while 
the  alternating  current  is  passing  through  it].  As  I  have  anticipated, 
great  heat  is  generated  by  their  absorption,  and  soon  the  plate  of  copper 
becomes  very  warm,  as  we  see  by  this  thermometer,  by  feeling  it  with 
the  hand,  or  even  by  the  steam  from  water  thrown  upon  it.  In  this  ex- 
periment the  copper  has  not  touched  the  coil  or  the  iron  wire  core, 
although  if  it  did  they  are  very  much  cooler  than  itself.  The  heat  has 
been  produced  by  the  absorption  of  the  waves  in  the  same  way  as  a 
42 


658  HENKY  A.  KOWLAND 

blackened  body  absorbs  the  rays  of  shorter  wave-length  from  the  lamp; 
and,  in  both  cases,  heat  is  the  result.1 

But  in  this  experiment,  as  in  the  first  one,  the  wave-like  nature  of  the 
disturbance  has  not  been  proved  experimentally.  We  have  caused  elec- 
tric sparks,  and  have  heated  the  copper  plate  across  an  interval  of  space, 
but  have  not  in  either  of  these  cases  proved  experimentally  the  progres- 
sive nature  of  the  disturbance;  for  a  ready  means  of  experimenting  on 
the  waves,  obtaining  their  wave-length  and  showing  their  interferences, 
has  hitherto  been  wanting.  This  deficiency  has  been  recently  overcome 
by  Professor  Hertz,  of  Carlsruhe,  who  has  made  a  study  of  the  action  of 
the  coil,  and  has  shown  us  how  to  use  it  for  experiments  on  the  ethereal 
waves,  whose  existence  had  before  been  made  certain  by  the  mathemat- 
ics of  Maxwell. 

I  scarcely  know  how  to  present  this  subject  to  a  non-technical  audience 
and  make  it  clear  how  a  coil  of  wire  with  a  break  in  it  can  be  used  to 
measure  the  velocity  and  wave-lengths  of  ethereal  waves.  However,  I 
can  but  try.  If  the  waves  moved  very  slowly,  we  could  readily  measure 
the  time  the  first  coil  took  to  affect  the  second,  and  show  that  this  time 
was  longer  as  the  distance  was  greater.  But  it  is  absolutely  inapprecia- 
ble by  any  of  our  instruments,  and  another  method  must  be  found.  To 
obtain  the  wave-length  Professor  Hertz  used  several  methods,  but  that 
by  the  formation  of  stationary  weaves  is  the  most  easily  grasped.  Mr. 
Ames  holds  in  his  hand  one  end  of  a  spiral  spring,  which  makes  a  very 
heavy  and  flexible  rope.  As  he  sends  a  wave  down  it,  you  see  that  it  is 
reflected  at  the  further  end,  and  returns  again  to  his  hand.  If,  how- 
ever, he  sends  a  succession  of  waves  down  the  rope,  the  reflected  waves 
interfere  with  the  direct  ones,  and  divide  the  rope  into  a  succession  of 
nodes  and  loops,  which  you  now  observe.  So  a  series  of  sound  waves, 
striking  on  a  wall,  form  a  system  of  stationary  waves  in  front  of  the  wall. 
With  this  in  view,  Professor  Hertz  established  his  apparatus  in  front  of 
a  reflecting  wall,  and  observed  the  nodes  and  loops  by  the  sparks  pro- 
duced in  a  ring  of  wire.  It  is  impossible  for  me  to  repeat  this  experi- 
ment before  you,  as  it  is  a  very  delicate  one,  and  the  sparks  produced  are 
almost  microscopic.  Indeed,  I  should  have  to  erect  an  entirely  differ- 
ent apparatus,  as  the  waves  from  the  one  before  me  are  nearly  %  mile 
long,  the  time  of  vibration  of  the  system  being  very  great,  that  is 
TWinnnnr  °^  a  second.  To  produce  shorter  waves  we  must  use  appa- 

1  The  thermopile  was  connected  with  a  delicate  mirror  galvanometer,  the  de- 
flections of  which  were  shown  on  a  screen. 


MODERN  VIEWS  WITH  KESPECT  TO  ELECTRIC  CURRENTS       659 

ratus  tuned,  as  it  were,  to  a  higher  pitch,  in  which  the  same  principle's, 
however,  employed,  but  the  ethereal  waves  are  shorter,  and  thus  several 
stationary  waves  can  be  contained  in  one  room. 

The  testing  coil  is  then  moved  to  different  portions  of  the  room,  and 
the  nodes  are  indicated  by  the  disappearance  of  the  sparks,  and  the 
loops  by  the  greater  brightness  of  them.  The  presence  of  stationary 
waves  is  thus  proved,  and  their  half  wave-length  found  from  the  dis- 
tance from  node  to  node,  for  stationary  waves  can  always  be  considered 
as  produced  by  the  interference  of  two  progressive  waves  advancing  in 
opposite  directions. 

However  interesting  a  further  description  of  Professor  Hertz's  experi- 
ments may  be,  we  have  gone  as  far  in  that  direction  as  our  subject  car- 
ries us,  for  we  have  demonstrated  that  the  production  of  a  current  in  a 
wire  is  accompanied  by  a  disturbance  in  the  surrounding  space;  and, 
although  I  have  not  experimentally  demonstrated  the  ethereal  waves,  yet 
I  have  proved  the  existence  of  electric  oscillations  in  the  coils  of  wire 
and  the  ether  surrounding  it. 

Our  mathematics  has  demonstrated,  and  experiments  like  those  of 
Professor  Hertz  have  confirmed  the  demonstration,  that  the  wave  dis- 
turbance in  the  ether  is  an  actual  fact. 

The  closing  of  a  battery  circuit,  then,  and  the  establishment  of  a  cur- 
rent of  electricity  in  a  wire  is  a  very  different  process  from  the  forma- 
tion of  a  current  of  water  in  a  pipe,  though,  after  the  first  shock,  the 
laws  of  the  flow  of  the  two  are  very  much  alike.  But  even  then,  the 
medium  around  the  current  of  electricity  has  very  strange  properties, 
showing  that  it  is  accompanied  by  a  disturbance  throughout  space.  The 
wire  is  but  the  core  of  the  disturbance,  which  latter  extends  indefinitely 
in  all  directions. 

One  of  the  strangest  things  about  it  is  that  we  can  calculate  with  per- 
fect exactness  the  velocity  of  the  wave  propagation  and  the  amount  of 
the  disturbance  at  every  point  and  at  any  instant  of  time;  but  as  yet  we 
cannot  conceive  of  the  details  of  the  mechanism  which  is  concerned  in 
the  propagation  of  an  electric  current.  In  this  respect  our  subject  resem- 
bles all  other  branches  of  physics  in  the  partial  knowledge  we  have  of  it. 
We  know  that  light  is  the  undulation  of  the  luminiferous  ether,  and  yet 
the  constitution  of  the  latter  is  unknown.  We  know  that  the  atoms  of 
matter  can  vibrate  with  purer  tones  than  the  most  perfect  piano,  and 
yet  we  cannot  even  conceive  of  their  constitution.  We  know  that  the 
sun  attracts  the  planets  with  a  force  whose  law  is  known,  and  yet  we 
fail  to  picture  to  ourselves  the  process  by  which  it  takes  our  earth  within 


660  HENKY  A.  KOWLAND 

its  grasp  at  the  distance  of  many  millions  of  miles  and  prevents  it  from 
departing  forever  from  its  life-giving  rays.  Science  is  full  of  this  half 
knowledge,  and  the  proper  attitude  of  the  mind  is  one  of  resignation 
toward  that  which  it  is  impossible  for  us  to  know  at  present  and  of  ear- 
nest striving  to  help  in  the  advance  of  our  science,  which  shall  finally 
allow  us  to  answer  all  these  questions. 

The  electric  current  is  an  unsolved  mystery,  but  we  have  made  a  very 
great  advance  in  understanding  it  when  we  know  that  we  must  look  out- 
side of  the  wire  at  the  disturbance  in  the  medium  before  we  can  under- 
stand it:  a  view  which  Faraday  dimly  held  fifty  years  ago,  which  was 
given  in  detail  in  the  great  work  of  Maxwell,  published  sixteen  years 
since,  and  has  been  the  guide  to  most  of  the  work  done  in  electricity 
for  a  very  long  time.  A  view  which  has  wrought  the  greatest  changes 
in  the  ideas  which  we  have  conceived  with  respect  to  all  electrical 
phenomena. 

So  far,  we  have  considered  the  case  of  alternating  electric  current  in 
a  wire  connecting  the  inner  and  outer  coatings  of  a  Leyden  jar.  The 
invention  of  the  telephone,  by  which  sound  is  carried  from  one  point  to 
another  by  means  of  electrical  waves,  has  forced  into  prominence  the 
subject  of  these  waves.  Furthermore,  the  use  of  alternating  currents 
for  electric  lighting  brings  into  play  the  same  phenomenon.  Here, 
again,  the  difference  between  a  current  of  water  and  a  current  of  elec- 
tricity is  very  marked.  A  sound  wave,  traversing  the  water  in  the  tube, 
produces  a  to  and  fro  current  of  water  at  any  given  point.  So,  in  the 
electrical  vibration  along  a  wire,  the  electricity  moves  to  and  fro  along 
it  in  a  manner  somewhat  similar  to  the  water,  but  with  this  difference: — 
the  disturbance  from  the  water  motion  is  confined  to  the  tube  and  the 
oscillation  of  the  water  is  greatest  in  the  centre  of  the  tube,  while,  in 
the  case  of  the  electric  current,  the  ether  around  the  wire  is  disturbed 
and  the  oscillation  of  the  current  is  greatest  at  the  surface  of  the  wire 
and  least  in  its  centre.  The  oscillations  in  the  water  take  place  in  the 
tube  without  reference  to  the  matter  outside  the  tube1,  whereas  the  elec- 
tric oscillations  in  the  wire  are  entirely  dependent  on  the  surrounding 
space,  and  the  velocity  of  the  propagation  is  nearly  independent  of  the 
nature  of  the  wire,  provided  only  that  it  is  a  good  conductor. 

We  have,  then,  in  the  case  of  electrical  waves  along  a  wire,  a  disturb- 
ance outside  the  wire  and  a  current  within  it,  and  the  equations  of 
Maxwell  allow  us  to  calculate  these  with  perfect  accuracy  and  give  all  the 
laws  with  respect  to  them. 

We  thus  find  that  the  velocity  of  propagation  of  the  waves  along  a 


MODERN  VIEWS  WITH  RESPECT  TO  ELECTRIC  CURRENTS       661 


wire,  hung  far  away  from  other  bodies  and  made  of  good  conducting  ma- 
terial, is  that  of  light,  or  185,000  miles  per  second;  but  when  it  is 
hung  near  any  conducting  matter,  like  the  earth,  or  inclosed  in  a  cable 
and  sunk  into  the  sea,  the  velocity  becomes  much  less.  When  hung  in 
space,  away  from  other  bodies,  it  forms,  as  it  were,  the  core  of  a  system 
of  waves  in  the  ether,  the  amplitude  of  the  disturbance  becoming  less 
and  less  as  we  move  away  from  the  wire.  But  the  most  curious  fact  is 
that  the  electric  current  penetrates  only  a  short  distance  into  the  wire, 


Or 


-  o 


DIAGRAM  1. 

being  mostly  confined  to  the  surface,  especially  where  the  number  of 
oscillations  per  second  is  very  great. 

The  electrical  waves  at  the  surface  of  a  conductor  are  thus,  in  some 
respects,  very  similar  to  the  waves  on  the  surface  of  the  water.  The 
greatest  motion  in  the  latter  case  is  at  the  surface,  while  it  diminishes 
as  we  pass  downward  and  soon  becomes  inappreciable.  Furthermore, 
the  depth  to  which  the  disturbance  penetrates  into  the  water  increases 
with  increase  of  the  length  of  the  wave,  being  confined  to  very  near  the 
surface  for  very  short  waves.  So  the  disturbance  in  the  copper  pene- 
trates deeper  as  the  waves  and  the  time  of  oscillation  are  longer,  and  the 
disturbance  is  more  nearly  confined  to  the  surface  as  the  waves  become 
shorter.  I  have  recently  made  the  complete  calculations  with  respect 


662 


HENRY  A.  ROWLAND 


to  these  waves,  and  have  drawn  some  diagrams  to  illustrate  the  penetra- 
tion of  the  alternating  current  into  metal  cylinders.  The  first  diagram 
represents  the  current  at  different  depths  in  a  copper  cylinder,  45  cm. 
diameter,  or  an  iron  one  144  cm.  diameter,  traversed  by  an  alternating 
current  with  200  reversals  per  second.  The  first  and  second  curves 
show  us  the  current  at  two  different  instants  of  time,  and  show  us  how 
the  phase  changes  as  we  pass  downward  into  the  cylinder.  By  reference 
to  the  third  curve  we  see  that  it  may  be  even  in  the  opposite  direction  in 
the  centre  of  the  cylinder  from  what  it  is  at  the  surface.  The  third 
curve  gives  us  the  amplitude  of  the  current  oscillations  at  different 
depths  irrespective  of  the  phase,  and  it  shows  us  that  the  current  at  the 


-^ 

6  

5 

6-,.. 

Y 

'4     - 

6             —  "* 

Y" 

3 

3 

3 

2 

a    - 

2 

1 

i 

I 

1 

i 

1 

2 

2     - 

2 

3 

3 

3 

----  " 

} 
"> 

4 

X 

fi" 

X4 

«N.^ 

DIAGRAM  2. 

centre  is  only  about  10  per  cent  of  that  at  the  surface  in  this  case.  The 
second  diagram  shows  us  the  distribution  in  the  same  cylinders  when  the 
number  of  reversals  of  the  current  is  increased  to  1800  per  second.  Here 
we  see  that  the  disturbance  is  almost  entirely  confined  to  the  surface,  for 
at  a  depth  of  only  7  mm.  the  disturbance  almost  entirely  vanishes. 

There  are  very  many  practical  applications  of  these  theoretical  results 
for  electric  currents.  The  most  obvious  one  is  to  the  case  of  conductors 
for  the  alternating  currents  used  in  producing  the  electric  light.  We 
find  that  when  these  are  larger  than  about  half  an  inch  diameter  they 
should  be  replaced  by  a  number  of  conductors  less  than  half  an  inch 
diameter,  or  by  strips  about  a  quarter  of  an  inch  thick,  and  of  any  con- 
venient width.  But  this  is  a  matter  to  be  attended  to  by  the  electric 
light  companies. 

Prof.  Oliver  J.  Lodge  has  recently,  in  the  British  Association,  drawn 


MODERN  VIEWS  WITH  RESPECT  TO  ELECTRIC  CURRENTS       663 

attention  to  the  application  of  these  results  to  lightning  rods.     Almost 
since  the  time  of  Franklin  there  have  been  those  who  advocated  the 
making  of  lightning  rods  hollow,  to  increase  the  surface  for  a  given 
amount  of  copper.    We  now  know  that  these  persons  had  no  reason  for 
their  belief,  as  they  simply  drew  the  inference  from  the  fact  that  elec- 
tricity at  best  is  on  the  surface.     Neither  were  the  advocates  of  the  solid 
rods  quite  correct,  for  they  reasoned  from  the  fact  that  electricity  in  a 
state  of  steady  flow  occupies  the  whole  area  of  the  conductor  equally. 
The  true  theory,  we  now  know,  indicates  that  neither  party  was  entirely 
correct  and  that  the  surface  is  a  very  important  factor  in  the  case  of  a 
current  of  electricity  so  sudden  as  that  from  a  lightning  discharge.    But 
increase  of  surface  can  best  be  obtained  by  multiplying  the  number  of 
conductors,  rather  than  making  them  flat  or  hollow;  and,  at  the  same 
time,  Maxwell's  principle  of  enclosing  the  building  within  a  cage  can.  be 
carried  out.     Theory  indicates  that  the  current  penetrates  only  one- 
tenth  the  distance  into  iron  that  it  does  into  copper.     As  the  iron  has 
seven  times  the  resistance  of  copper,  we  should  need  70  times  the  sur- 
face of  iron  that  we  should  of  copper.     Hence  I  prefer  copper  wire 
about  a  quarter  of  an  inch  diameter  and  nailed  directly  to  the  house 
without  insulators,  and  passing  down  the  four  corners,  around  the  eaves 
and  over  the  roof,  for  giving  protection  from  lightning  in  all  cases  where 
a  metal  roof  and  metal  down  spouts  do  not  accomplish  the  same  purpose. 
Whether  the  discharge  of  lightning  is  oscillatory  or  not  does  not  enter 
into  the  question,  provided  it  is  only  sufficiently  sudden.     I  have  re- 
cently solved  the  mathematical  problem  of  the  electric  oscillations  along 
a  perfectly  conducting  wire  joining  two  infinite  and  perfectly  conducting 
planes  parallel  to  each  other,  and  find  that  there  is  no  definite  time  of 
oscillation,  but  that  the  system  is  capable  of  vibrating  in  'any  time  in 
which  it  is  originally  started.     The  case  of  lightning  between  a  cloud  of 
limited  extent  and  the  earth  along  a  path  through  the  air  of  great  re- 
sistance is  a  very  different  problem.     Both  the  cloud  and  the  path  of  the 
electricity  are  poor  conductors,  which  tends  to  lengthen  the  time.     If  I 
were  called  on  to  estimate  as  nearly  as  possible  what  took  place  in  a  flash 
of  lightning,  I  would  say  that  I  did  not  believe  that  the  discharge  was 
always  oscillating,  but  more  often  consisted  of  one  or  more  streams  of 
electricity  at  intervals  of  a  small  fraction  of  a  second,  each  one  continu- 
ing for  not  less  than  1 0  0*0  o  o  second.     An  oscillating  current  with  100,000 
reversals  per  second  would  pentetrate  about  ^  inch  into  copper  and  ^-J-g- 
inch  into  iron.     The  depth  for  copper  would  constitute  a  considerable 
portion  of  a  wire  £  inch  diameter,  and,  as  there  are  other  considerations 


664  HENRY  A.  BOWL  AND 

to  be  .taken  into  account,  I  believe  it  is  scarcely  worth  while  making 
tubes,  or  flat  strips,  for  such  small  sizes. 

It  is  almost  impossible  to  draw  proper  conclusions  from  experiments 
on  this  subject  in  the  laboratory  such  as  those  of  Prof.  Oliver  J.  Lodge. 
The  time  of  oscillation  of  the  current  in  most  pieces  of  laboratory  ap- 
paratus is  so  very  small,  being  often  the  T70  000777  °^  a  second,  that 
entirely  wrong  inferences  may  be  drawn  from  them.  As  the  size  of 
the  apparatus  increases,  the  time  of  oscillation  increases  in  the  same  pro- 
portion, and  changes  the  whole  aspect  of  the  case.  I  have  given 
TT7Vr7  of  a  second  as  the  shortest  time  a.  lightning  flash  could  proba- 
bly occupy.  I  strongly  suspect  it  is  often  much  greater,  and  thus  de- 
parts even  further  from  the  laboratory  experiments  of  Professor  Lodge, 
who  has,  however,  done  very  much  toward  drawing  attention  to  this 
matter  and  showing  the  importance  of  surface  in  this  case.  All  shapes 
of  the  rod  with  equal  surface  are  not,  however,  equally  efficient.  Thus, 
the  inside  surface  of  a  tube  does  not  count  at  all.  Neither  do  the  corru- 
gations on  a  rod  count  for  the  full  value  of  the  surface  they  expose,  for 
the  current  is  not  distributed  uniformly  over  the  surface;  but  I  have 
recently  proved  that  rapidly  alternating  currents  are  distributed  over  the 
surface  of  very  good  conductors  in  the  same  manner  as  electricity  at 
rest  would  be  distributed  over  them,  so  that  the  exterior  angles  and  cor- 
ners possess  much  more  than  their  share  of  the  current,  and  corruga- 
tions on  the  wire  concentrate  the  current  on  the  outer  angles  and  dimin- 
ish, it  in  the  hollows.  Even  a  flat  strip  has  more  current  on  the  edges 
than  in  the  centre. 

For  these  reasons,  shape,  as  well  as  extent  of  surface,  must  be  taken 
into  account,  and  strips  have  not  always  an  advantage  over  wires  for 
quick  discharges. 

The  fact  that  the  lightning  rod  is  not  melted  on  being  struck  by 
lightning  is  not  now  considered  as  any  proof  that  it  has  done  its  work 
properly.  It  must,  as  it  were,  seize  upon  the  discharge  and  offer  it  an 
easier  passage  to  the  earth  than  any  other.  Such  sudden  currents  of 
electricity  we  have  seen  to  obey  very  different  laws  from  continuous  ones, 
and  their  tendency  to  stick  to  a  conductor  and  not  fly  off  to  other  ob- 
jects depends  not  only  on  having  them  of  small  resistance,  but  also  on 
having  what  we  call  the  self-induction  as  small  as  possible.  This  latter 
can  be  diminished  by  having  the  lightning  rod  spread  sideways  as  much 
as  possible,  either  by  rolling  it  into  strips,  or  better,  by  making  a  network 
of  rods  over  the  roof,  with  several  connections  to  the  earth  at  the  corners, 
as  I  have  before  described. 


MODERN  VIEWS  WITH  RESPECT  TO  ELECTRIC  CURRENTS       665 

Thus  we  see  that  the  theory  of  lightning  rods,  which  appeared  so  sim- 
ple in  the  time  of  Franklin,  is  to-day  a  very  complicated  one,  and  re- 
quires for  its  solution  a  very  complete  knowledge  of  the  dynamics  of  elec- 
tric currents.  In  the  light  of  our  present  knowledge  the  frequent  fail- 
ure of  the  old  system  of  rods  is  no  mystery,  for  I  doubt  if  there  are  a 
hundred  buildings  in  the  country  properly  protected  from  lightning. 
With  our  modern  advances,  perfect  protection  might  be  guaranteed  in  all 
cases,  if  expense  were  no  object. 

So  much  for  the  rod  itself,  and  now  let  us  turn  to  other  portions  of 
the  electrical  system,  for  we  have  seen  that,  in  any  case,  the  conductor  is 
only  the  core  of  a  disturbance  which  extends  to  great  distances  on  all 
sides.  Were  the  clouds,  the  earth  and  the  streak  of  heated  air  called  the 
lightning  flash  all  perfect  conductors  we  could  calculate  the  entire  dis- 
turbance. It  might  then  consist  of  a  series  of  stationary  waves  between 
the  two  planes,  extending  indefinitely  on  all  sides  but  with  gradually  de- 
creasing amplitude  as  we  pass  away  from  the  centre.  The  oscillations, 
once  set  up,  would  go  on  forever,  as  there  would  be  no  poor  conductors  to 
damp  them.  But  when  the  clouds  and  the  path  of  the  lightning  both 
have  very  great  resistance,  the  energy  is  very  soon  converted  into  heat 
and  the  oscillations  destroyed.  I  have  given  it  as  my  opinion  that  this 
is  generally  the  case  and  that  the  oscillations  seldom  take  place,  but  I 
may  be  wrong,  as  there  is  little  to  guide  me  except  guesswork.  If  they 
take  place,  however,  we  have  a  ready  explanation  of  what  is  sometimes 
called  a  back  stroke  of  lightning.  That  is,  a  man  at  the  other  end  of 
the  cloud  a  mile  or  more  distant  from  the  lightning  stroke  sometimes  re- 
ceives a  shock,  or  a  new  lightning  flash  may  form  at  that  point  and  kill 
him.  This  may  be  caused,  according  to  our  present  theory,  by  the 
arrival  of  the  waves  of  electrical  disturbance  which  might  themselves 
cause  a  slight  shock  or  even  overturn  the  equilibrium  then  existing  and 
cause  a  new  electric  discharge. 

We  have  now  considered  the  case  of  oscillations  of  electricity  in  a  few 
instances  and  can  turn  to  that  of  steady  currents.  The  closing  of  an 
electric  current  sends  ethereal  waves  throughout  space,  but  after  the 
first  shock  the  current  flows  steadily  without  producing  any  more  waves. 
However,  the  properties  of  the  space  around  the  wire  have  been  per- 
manently altered,  as  we  have  already  seen.  Let  us  now  study  these  prop- 
erties more  in  detail.  I  have  before  me  a  wire  in  which  I  can  produce  a 
powerful  current  of  electricity,  and  we  have  seen  that  the  space  around 
it  has  been  so  altered  that  a  delicately  suspended  magnetic  needle  can- 
not remain  quiet  in  all  positions  but  stretches  itself  at  right  angles  to 


666  HENRY  A.  ROWLAND 

the  wire,  the  north  pole  tending  to  revolve  around  it  in  one  direction 
and  the  south  pole  in  the  other.  This  is  a  very  old  experiment,  but  we 
now  regard  it  as  evidence  that  the  properties  of  the  space  around  the  wire 
have  been  altered  rather  than  that  the  wire  acts  on  the  magnet  from  a 
distance. 

Put,  now,  a  plate  of  glass  around  the  wire,  the  latter  being  vertical 
and  the  former  with  its  plane  horizontal,  and  pass  a  powerful  current 
through  the  wire.  On  now  sprinkling  iron  filings  on  the  plate,  they 
arrange  themselves  in  circles  around  the  wire  and  thus  point  out  to  us 
the  celebrated  lines  of  magnetic  force  of  Faraday.  Using  two  wires 
with  currents  in  the  same  direction  we  get  these  other  curves,  and,  test- 
ing the  forces  acting  on  the  wire,  we  find  that  they  are  trying  to  move 
towards  each  other. 

Again,  pass  the  currents  in  the  opposite  directions  and  we  get  these 
other  curves  and  the  currents  repel  each  other.  If  we  assume  that  the 
lines  of  force  are  like  rubber  bands,  which  tend  to  shorten  in  the  direc- 
tion of  their  length  and  repel  each  other  sideways,  Faraday  and  Maxwell 
have  shown  that  all  magnetic  attraction  and  repulsions  are  explained. 
The  property  which  the  presence  of  the  electric  current  has  conferred  on 
the  luminiferous  ether  is  then  one  by  which  it  tends  to  shorten  in  one 
direction  and  spread  out  in  the  other  two  directions. 

We  have  thus  done  away  with  action  at  a  distance,  and  have  account- 
ed for  magnetic  attraction  by  a  change  in  the  intervening  medium  as 
Faraday  partly  did  almost  fifty  years  ago.  For  this  change  in  the  sur- 
rounding medium  is  as  much  a  part  of  the  electric  current  as  any  thing 
that  goes  on  within  the  wire. 

To  illustrate  this  tension  along  the  lines  of  force,  I  have  constructed 
this  model,  which  represents  the  section  of  a  coil  of  wire  with  a  bar  of 
iron  within  it.  The  rubber  bands  represent  the  lines  of  force  which  pass 
around  the  coil  and  through  the  iron  bar,  as  they  have  an  easier  passage 
through  the  iron  than  the  air.  As  we  draw  the  bar  down  and  let  it  go, 
you  see  that  it  is  drawn  upward  and  oscillates  around  its  position  of 
equilibrium  until  friction  brings  it  to  rest.  Here,  again,  I  have  a  coil 
of  wire  with  an  iron  bar  within  it  with  one  end  resting  on  the  floor. 
As  we  pass  the  current  and  the  lines  of  magnetic  force  form  around 
the  coil  and  pass  through  the  iron,  it  is  lifted  upwards  although  if 
weighs  24  pounds  and  oscillates  around  its  position  of  equilibrium 
exactly  the  same  as  though  it  were  sustained  by  rubber  bands  as 
in  the  model.  The  rubber  bands  in  this  case  are  invisible  to  our 
eye,  but  our  mental  vision  pictures  them  to  us  as  lines  of  magnetic 


MODERN  VIEWS  WITH  RESPECT  TO  ELECTRIC  CURRENTS       667 

force  in  the  luminiferous  ether  drawing  the  bar  upward  by  their  con- 
tractile force.  This  contractile  force  is  no  small  quantity,  as  it  may 
amount,  in  some  cases,  to  one  or  even  two  hundred  pounds  to  the  square 
inch,  and  thus  rivals  the  greatest  pressure  which  we  use  in  our  steam 
engines. 

Thus  the  luminiferous  ether  is,  to-day,  a  much  more  important  factor 
in  science  than  the  air  we  breathe.  We  are  constantly  surrounded  by 
the  two,  and  the  presence  of  the  air  is  manifest  to  us  all;  we  feel  it,  he 
hear  by  its  aid,  and  we  even  see  it,  under  favorable  circumstances,  and 
the  velocity  of  its  motion  as  well  as  the  amount  of  moisture  it  carries  is  a 
constant  topic  of  conversation  with  mankind  at  large.  The  luminifer- 
ous ether,  on  the  other  hand,  eludes  all  our  senses  and  it  is  only  with 
imagination,  the  eye  of  the  mind,  that  its  presence  can  be  perceived. 
By  its  aid  in  conveying  the  vibrations  we  call  light,  we  are  enabled  to  see 
the  world  around  us,  and  by  its  other  motions  which  cause  magnetism, 
the  mariner  steers  his  ship  through  the  darkest  night  when  the  heavenly 
bodies  are  hid  from  view.  "When  we  speak  in  a  telephone,  the  vibra- 
tions of  the  voice  are  carried  forward  to  the  distant  point  by  waves  in 
the  luminiferous  ether,  there  again  to  be  resolved  into  the  sound  waves 
of  the  air.  When  we  use  the  electric  light  to  illuminate  our  streets,  it 
is  the  luminiferous  ether  which  conveys  the  energy  along  the  wires  as 
well  as  transmits  it  to  our  eye  after  it  has  assumed  the  form  of  light. 
We  step  upon  an  electric  street  car  and  feel  it  driven  forward  with  the 
power  of  many  horses,  and  again  it  is  the  luminiferous  ether,  whose  im- 
mense force  we  have  brought  under  our  control  and  made  to  serve  our 
purpose.  No  longer  a  feeble,  uncertain  sort  of  medium,  but  a  mighty 
power,  extending  throughout  all  space  and  binding  the  whole  universe 
together,  so  that  it  becomes  a  living  unit  in  which  no  one  portion  can  be 
changed  without  ultimately  involving  every  other  portion. 

To  this,  ladies  and  gentlemen,  we  have  been  led  by  the  study  of  elec- 
trical phenomena,  and  the  ideas  which  I  have  set  forth  constitute  the 
most  modern  views  held  by  physicists  with  respect  to  electric  currents. 


G 


ADDRESS     DELIVERED    AS    PRESIDENT    OF     THE     AMERICAN     PHYSICAL     SOCIETY,    AT    ITS 
MEETING    IN    NEW    YORK,    OCTOBER    28,     1899 

[American  Journal  of  Science  [4]    VIII,  401-411,  1899;   Science,  X,  825-833,   1899J; 
Johns  Hopkins  University  Circulars,  No.  143,  pp.  17-20,  1900] 

GENTLEMEN  AND  FELLOW  PHYSICISTS  OF  AMERICA: — We  meet  to-day 
on  an  occasion  which  marks  an  epoch  in  the  history  of  physics  in  Amer- 
ica; may  the  future  show  that  it  also  marks  an  epoch  in  the  history  of 
the  science  which  this  society  is  organized  to  cultivate!  For  we  meet 
here  in  the  interest  of  a  science  above  all  sciences  which  deals  with  the 
foundation  of  the  universe,  with  the  constitution  of  matter  from  which 
everything  in  the  universe  is  made  and  with  the  ether  of  space  by  which 
alone  the  various  portions  of  matter  forming  the  universe  affect  each 
other  even  at  such  distances  as  we  may  never  expect  to  traverse,  what- 
ever the  progress  of  our  science  in  the  future. 

We,  who  have  devoted  our  lives  to  the  solution  of  problems  connected 
with  physics,  now  meet  together  to  help  each  other  and  to  forward  the 
interests  of  the  subject  which  we  love, — a  subject  which  appeals  most 
strongly  to  the  better  instincts  of  our  nature  and  the  problems  which 
tax  our  minds  to  the  limit  of  their  capacity  and  suggest  the  grandest 
and  noblest  ideas  of  which  they  are  capable. 

In  a  country  where  the  doctrine  of  the  equal  rights  of  man  has  been 
distorted  to  mean  the  equality  of  man  in  other  respects,  we  form  a  small 
and  unique  body  of  men,  a  new  variety  of  the  human  race,  as  one  of 
our  greatest  scientists  calls  it,  whose  views  of  what  constitutes  the  great- 
est achievement  in  life  are  very  different  from  those  around  us.  In  this 
respect  we  form  an  aristocracy,  not  of  wealth,  not  of  pedigree,  but  of 
intellect  and  of  ideals,  holding  him  in  the  highest  respect  who  adds  the 
most  to  our.  knowledge  or  who  strives  after  it  as  the  highest  good. 

Thus  we  meet  together  for  mutual  sympathy  and  the  interchange  of 
knowledge,  and  may  we  do  so  ever  with  appreciation  of  the  benefits  to 
ourselves  and  possibly  to  our  science.  Above  all,  let  us  cultivate  the 
idea  of  the  dignity  of  our  pursuit  so  that  this  feeling  may  sustain  us  in 
the  midst  of  a  world  which  gives  its  highest  praise,  not  to  the  investiga- 


THE  HIGHEST  AIM  OF  THE  PHYSICIST  669 

tion  in  the  pure  ethereal  physics  which  our  society  is  formed  to  cultivate, 
but  to  the  one  who  uses  it  for  satisfying  the  physical  rather  than  the 
intellectual  needs  of  mankind.  He  who  makes  two  blades  of  grass  grow 
where  one  grew  before  is  the  benefactor  of  mankind;  but  he  who  ob- 
scurely worked  to  find  the  laws  of  such  growth  is  the  intellectual  supe- 
rior as  well  as  the  greater  benefactor  of  the  two. 

How  stands  our  country,  then,  in  this  respect?  My  answer  must  still 
be  now,  as  it  was  fifteen  years  ago,  that  much  of  the  intellect  of  the 
country  is  still  wasted  in  the  pursuit  of  so-called  practical  science  which 
ministers  to  our  physical  needs  and  but  little  thought  and  money  is 
given  to  the  grander  portion  of  the  subject  which  appeals  to  our  intellect 
alone.  But  your  presence  here  gives  evidence  that  such  a  condition  is 
not  to  last  forever. 

Even  in  the  past  we  have  a  few  names  whom  scientists  throughout  the 
world  delight  to  honor:  Franklin,  who  almost  revolutionized  the 
science  of  electricity  by  a  few  simple  but  profound  experiments;  Count 
Eumford,  whose  experiments  almost  demonstrated  the  nature  of  heat; 
Henry,  who  might  have  done  much  for  the  progress  of  physics  had  he 
published  more  fully  the  results  of  his  investigations;  Mayer,  whose 
simple  and  ingenious  experiments  have  been  a  source  of  pleasure  and 
profit  to  many.  This  is  the  meager  list  of  those  whom  death  allows  me 
to  speak  of  and  who  have  earned  mention  here  by  doing  something  for 
the  progress  of  our  science.  And  yet  the  record  has  been  searched  for 
more  than  a  hundred  years.  How  different  had  I  started  to  record 
those  who  have  made  useful  and  beneficial  inventions! 

But  I  know,  when  I  look  in  the  faces  of  those  before  me,  where  the 
eager  intellect  and  high  purpose  sit  enthroned  on  bodies  possessing  the 
vigor  and  strength  of  youth,  that  the  writer  of  a  hundred  years  hence 
can  no  longer  throw  such  a  reproach  upon  our  country.  Nor  can  we 
blame  those  who  have  gone  before  us.  The  progress  of  every  science 
shows  us  the  condition  of  its  growth.  Very  few  persons,  if  isolated  in 
a  semi-civilized  land,  have  either  the  desire  or  the  opportunity  of  pur- 
suing the  higher  branches  of  science.  Even  if  they  should  be  able  to  do 
so,  their  influence  on  their  science  depends  upon  what  they  publish 
and  make  known  to  the  world.  A  hermit  philosopher  we  can  imagine 
might  make  many  useful  discoveries.  Yet,  if  he  keeps  them  to  himself, 
he  can  never  claim  to  have  benefited  the  world  in  any  degree.  His  un- 
published results  are  his  private  gain,  but  the  world  is  no  better  off 
until  he  has  made  them  known  in  language  strong  enough  to  call  atten- 
tion to  them  and  to  convince  the  world  of  their  truth.  Thus,  to  encour- 
age the  growth  of  any  science,  the  best  thing  we  can  do  is  to  meet 


670  HENEY  A.  EOWLAND 

together  in  its  interest,  to  discuss  its  problems,  to  criticise  each  other's 
work  and,  best  of  all,  to  provide  means  by  which  the  better  portion  of 
it  may  be  made  known  to  the  world.  Furthermore,  let  us  encourage 
discrimination  in  our  thoughts  and  work.  Let  us  recognize  the  eras 
when  great  thoughts  have  been  introduced  into  our  subject  and  let  us 
honor  the  great  men  who  introduced  and  proved  them  correct.  Let  us 
forever  reject  such  foolish  ideas  as  the  equality  of  mankind  and  care- 
fully give  the  greater  credit  to  the  greater  man.  So,  in  choosing  the 
subjects  for  our  investigation,  let  us,  if  possible,  work  upon  those  sub- 
jects which  will  finally  give  us  an  advanced  knowledge  of  some  great 
subject.  I  am  aware  that  we  cannot  always  do  this:  our  ideas  will  often 
flow  in  side  channels:  but,  with  the  great  problems  of  the  universe 
before  us,  we  may  some  time  be  able  to  do  our  share  toward  the  greater 
end. 

What  is  matter;  what  is  gravitation;  what  is  ether  and  the  radiation 
through  it;  what  is  electricity  and  magnetism;  how  are  these  connected 
together  and  what  is  their  relation  to  heat?  These  are  the  greater 
problems  of  the  universe.  But  many  infinitely  smaller  problems  we 
must  attack  and  solve  before  we  can  even  guess  at  the  solution  of  the 
greater  ones. 

In  our  attitude  toward  these  greater  problems  how  do  we  stand  and 
what  is  the  foundation  of  our  knowledge? 

Newton  and  the  great  array  of  astronomers  who  have  succeeded  him 
have  proved  that,  within  planetary  distances,  matter  attracts  all  others 
with  a  force  varying  inversely  as  the  square  of  the  distance.  But  what 
sort  of  proof  have  we  of  this  law?  It  is  derived  from  astronomical 
observations  on  the  planetary  orbits.  It  agrees  very  well  within  these 
immense  spaces;  but  where  is  the  evidence  that  the  law  holds  for  smaller 
distances?  We  measure  the  lunar  distance  and  the  size  of  the  earth 
and  compare  the  force  at  that  distance  with  the  force  of  gravitation  on 
the  earth's  surface.  But  to  do  this  we  must  compare  the  matter  in  the 
earth  with  that  in  the  sun.  This  we  can  only  do  by  assuming  the  law 
to  be  proved.  Again,  in  descending  from  the  earth's  gravitation  to  that 
of  two  small  bodies,  as  in  the  Cavendish  experiment,  we  assume  the  law 
to  hold  and  deduce  the  mass  of  the  earth  in  terms  of  our  unit  of  mass. 
Hence,  when  we  say  that  the  mass  of  the  earth  is  5£  times  that  of  an 
equal  volume  of  water  we  assume  the  law  of  gravitation  to  be  that  of 
Newton.  Thus  a  proof  of  the  law  from  planetary  down  to  terrestrial 
distances  is  physically  impossible. 

Again,  that  portion  of  the  law  which  says  that  gravitational  attrac- 


THE  HIGHEST  AIM  OF  THE  PHYSICIST  671 

tion  is  proportional  to  the  quantity  of  matter,  which  is  the  same  as 
saying  that  the  attraction  of  one  body  by  another  is  not  affected  by  the 
presence  of  a  third,  the  feeble  proof  that  we  give  by  weighing  bodies  in 
a  balance  in  different  positions  with  respect  to  each  cannot  be  accepted 
on  a  larger  scale.  When  we  can  tear  the  sun  into  two  portions  and  prove 
that  either  of  the  two  halves  attracts  half  as  much  as  the  whole,  then 
we  shall  have  a  proof  worth  mentioning. 

Then  as  to  the  relation  of  gravitation  and  time  what  can  we  say? 
Can  we  for  a  moment  suppose  that  two  bodies  moving  through  space 
with  great  velocities  have  their  gravitation  unaltered?  I  think  not. 
Neither  can  we  accept  Laplace's  proof  that  the  force  of  gravitation  acts 
instantaneously  through  space,  for  we  can  readily  imagine  some  com- 
pensating features  unthought  of  by  Laplace. 

How  little  we  know  then  of  this  law  which  has  been  under  observa- 
tion for  two  hundred  years! 

Then  as  to  matter  itself  how  have  our  views  changed  and  how  are 
they  constantly  changing.  The  round  hard  atom  of  Newton  which 
God  alone  could  break  into  pieces  has  become  a  molecule  composed  of 
many  atoms,  and  each  of  these  smaller  atoms  has  become  so  elastic  that 
after  vibrating  100,000  times  its  amplitude  of  vibration  is  scarcely 
diminished.  It  has  become  so  complicated  that  it  can  vibrate  with  as 
many  thousand  notes.  We  cover  the  atom  with  patches  of  electricity 
here  and  there  and  make  of  it  a  system  compared  with  which  the  plane- 
tary system,  nay  the  universe  itself,  is  simplicity.  Nay  more:  some  of 
us  even  claim  the  power,  which  Newton  attributed  to  God  alone,  of 
breaking  the  atom  into  smaller  pieces  whose  size  is  left  to  the  imagina- 
tion. Where,  then,  is  that  person  who  ignorantly  sneers  at  the  study 
of  matter  as  a  material  and  gross  study?  Where,  again,  is  that  man  with 
gifts  so  God-like  and  mind  so  elevated  that  he  can  attack  and  solve  its 
problem? 

To  all  matter  we  attribute  two  properties,  gravitation  and  inertia. 
Without  these  two  matter  cannot  exist.  The  greatest  of  the  natural 
laws  states  that  the  power  of  gravitational  attraction  is  proportional  to 
the  mass  of  the  body.  This  law  of  Newton,  almost  neglected  in  the 
thoughts  of  physicists,  undoubtedly  has  vast  import  of  the  very  deepest 
meaning.  Shall  it  mean  that  all  matter  is  finally  constructed  of  uniform 
and  similar  primordial  atoms  or  can  we  find  some  other  explanation? 

That  the  molecules  of  matter  are  not  round,  we  know  from  the  facts 
of  crystallography  and  the  action  of  matter  in  rotating  the  plane  of 
polarization  of  light. 


672  HENRY  A.  EOWLAND 

That  portions  of  the  molecules  and  even  of  the  atoms  are  electrically 
charged,  we  know  from  electrolysis,  the  action  of  gases  in  a  vacuum 
tube  and  from  the  Zeeman  effect. 

That  some  of  them  act  like  little  magnets,  we  know  from  the  mag- 
netic action  of  iron,  nickel  and  cobalt. 

That  they  are  elastic,  the  spectrum  shows,  and  that  the  vibrating 
portion  carries  the  electrified  charge  with  it  is  shown  by  the  Zeeman 
effect. 

Here,  then,  we  have  made  quite  a  start  in  our  problem:  but  how  far 
are  we  from  the  complete  solution?  How  can  we  imagine  the  material 
of  which  ordinary  or  primordial  atoms  are  made,  dealing  as  we  do  only 
with  aggregation  of  atoms  alone?  Forever  beyond  our  sight,  vibrating 
an  almost  infinite  number  of  times  in  a  second,  moving  hither  and  yon 
with  restless  energy  at  all  temperatures  beyond  the  absolute  zero  of 
temperature,  it  is  certainly  a  wonderful  feat  of  human  reason  and 
imagination  that  we  know  as  much  as  we  do  at  present.  Encouraged  by 
these  results,  let  us  not  linger  too  long  in  their  contemplation  but  pre?^ 
forward  to  the  new  discoveries  which  await  us  in  the  future. 

Then  as  to  electricity,  the  subtile  spirit  of  the  amber,  the  demon  who 
reached  out  his  glutinous  arms  to  draw  in  the  light  bodies  within  his 
reach,  the  fluid  which  could  run  through  metals  with  the  greatest  ease 
but  could  be  stopped  by  a  frail  piece  of  glass!  Where  is  it  now?  Van- 
ished, thrown  on  the  waste  heap  of  our  discarded  theories  to  be  replaced 
by  a  far  nobler  and  exalted  one  of  action  in  the  ether  of  space. 

And  so  we  are  brought  to  consider  that  other  great  entity — the  ether: 
filling  all  space  without  limit,  we  imagine  the  ether  to  be  the  only 
means  by  which  two  portions  of  matter  distant  from  each  other  can 
have  any  mutual  action.  By  its  means  we  imagine  every  atom  in  the 
universe  to  be  bound  to  every  other  atom  by  the  force  of  gravitation 
and  often  by  the  force  of  magnetic  and  electric  action,  and  we  conceive 
that  it  alone  conveys  the  vibratory  motion  of  each  atom  or  molecule 
out  into  space  to  be  ever  lost  in  endless  radiation,  passing  out  into 
infinite  space  or  absorbed  by  some  other  atoms  which  happen  to  be  in 
its  path.  By  it  all  electromagnetic  energy  is  conveyed  from  the  feeble 
attraction  of  the  rubbed  amber  through  the  many  thousand  horse-power 
conveyed  by  the  electric  wires  from  Niagara  to  the  mighty  rush  of 
energy  always  flowing  from  the  sun  in  a  flood  of  radiation.  Actions 
feeble  and  actions  mighty  from  inter-molecular  distances  through  inter- 
planetary and  inter-stellar  distances  until  we  reach  the  mighty  dis- 
tances which  bound  the  universe — all  have  their  being  in  this  wondrous 
ether. 


THE  HIGHEST  AIM  OF  THE  PHYSICIST  673 

And  yet,  however  wonderful  it  may  be,  its  laws  are  far  more  simple 
than  those  of  matter.  Every  wave  in  it,  whatever  its  length  or  inten- 
sity, proceeds  onwards  in  it  according  to  well  known  laws,  all  with  the 
same  speed,  unaltered  in  direction  from  its  source  in  electrified  matter, 
to  the  confines  of  the  universe  unimpaired  in  energy  unless  it  is  dis- 
turbed by  the  presence  of  matter.  However  the  waves  may  cross  each 
other,  each  proceeds  by  itself  without  interference  with  the  others. 

So  with  regard  to  gravitation,  we  have  no  evidence  that  the  presence 
of  a  third  body  affects  the  mutual  attraction  of  two  other  bodies  or 
that  the  presence  of  a  third  quantity  of  electricity  affects  the  mutual 
attraction  of  two  other  quantities.  The  same  for  magnetism. 

For  this  reason  the  laws  of  gravitation  and  of  electric  and  magnetic 
action  including  radiation  are  the  simplest  of  all  laws  when  we  confine 
them  to  a  so-called  vacuum,  but  become  more  and  more  complicated 
when  we  treat  of  them  in  space  containing  matter. 

Subject  the  ether  to  immense  electrostatic,  magnetic  or  gravitational 
forces  and  we  find  absolutely  no  signs  of  its  breaking  down  or  even 
change  of  properties.  Set  it  into  vibration  by  means  of  an  intensely 
hot  body  like  that  of  the  sun  and  it  conveys  many  thousand  horse-power 
for  each  square  foot  of  surface  as  quietly  and  with  apparently  unchanged 
laws  as  if  it  were  conveying  the  energy  of  a  tallow  dip. 

Again,  subject  a  millimeter  of  ether  to  the  stress  of  many  thousand, 
nay  even  a  million,  volts  and  yet  we  see  no  signs  of  breaking  down. 

Hence  the  properties  of  the  ether  are  of  ideal  simplicity  and  lead  to 
the  simplest  of  natural  laws.  All  forces  which  act  at  a  distance,  always 
obey  the  law  of  the  inverse  square  of  the  distance  and  we  have  also  the 
attraction  of  any  number  of  parts  placed  near  each  other  equal  to  the 
arithmetical  sum  of  the  attractions  when  those  parts  are  separated.  So 
also  the  simple  law  of  ethereal  waves  which  has  been  mentioned  above. 

At  the  present  time,  through  the  labors  of  Maxwell  supplemented  by 
those  of  Hertz  and  others,  we  have  arrived  at  the  great  generalization 
that  all  wave  disturbances  in  the  ether  are  electromagnetic  in  their 
nature.  We  know  of  little  or  no  ethereal  disturbance  which  can  be  set 
up  by  the  motion  of  matter  alone:  the  matter  must  be  electrified  in 
order  to  have  sufficient  hold  on  the  ether  to  communicate  its  motion 
to  the  ether.  The  Zeeman  effect  even  shows  this  to  be  the  case  where 
molecules  are  concerned  and  when  the  period  of  vibration  is  immensely 
great.  Indeed  the  experiment  on  the  magnetic  action  of  electric  con- 
vection shows  the  same  thing.  By  electrifying  a  disc  in  motion  it 
appears  as  if  the  disc  holds  fast  to  the  ether  and  drags  it  with  it,  thus 

setting  up  the  peculiar  ethereal  motion  known  as  magnetism. 
43 


674  HENRY  A.  KOWLAND 

Have  we  not  another  case  of  a  similar  nature  when  a  huge  gravita- 
tional mass  like  that  of  the  earth  revolves  on  its  axis?  Has  not  matter 
a  feeble  hold  on  the  ether  sufficient  to  produce  the  earth's  magnetism? 

But  the  experiment  of  Lodge  to  detect  such  an  action  apparently 
showed  that  it  must  be  very  feeble.  Might  not  his  experiment  have 
succeeded  had  he  used  an  electrified  revolving  disc? 

To  detect  something  dependent  on  the  relative  motion  of  the  ether 
and  matter  has  been  and  is  the  great  desire  of  physicists.  But  we 
always  find  that,  with  one  possible  exception,  there  is  always  some  com- 
pensating feature  which  renders  our  efforts  useless.  This  one  experi- 
ment is  the  aberration  of  light,  but  even  here  Stokes  has  shown  that  it 
may  be  explained  in  either  of  two  ways:  first,  that  the  earth  moves 
through  the  ether  of  space  without  disturbing  it,  and  second,  that  it 
carries  the  ether  with  it  by  a  kind  of  motion  called  irrotational.  Even 
here,  however,  the  amount  of  action  probably  depends  upon  relative 
motion  of  the  luminous  source  to  the  recipient  telescope. 

So  the  principle  of  Doppler  depends  also  on  this  relative  motion  and 
is  independent  of  the  ether. 

The  result  of  the  experiments  of  Foucault  on  the  passage  of  light 
through  moving  water  can  no  longer  be  interpreted  as  due  to  the  partial 
movement  of  the  ether  with  the  moving  water,  an  inference  due  to 
imperfect  theory  alone.  The  experiment  of  Lodge,  who  attempted  to 
set  the  ether  in  motion  by  a  rapidly  rotating  disc,  showed  no  such  result. 

The  experiment  of  Michelson  to  detect  the  ethereal  wind,  although 
carried  to  the  extreme  of  accuracy,  also  failed  to  detect  any  relative 
motion  of  the  matter  and  the  ether. 

But  matter  with  an  electrical  charge  holds  fast  to  the  ether  and 
moves  it  in  the  manner  required  for  magnetic  action. 

When  electrified  bodies  move  together  through  space  or  with  refer- 
ence to  each  other  we  can  only  follow  their  mutual  actions  through  very 
slow  and  uniform  velocities.  When  they  move  with  velocities  com- 
parable with  that  of  light,  equal  to  it  or  even  beyond  it,  we  calculate 
their  mutual  actions  or  action  on  the  ether  only  by  the  light  of  our 
imagination  unguided  by  experiment.  The  conclusions  of  J.  J.  Thom- 
son, Heaviside  and  Hertz  are  all  results  of  the  imagination  and  they  all 
rest  upon  assumptions  more  or  less  reasonable  but  always  assumptions. 
A  mathematical  investigation  always  obeys  the  law  of  the  conservation 
of  knowledge:  we  never  get  out  more  from  it  than  we  put  in.  The 
knowledge  may  be  changed  in  form,  it  may  be  clearer  and  more  exactly 
stated,  but  the  total  amount  of  the  knowledge  of  nature  given  out  by 


THE  HIGHEST  AIM  or  THE  PHYSICIST  675 

the  investigation  is  the  same  as  we  started  with.  Hence  we  can  never 
predict  the  result  in  the  case  of  velocities  beyond  our  reach,  and  such 
calculations  as  the  velocity  of  the  cathode  rays  from  their  electro- 
magnetic action  has  a  great  element  of  uncertainty  which  we  should  do 
well  to  remember. 

Indeed,  when  it  comes  to  exact  knowledge,  the  limits  are  far  more 
circumscribed. 

How  is  it,  then,  that  we  hear  physicists  and  others  constantly  stating 
what  will  happen  beyond  these  limits?  Take  velocities,  for  instance, 
such  as  that  of  a  material  body  moving  with  the  velocity  of  light.  There 
is  no  known  process  by  which  such  a  velocity  can  be  obtained  even 
though  the  body  fell  from  an  infinite  distance  upon  the  largest  aggrega- 
tion of  matter  in  the  universe.  If  we  electrify  it,  as  in  the  cathode 
rays,  its  properties  are  so  changed  that  the  matter  properties  are  com- 
pletely masked  by  the  electromagnetic. 

It  is  a  common  error  which  young  physicists  are  apt  to  fall  into  to 
obtain  a  law,  a  curve  or  a  mathematical  expression  for  given  experi- 
mental limits  and  then  to  apply  it  to  points  outside  those  limits.  This 
is  sometimes  called  extrapolation.  Such  a  process,  unless  carefully 
guarded,  ceases  to  be  a  reasoning  process  and  becomes  one  of  pure 
imagination  specially  liable  to  error  when  the  distance  is  too  great. 

But  it  is  not  my  purpose  to  enter  into  detail.  What  I  have  given 
suffices  to  show  how  little  we  know  of  the  profounder  questions  involved 
in  our  subject. 

It  is  a  curious  fact  that,  having  minds  tending  to  the  infinite,  with 
imaginations  unlimited  by  time  and  space,  the  limits  of  our  exact 
knowledge  are  very  small  indeed.  In  time  we  are  limited  by  a  few 
hundred  or  possibly  thousand  years:  indeed  the  limit  in  our  science  is 
far  less  than  the  smaller  of  these  periods.  In  space  we  have  exact 
knowledge  limited  to  portions  of  our  earth's  surface  and  a  mile  or  so 
below  the  surface,  together  with  what  little  we  can  learn  from  looking 
through  powerful  telescopes  into  the  space  beyond.  In  temperature 
our  knowledge  extends  from  near  the  absolute  zero  to  that  of  the  sun 
but  exact  knowledge  is  far  more  limited.  In  pressures  we  go  from  the 
Crookes  vacuum  still  containing  myriads  of  flying  atoms  to  pressures 
limited  by  the  strength  of  steel  but  still  very  minute  compared  with  the 
pressures  at  the  centre  of  the  earth  and  sun,  where  the  hardest  steel 
would  flow  like  the  most  limpid  water.  In  velocities  we  are  limited  to 
a  few  miles  per  second;  in  forces,  to  possibly  100  tons  to  the  square 
inch;  in  mechanical  rotations,  to  a  few  hundred  times  per  second. 


676  HENRY  A.  ROWLAND 

All  the  facts  which  we  have  considered,  the  liability  to  error  in  what- 
ever direction  we  go,  the  infirmity  of  our  minds  in  their  reasoning 
power,  the  fallibility  of  witnesses  and  experimenters,  lead  the  scientist 
to  be  specially  skeptical  with  reference  to  any  statement  made  to  him 
or  any  so-called  knowledge  which  may  be  brought  to  his  attention.  The 
facts  and  theories  of  our  science  are  so  much  more  certain  than  those  of 
history,  of  the  testimony  of  ordinary  people  on  which  the  facts  of 
ordinary  history  or  of  legal  evidence  rest,  or  of  the  value  of  medicines  to 
which  we  trust  when  we  are  ill,  indeed  to  the  whole  fabric  of  supposed 
truth  by  which  an  ordinary  person  guides  his  belief  and  the  actions  of 
his  life,  that  it  may  seem  ominous  and  strange  if  what  I  have  said  of 
the  imperfections  of  the  knowledge  of  physics  is  correct.  How  shall  we 
regulate  our  minds  with  respect  to  it:  there  is  only  one  way  that  I 
know  of  and  that  is  to  avoid  the  discontinuity  of  the  ordinary,  indeed 
the  so-called  cultivated  legal  mind.  There  is  no  such  thing  as  absolute 
truth  and  absolute  falsehood.  The  scientific  mind  should  never  recog- 
nize the  perfect  truth  or  the  perfect  falsehood  of  any  supposed  theory 
or  observation.  It  should  carefully  weigh  the  chances  of  truth  and 
error  and  grade  each  in  its  proper  position  along  the  line  joining  abso- 
lute truth  and  absolute  error. 

The  ordinary  crude  mind  has  only  two  compartments,  one  for  truth 
and  one  for  error;  indeed  the  contents  of  the  two  compartments  are 
sadly  mixed  in  most  cases:  the  ideal  scientific  mind,  however,  has  an 
infinite  number.  Each  theory  or  law  is  in  its  proper  compartment  indi- 
cating the  probability  of  its  truth.  As  a  new  fact  arrives  the  scientist 
changes  it  from  one  compartment  to  another  so  as,  if  possible,  to  always 
keep  it  in  its  proper  relation  to  truth  and  error.  Thus  the  fluid  nature 
of  electricity  was  once  in  a  compartment  near  the  truth.  Faraday's  and 
Maxwell's  researches  have  now  caused  us  to  move  it  to  a  compartment 
nearly  up  to  that  of  absolute  error. 

So  the  law  of  gravitation  within  planetary  distances  is  far  toward 
absolute  truth,  but  may  still  need  amending  before  it  is  advanced  farther 
in  that  direction. 

The  ideal  scientific  mind,  therefore,  must  always  be  held  in  a  state 
of  balance  which  the  slightest  new  evidence  may  change  in  one  direction 
or  another.  It  is  in  a  constant  state  of  skepticism,  knowing  full  well 
that  nothing  is  certain.  It  is  above  all  an  agnostic  with  respect  to  all 
facts  and  theories  of  science  as  well  as  to  all  other  so-called  beliefs  and 
theories. 

Yet  it  would  be  folly  to  reason  from  this  that  we  need  not  guide  our 


THE  HIGHEST  AIM  OF  THE  PHYSICIST  677 

life  according  to  the  approach  to  knowledge  that  we  possess.  ,  Nature  is 
inexorable;  it  punishes  the  child  who  unknowingly  steps  off  a  precipice 
quite  as  severely  as  the  grown  scientist  who  steps  over,  with  full  knowl- 
edge of  all  the  laws  of  falling  bodies  and  the  chances  of  their  being 
correct.  Both  fall  to  the  bottom  and  in  their  fall  obey  the  gravitational 
laws  of  inorganic  matter,  slightly  modified  by  the  muscular  contortions 
of  the  falling  object  but  not  in  any  degree  changed  by  the  previous 
belief  of  the  person.  Natural  laws  there  probably  are,  rigid  and  un- 
changing ones  at  that.  Understand  them  and  they  are  beneficent:  we 
can  use  them  for  our  purposes  and  make  them  the  slaves  of  our  desires. 
Misunderstand  them  and  they  are  monsters  who  may  grind  us  to  powder 
or  crush  us  in  the  dust.  Nothing  is  asked  of  us  as  to  our  belief:  they 
act  unswervingly  and  we  must  understand  them  or  suffer  the  conse- 
quences. Our  only  course,  then,  is  to  act  according  to  the  chances  of 
our  knowing  the  right  laws.  If  we  act  correctly,  right;  if  we  act  incor- 
rectly, we  suffer.  If  we  are  ignorant  we  die.  What  greater  fool,  then, 
than  he  who  states  that  belief  is  of  no  consequence  provided  it  is  sincere. 
An  only  child,  a  beloved  wife,  lies  on  a  bed  of  illness.  The  physician 
says  that  the  disease  is  mortal;  a  minute  plant  called  a  microbe  has 
obtained  entrance  into  the  body  and  is  growing  at  the  expense  of  its 
tissues,  forming  deadly  poisons  in  the  blood  or  destroying  some  vital 
organ.  The  physician  looks  on  without  being  able  to  do  anything. 
Daily  he  comes  and  notes  the  failing  strength  of  his  patient  and  daily 
the  patient  goes  downward  until  he  rests  in  his  grave.  But  why  has  the 
physician  allowed  this?  Can  we  doubt  that  there  is  a  remedy  which 
shall  kill  the  microbe  or  neutralize  its  poison?  Why,  then,  has  he  not 
used  it?  He  is  employed  to  cure  but  has  failed.  His  bill  we  cheerfully 
pay  because  he  has  done  his  best  and  given  a  chance  of  cure.  The 
answer  is  ignorance.  The  remedy  is  yet  unknown.  The  physician  is 
waiting  for  others  to  discover  it  or  perhaps  is  experimenting  in  a  crude 
and  unscientific  manner  to  find  it.  Is  not  the  inference  correct,  then, 
that  the  world  has  been  paying  the  wrong  class  of  men?  Would  not 
this  ignorance  have  been  dispelled  had  the  proper  money  been  used  in 
the  past  to  dispel  it?  Such  deaths  some  people  consider  an  act  of  God. 
What  blasphemy  to  attribute  to  God  that  which  is  due  to  our  own  and 
our  ancestors'  selfishness  in  not  founding  institutions  for  medical  re- 
search in  sufficient  number  and  with  sufficient  means  to  discover  the 
truth.  Such  deaths  are  murder.  Thus  the  present  generation  suffers 
for  the  sins  of  the  past  and  we  die  because  our  ancestors  dissipated  their 
wealth  in  armies  and  navies,  in  the  foolish  pomp  and  circumstance  of 


678  HENRY  A.  ROWLAND 

society,  and  neglected  to  provide  us  with  a  knowledge  of  natural  laws. 
In  this  sense  they  were  the  murderers  and  robbers  of  future  generations 
of  unborn  millions  and  have  made  the  world  a  charnel  house  and  place 
of  mourning  where  peace  and  happiness  might  have  been.  Only  their 
ignorance  of  what  they  were  doing  can  be  their  excuse,  but  this  excuse 
puts  them  in  the  class  of  boors  and  savages  who  act  according  to  selfish 
desire  and  not  to  reason  and  to  the  calls  of  duty.  Let  the  present  gener- 
ation take  warning  that  this  reproach  be  not  cast  on  it,  for  it  cannot 
plead  ignorance  in  this  respect. 

This  illustration  from  the  department  of  medicine  I  have  given  be- 
cause it  appeals  to  all.  But  all  the  sciences  are  linked  together  and 
must  advance  in  concert.  The  human  body  is  a  chemical  and  physical 
problem,  and  these  sciences  must  advance  before  we  can  conquer  disease. 

But  the  true  lover  of  physics  needs  no  such  spur  to  his  actions.  The 
cure  of  disease  is  a  very  important  object  and  nothing  can  be  nobler  than 
a  life  devoted  to  its  cure. 

The  aims  of,  the  physicist,  however,  are  in  part  purely  intellectual: 
he  strives  to  understand  the  universe  on  account  of  the  intellectual 
pleasure  derived  from  the  pursuit,  but  he  is  upheld  in  it  by  the  knowl- 
edge that  the  study  of  nature's  secrets  is  the  ordained  method  by  which 
the  greatest  good  and  happiness  shall  finally  come  to  the  human  race. 

Where,  then,  are  the  great  laboratories  of  research  in  this  city,  in 
this  country,  nay,  in  the  world?  We  see  a  few  miserable  structures  here 
and  there  occupied  by  a  few  starving  professors  who  are  nobly  striving 
to  do  the  best  with  the  feeble  means  at  their  disposal.  But  where  in 
the  world  is  the  institute  of  pure  research  in  any  department  of  science 
with  an  income  of  $100,000.000  per  year?  Where  can  the  discoverer  in 
pure  science  earn  more  than  the  wages  of  a  day  laborer  or  cook?  But 
$100,000,000  per  year  is  but  the  price  of  an  army  or  of  a  navy  designed 
to  kill  other  people.  Just  think  of  it,  that  one  per  cent  of  this  sum 
seems  to  most  people  too  great  to  save  our  children  and  descendants 
from  misery  and  even  death! 

But  the  twentieth  century  is  near — may  we  not  hope  for  better  things 
before  its  end?  May  we  not  hope  to  influence  the  public  in  this 
direction? 

Let  us  go  forward,  then,  with  confidence  in  the  dignity  of  our  pur- 
suit. Let  us  hold  our  heads  high  with  a  pure  conscience  while  we  seek 
the  truth,  and  may  the  American  Physical  Society  do  its  share  now  and 
in  generations  yet  to  come  in  trying  to  unravel  the  great  problem  of 
the  constitution  and  laws  of  the  universe. 


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9.  Note  on  Kohlrausch's  Determination  of  the  Absolute  Value  of  the 

Siemens  Mercury  Unit  of  Electrical  Resistance. 
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American  Journal  of  Science  (3),  X,  14-17,  1875. 

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See  also  Monatsberichte  Akad.  Berlin,  pp.  211-216,  1876. 

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14.  Note  on  the  Theory  of  Electric  Absorption. 

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15.  Kesearch  on  the  Absolute  Unit  of  Electrical  Eesistance. 

American  Journal  of  Science  (3),  XV,  281-291,  325-336,  430-439,  1878. 

16.  On  the  Mechanical  Equivalent  of  Heat,  with  Subsidiary  Eesearches 

on  the  Variation  of  the  Mercurial  from  the  Air-Thermometer  and 

on  the  Variation  of  the  Specific  Heat  of  Water. 

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75-200,  1880. 
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17.  On  Professors  Ayrton  and  Perry's  New  Theory  of  the  Earth's  Mag- 

netism, with  a  Note  on  a  New  Theory  of  the  Aurora. 
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American  Journal  of  Science  (3),  XVIH,  360-371,  1879. 

19.  Preliminary  Notes  on  Mr.  Hall's  Eecent  Discovery. 

American  Journal  of  Mathematics,  II,  354-356,  1879. 
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20.  Physical  Laboratory ;   Comparison  of  Standards. 

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Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  XVI, 

38-45,  1881. 
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22.  On  the  Efficiency  of  Edison's  Electric  Light.     By  H.  A.  Eowland 

and  G.  F.  Barker. 
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Bodies  are  Present. 

American  Journal  of  Mathematics,  III,»  226-268,   1880. 

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BIBLIOGRAPHY  683 

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Rotation  of  Polarized  Light. 
Philosophical  Magazine  (5),  XI,  254-261,  1881. 

26.  On  Geissler  Thermometers. 

American  Journal  of   Science   (3),  XXI,  451-453,  1881. 

27.  Electric  Absorption  of  Crystals.     By  H.  A.  Rowland  and  E.  L. 

Nichols. 

Philosophical  Magazine  (5),  XI,  414-419,  1881. 
Proceedings  of  the  Physical  Society,  IV,  215-221,  1881. 

28.  On  Atmospheric  Electricity. 

Johns  Hopkins  University  Circulars  No.  19,  pp.  4,  5,  1882. 

29.  Preliminary  Notice  of  the  Results  Accomplished  in  the  Manufacture 

and  Theory  of  Gratings  for  Optical  Purposes. 
Johns  Hopkins  University  Circulars,  No.  17,  pp.  248,  249,  1882. 
Philosophical  Magazine   (4),  XIII,  469-474,  1882. 
Nature,  26,  211-213,  1882. 
Journal  de  Physique,  II,  5-11,  1883. 

30.  On  Concave  Gratings  for  Optical  Purposes. 

American  Journal  of  Science   (3),  XXVI,  87-98,  1883. 
Philosophical  Magazine   (5),  XVI,  197-210,  1883. 

31.  On  Mr.  Glazebrook's  Paper  on  the  Aberration  of  Concave  Gratings. 

American  Journal  of  Science   (3),  XXVI,  214,  1883. 
Philosophical  Magazine   (5),  XVI,  210,  1883. 

32.  On  the  Propagation  of  an  Arbitrary  Electro-magnetic  Disturbance, 

on   Spherical  Waves   of  Light  and  the  Dynamical   Theory  of 

Diffraction. 

American  Journal  of  Mathematics,  VI,  359-381,  isot. 
Philosophical  Magazine   (5),  XVII,  413-437,  1884. 

33.  Screw. 

Encyclopaedia  Britannica,  Ninth  Edition,  Vol.  21. 

34.  The  Determination  of  the  Ohm.     Extract  from  a  letter  to  the  Inter- 

national Congress  at  Paris,  1884. 

Proces-Verbaux,  Deuxieme  Session,  p.  37,  Paris  1884. 

35.  The  Theory  of  the  Dynamo. 

Keport  of  the  Electrical  Conference  at  Philadelphia  in  November, 

1884,  pp.  72-83,  90,  91,  104,  107.     Washington,  1886. 
Electrical  Keview  (N.  Y.),  Nov.  1,  8,  15,  22,  1884. 

36.  On  Lightning  Protection. 

Report  of  the  Electrical  Conference  at  Philadelphia  in  November, 
1884,  pp.  172-174. 


684  HENRY  A.  ROWLAND 

37.  On  the  Value  of  the  Ohm. 

La  Lumiere  Electrique,  XXVI,  pp.  188,  477,  1887. 

38.  On  a  Simple  and  Convenient  Form  of  Water-battery. 

American  Journal  of  Science  (3),  XXXIII,  147,  1887. 

Philosophical  Magazine  (5),  XXIII,  303,  1887. 

Johns  Hopkins  University  Circulars   No.   57,   p.   80,   1887. 

39.  On  the  Eelative  Wave-lengths  of  the  Lines  of  the  Solar  Spectrum. 

American  Journal  of  Science   (3),  XXXIII,  182-190,  1887. 
Philosophical  Magazine  (5),  XXIII,  257-265,  1887. 

40.  On  an  Explanation  of  the  Action  of  a  Magnet  on  Chemical  Action. 

By  H.  A.  Eowland  and  Louis  Bell. 
American  Journal  of  Science    (3),  XXXVI,  39-47,   1888. 
Philosophical  Magazine  (5),  XXVI,  105-114,  1888. 

41.  Table  of  Standard  Wave-lengths. 

Philosophical   Magazine    (5),   XXVII,   479-484,   1889. 
Johns  Hopkins  University  Circulars  No.  73,  p.  69,  1889. 

42.  A  Few  Notes  on  the  Use  of  Gratings. 

Johns  Hopkins  University  Circulars  No.  73,  pp.  73,  74,  1889. 

43.  On  the  Electro-magnetic  Effect  of  Convection-Currents.     By  H.  A. 

Rowland  and  C.  T.  Ilutchinson. 
Philosophical  Magazine  (5),  XXVII,  445-460,  1889. 

44.  On  the  Ratio  of  the  Electro-static  to  the  Electro-magnetic  Unit  of 

Electricity.     By  H.  A.  Rowland,  E.  H.  Hall,  and  L.  B.  Fletcher. 
American  Journal  of  Science  (3),  XXXVIII,  289-298,  1889. 
Philosophical  Magazine   (5),  XXVIII,  304-315,   1889. 

45.  Electro-magnetic  Waves  and  Oscillations  at  the  Surface  of  Con- 

ductors. 
American  Journal  of  Mathematics,  XI,  373-387,  1889. 

46.  Report  of  Progress  in  Spectrum  Work. 

The  Chemical  News,  LXIII,  133,  1891. 

Johns  Hopkins  University  Circulars  No.  85,  pp.  41,  42,  1891. 

American  Journal  of  Science  (3),  XLI,  243,  244,  1891. 

47.  Notes  on  the  Theory  of  the  Transformer. 

Philosophical  Magazine   (5),  XXXIV,  54-57,  1892. 

Electrical  World  XX,   20,   1892. 

Johns  Hopkins  University  Circulars  No.  99,  pp.  104,  105,  1892. 

48.  Notes  on  the  Effect  of  Harmonics  in  the  Transmission  of  Power  by 

Alternating  Currents. 
Electrical  World,  XX,  368,  1892. 
La  Lumiere  Electrique,  XLVII,  42-44,  1893. 


BIBLIOGRAPHY  685 

49.  Gratings  in  Theory  and  Practice. 

Philosophical  Magazine  (5),  XXXV,  397-419,  1893. 
Astronomy   and  Astro-Physics,  XII,   129-149,   1893. 

50.  A  New  Table  of  Standard  Wave-lengths. 

Philosophical  Magazine   (5),   XXXVI,  49-75,   1893. 

Astronomy   and   Astro-Physics,   XII,   321-347,   1893. 

Johns  Hopkins   University  Circulars  No.   106,   p.   110,   1893. 

51.  On  a  Table  of  Standard  Wave-lengths  of  the  Spectral  Lines. 

Memoirs  of  the  American  Academy  of  Arts  and  Sciences,  XII,  101- 
186,  1896. 

52.  The  Separation  of  the  Bare  Earths. 

Johns  Hopkins  University  Circulars  No.  112,  pp.  73,  74,  1894. 

53.  Modern  Theories  as  to  Electricity. 

The  Engineering  Magazine,  VIII,  589-596,  1895. 

54.  A  Preliminary  Table  of  Solar  Spectrum  Wave-lengths. 

Astrophysical  Journal,   I-V,   1895-1897. 

55.  Corrections  and  Additions  to  Professor  H.  A.  Rowland's  Table  of 

Solar  Spectrum  Wave-lengths. 
Astrophysical  Journal  VI,  384-392,  1897. 

56.  The  Arc-Spectra  of  the  Elements.     I.  Boron  and  Beryllium.     II. 

Germanium.     III.  Platinum  and  Osmium.     IV.  Rhodium,  Ru- 
thenium and  Palladium.    By  II.  A.  Rowland  and  R.  R.  Tatnall. 
Astrophysical  Journal,  I,   14-17,   149-153,   1895;  II,   184-187,   1895;   m, 
286-291,  1896. 

57.  Notes  of  Observations  on  the  Rontgen  Rays.     By  H.  A.  Rowland, 

N.  R.  Carmichael  and  L.  J.  Briggs. 

American  Journal  of  Science  (4),  I,  247,  248,  1896. 

Philosophical  Magazine   (5),  XLI,  381-382,  1896. 

58.  Notes  on  Rontgen  Rays.     By  H.  A.  Rowland,  N.  R.  Carmichael  and 

L.  J.  Briggs. 
Electrical  World,   XXVII,   452,   1896. 

59.  The  Rontgen  Ray  and  its  Relation  to  Physics. 

Transactions   of   the   American   Institute    of   Electrical    Engineers, 
XIII,  403-410,  430,  431,  1896. 

60.  Electrical  Measurement  by  Alternating  Currents. 

American  Journal  of  Science  (4),  IV,  429-448,  1897. 
Philosophical  Magazine   (5),  XLV,  66-85,  1898. 

61.  Arc-Spectra  of  Vanadium,  Zirconium  and  Lanthanum.     By  H.  A. 

Rowland  and  C.  N.  Harrison. 

Astrophysical  Journal,  VII,  273-294,  373-389,  1898. 


686  HENRY  A.  KOWLAND 

62.  Electrical  Measurements.     By  H.  A.  Eowland  and  T.  D.  Penniman. 

American  Journal  of  Science   (4),  VIII,  35-57,  1899. 
Johns    Hopkins    University     Circulars    No.     135,    pp.     51,     52,     1898 
(abstract) . 

63.  Eesistance  to  Ethereal  Motion.     By  H.  A,  Eowland,  N.  E.  Gilbert 

and  P.  C.  McJunckin. 

Johns  Hopkins  University  Circulars  No.  146,  p.  60,  1900. 

64.  Diffraction  Gratings. 

Encyclopaedia  Britannica,  New  Volumes,  III,  458,  459,  1902. 

ADDEESSES 

1.  A  Plea  for  Pure  Science.  Address  as  Vice-President  of  Section  B 
of  the  American  Association  for  the  Advancement  of  Science, 
Minneapolis,  August  15,  1883. 

Proceedings  of  the  American  Association  for  the  Advancement  of 

Science,  XXXII,  105-126,  1883. 
Science,  II,  242-250,  1883. 
Journal  of  the  Franklin  Institute,  CXVI,  279-299,  1883. 

2.  The  Physical  Laboratory  in  Modern  Education.     Address  for  Com- 

memoration Day  of  the  Johns  Hopkins  University,   February 

22,  1886. 

Johns  Hopkins  University  Circulars  No.  50,  pp.  103-105,  1886. 

3.  Address  as  President  of  the  Electrical  Conference  at  Philadelphia, 

September  8,  1884. 

Report  of  the  Electrical  Conference  at  Philadelphia  in  September, 
1884,  Washington,  1886. 

4.  The  Electrical  and  Magnetic  Discoveries  of  Faraday.     Address  at 

the  Opening  of  the  Electrical  Club  House  of  New  York  City, 

1888. 

Electrical  Review,  Feb.  4,  1888. 

5.  On  Modern  Views  with  Eespect  to  Electric   Currents.     Address 

before   the   American   Institute   of   Electrical   Engineers,   New 
York,  May  22,  1889. 

Transactions  of  the  American  Institute  of  Electrical  Engineers,  VI, 

342-357,  1889. 
Electrical  World,  XIII,  p.  319,  1889. 

See  also  Electrical  World,  XIII,  p.  142,  1889. 


BIBLIOGRAPHY  687 

6.  The  Highest  Aim  of  the  Physicist.     Address  as  President  of  the 
American  Physical  Society,  New  York,  October  28,  1899. 
Science,   X,   825-833,   1899. 

American  Journal  of  Science  (4),  VIII,  401-411,  1899. 
Johns  Hopkins  University  Circulars  No.  143,  pp.  17-20,  1900. 

REPORTS  AND  BOOKS 

1.  Report  of  the  Electrical  Commission  Appointed  to  Consider  the 

Location,  Arrangement  and  Operation  of  Electric  Wires  in  the 

District  of  Columbia.     Washington,  1892. 

By  Andrew  Rosewater,  H.  A.  Rowland,  and  Francis  R.  Skunk. 

2.  Elements  of  Physics. 

By  H.  A.  Rowland  and  J.  S.  Ames,  New  York,  1900,  XIII  +  263.  pp. 


DESCRIPTION 

OF 

DIVIDING   ENGINES 


44 


UN'    f.RSITY 


A  DESCRIPTION  OF  THE  DIVIDING  ENGINES  DESIGNED 
BY  PROFESSOR  ROWLAND.1 

Three  dividing  engines  were  made  under  Professor  Rowland's  direc- 
tion, all  embodying  the  same  general  principles  as  given  in  his  article 
on  the  "  Screw  "  in  the  Encyclopedia  Britannica  (this  volume  p.  506). 
The  screws  of  all  three  have  approximately  twenty  threads  to  the  inch; 
and  the  number  of  teeth  in  the  ratchet  wheels  of  the  first,  second  and 
third  machines  is  such  that  they  rule  14,438,  15,020  and  20,000  lines  in 
an  inch.  The  three  machines  are  kept  in  the  sub-basement  of  the 
Physical  Laboratory  of  the  Johns  Hopkins  University  under  such  con- 
ditions as  will  secure  a  practically  constant  temperature  for  long 
intervals  of  time.  Each  machine  is  driven  by  a  separate  water-motor 
whose  speed  can  be  regulated  at  will. 

The  machines  have  been  used  almost  exclusively  for  the  ruling  of 
Diffraction  gratings,  although  a  few  centimetre  scales  have  been  made. 
The  gratings  have  been,  with  only  four  or  five  exceptions,  made  of 
"  speculum  metal/'  having  the  composition,  copper  126  Ibs.  4  oz.,  tin 
58  Ibs.  9  oz.,  and  as  homogeneous  as  possible.  The  rough  metal  plates 
were  cast  under  Professor  Rowland's  direction,  and  were  then  figured 
and  polished.  After  the  ruling  was  completed,  the  gratings  were  care- 
fully tested  in  order  to  see  if  they  were  free  from  "ghosts,"  diffused 
light  and  defective  definition. 

To  test  the  screw,  ratchet-head  and  thrust  screw  for  periodic  errors, 
P-ofessor  Rowland  used  the  following  method:  he  ruled  a  space  of 
about  one  centimetre  on  a  polished  surface,  then  pushed  the  carriage 
ba-'k  this  distance,  turned  the  grating-holder  through  a  minute  angle 
ai  again  ruled  a  surface  of  about  the  same  width  as  before.  There  is 
th  -  produced  a  cross-ruling,  the  lines  being  slightly  inclined  to  each 
ot;'?r;  and  when  examined  by  reflected  light,  a  series  of  undulations  is 

1  Unfortunately  Professor  Rowland  never  published  a  description  of  these  machines ; 
&nC  the  Committee  has  failed  to  find  any  information  concerning  the  inception  of 
the  idea  or  the  history  of  the  construction  of  the  first  machine.  It  has  been 
thought  best,  therefore,  to  give,  first,  a  general  description  of  the  design  of  the 
engines  with  various  necessary  details  of  some  of  the  working  parts  and,  second, 
drawings  made  to  scale,  showing  all  the  connections  of  the  intricate  mechanism ; 
both  of  these  have  been  prepared  under  the  direction  of  J.  8.  Ames,  Secretary  of 
the  Committee,  and  have  been  approved  by  the  Committee. 


692  HENRY  A.  KOWLAND 

seen  to  cross  the  lines  at  right  angles,  corresponding  to  the  points  of 
intersection  of  the  two  sets  of  rulings.  This  pattern  resembles  closely 
in  appearance  that  of  watered  silk.  The  corrector  of  the  machine  is 
adjusted  until  this  undulatory  pattern  is  as  regular  and  has  as  small 
an  amplitude  as  possible. 

Any  description  of  Eowland's  dividing  engines,  however  brief,  would 
be  incomplete  without  some  mention  of  Mr.  Theodore  Schneider  who 
for  twenty-five  years  was  Professor  Eowland's  mechanician  and  assistant 
and  who  died  only  a  few  weeks  before  him.  It  was  he  who  made  the 
screws  and  most  of  the  working  parts  of  the  machines,  and  it  was  he 
who  superintended  the  ruling  of  every  grating  that  has  left  the  Physical 
Laboratory  of  the  Johns  Hopkins  University  for  use  elsewhere  in  the 
world. 

GENERAL  DESIGN  OF  DIVIDING  ENGINE* 

The  object  of  this  machine  is  to  rule  straight  lines  on  metal  or  glass 
surfaces,  exactly  parallel  and  at  exactly  equal  distances  apart.  The  sur- 
face to  be  ruled  is  attached  to  a  frame  which  is  moved  forward  by  a  nut 
as  it  is  advanced  by  a  screw;  the  ruling  edge  is  generally  a  diamond 
mounted  in  such  a  manner  as  to  be  drawn  to  and  fro  across  the  surface  to 
be  ruled,  but  to  be  in  contact  with  it  during  <only  one  of  these  motions. 

Kotary  motion  is  imparted  to  the  main  shaft  (48  A)  by  means  of  a 
driving  pulley,  operated  by  a  belt  attached  to  a  water  motor  (not  shown 
in  the  cuts).  Mounted  on  the  main  shaft  are  the  cams  (46,  47)  for 
operating  the  pawl-levers,  which  turn  the  screw  and  advance  the  nut; 
the  cam  (55)  controlling  the  mechanism  for  raising  the  diamond;  and 
the  crank  (50)  which  by  means  of  the  connecting  rod  and  cross-head 
impart  a  reciprocating  motion  to  the  ruling  carriage  and  its  diamond. 
By  means  of  adjustments  in  the  crank  and  connecting  rod,  the  length 
of  stroke  of  the  diamond  may  be  varied,  and  rulings  of  different  lengths 
are  thus  obtained. 

In  each  revolution  of  the  main  shaft,  the  cycle  of  operations  that  occur 
is  as  follows:  Let  the  diamond  be  on  the  plate  in  a  position  to  begin 
ruling.  It  is  moved  forward,  i.  e.  toward  the  shaft,  by  means  of  the 
ruling  frame  and  parts  described,  and  a  line  is  ruled.  The  stroke  of 
the  engine  being  now  about  to  reverse,  the  cam  controlling  the  mechan- 
ism for  lifting  the  diamond  performs  its  duty;  and,  while  the  engine 
is  on  its  return  stroke,  with  the  diamond  off  the  plate,  the  latter  is 

2  The  figures  in  the  text  refer  to  the  numbered  parts  in  the  cuts  which  follow  the 
article. 


DESCRIPTION  OF  THE  DIVIDING  ENGINES  693 

advanced  a  space  equal  to  the  desired  distance  between  the  rulings. 
This  is  done  by  the  cams  operating  the  pawl-levers  (26  and  40),  which 
cause  the  pawl  (41)  to  rise  to  a  pre-determined  position  corresponding 
to  one  or  more  teeth  of  the  graduated  ratchet  head,  then  to  engage  this 
wheel  and,  being  now  forced  down  to  its  normal  position,  to  cause  the 
wheel  and  the  feed-screw,  to  which  it  is  attached,  to  turn  through  a 
small  definite  angle.  The  rotation  of  the  screw  causes  the  nut  to 
advance  towards  the  ratchet  head;  and  the  nut  pushes  forward  the 
plate-carriage  to  which  the  plate  to  be  ruled  is  secured.  The  engine 
being  now  at  the  end  of  its  return  stroke,  the  diamond  is  lowered  into 
contact  with  the  plate,  and  is  ready  for  ruling  the  next  line.  These 
operations  are  repeated  until  the  requisite  number  of  lines  is  ruled. 
During  each  cycle  of  operations  a  slight  additional  motion  is  imparted 
to  the  nut  and  thus  to  the  plate-carriage  by  means  of  the  corrector 
mechanism,  in  order  that  any  periodic  errors  of  the  screw,  screw-head, 
etc.,  may  be  eliminated. 

The  ruling-carriage  with  its  diamond  holder  moves  along  truncated 
V-ways,  as  shown  in  the  cuts,  the  surfaces  in  contact  being  the 
steel  ways  and  the  box-wood  linings  to  the  grooves  on  the  carriage. 
These  box-wood  linings  press  against  both  the  sides  and  the  top  of  the 
ways  and  are  adjustable.  The  plate-carriage  moves  along  V-ways,  the 
surfaces  in  contact  being  the  steel  ways  and  the  cast-iron  carriage. 
These  two  pairs  of  ways  are  accurately  at  right  angles  to  each  other. 

DETAILED  DESCRIPTIONS 

I.  Mechanism  connecting  the  plate-carriage  and  the  nut.     See  Fig.  5. 
The  plate-carriage  carries  a  thrust  collar  (20)  through  which  the 

feed-screw  passes  freely.  It  is  held  in  position  by  pins  engaging  in  the 
top  and  bottom  of  the  plate-carriage.  The  thrust  of  the  nut  in  advan- 
cing is  communicated  by  two  lugs,  one  on  each  side  of  the  nut  casings 
(21),  to  two  correspondingly  located  screw-heads  in  the  thrust  collar; 
and,  finally,  screw-heads  in  the  top  and  bottom  of  the  thrust-collar 
transfer  the  thrust  to  correspondingly  located  lugs  (22)  in  the  plate- 
carriage. 

II.  Pawl  mechanism.     See  Fig.  4. 

The  degree  of  rotation  imparted  to  the  graduated  ratchet-head  de- 
pends upon  the  number  of  teeth  the  pawl  engages  in  each  revolution 
of  the  main-shaft  and  may  be  varied  by  altering  the  size  of  the  cams 
(46  and  47)  on  which  the  pawl-levers  26  and  40  rest.  The  pawl-lever 


694  HENRY  A.  ROWLAND 

(26),  to  which  the  bell-crank  (42)  is  pivoted,  causes  the  pawl  to  rise  to  a 
height  corresponding  to  the  number'  of  teeth  to  be  engaged  on  the 
graduated  ratchet-head.  The  other  lever  (40)  has  the  function  of 
engaging  and  disengaging  the  pawl.  The  cycle  of  operations  that 
occurs  in  one  revolution  of  the  main  shaft  is  as  follows:  The  pawl-lever 
(26)  is  raised  by  the  cam  (47),  and  in  so  doing  gauges  the  degree  of 
revolution  to  be  imparted  to  the  graduated  ratchet-head  and  feed- 
screw. The  other  lever  (40),  which  is  pivoted  on  the  pawl-lever  (26), 
is  raised  further,  and  thereby  permits  cam  (46)  and  the  bell-crank  (42) 
to  carry  the  pawl  (41)  forward  into  engagement  with  the  graduated 
ratchet-head.  The  weight  (45)  attached  to  the  bell-crank  arm  insures 
a  positive  engagement  of  the  pawl.  The  depth  to  which  the  pawl  enters 
between  the  teeth  of  the  graduated  ratchet-head  is  governed  by  the 
adjusting  screw  (43)  and  a  stop  on  pa,wl-lever  (26).  The  pawl  being 
engaged,  both  levers  (26  and  40)  now  descend,  causing  the  graduated 
ratchet-head  and  feed-screw  to  turn  to  an  extent  governed  by  the 
number  of  teeth  engaged.  Lever  (40)  now  descends  to  a  position  coin- 
cident with  that  of  the  lever  (26),  and  in  so  doing  causes  the  stop  on 
lever  (40)  to  press  against  the  adjusting  screw  (44)  on  the  bell-crank, 
and  thereby  withdraws  the  pawl  from  the  teeth  of  the  graduated  ratchet- 
head. 

III.  Diamond  and  ruling  head.     See  Figs.  1  and  5. 

The  diamond  (1)  is  firmly  secured  by  means  of  solder  in  a  holder 
(2),  which  may  be  adjusted  to  different  inclinations.  The  frame 
carrying  the  diamond,  holder  and  dash-pot  has  an  axle,  centering  in 
bearing  screws  (3)  and  contained  in  an  adjustable  support  (4).  This 
support  may  be  raised  or  lowered  to  meet  the  requirements  of  plates  of 
different  thickness.  Normally,  the  end  of  the  frame  carrying  the 
diamond  and  holder,  owing  to  its  predominance  of  weight,  would  cause 
the  diamond  to  be  in  contact  with  the  plate  continuously.  In  order  to 
raise  it  on  the  return  stroke  of  the  engine,  a  weighted  lift  rod  (57)  is 
caused  to  press  on  the  end  of  the  frame  near  the  dash-pot.  The  height 
to  which  the  diamond  is  thus  lifted  off  the  plate  is  governed  by  nuts, 
which  may  be  adjusted  on  the  stem  of  the  lift-rod  and  which  on  their 
descent  come  to  rest  on  the  plate  56  A. 

The  raising  of  the  weighted  lift-rod  is  primarily  caused  by  cam  (55) 
on  the  main  shaft;  the  intermediate  mechanism  consists  of  the  lever 
(54),  vertical  oscillating  rod  (53),  reciprocating  rod  (35),  rocking  stem 
(34),  and  lifting  lever  (56).  The  action  of  the  dashers  and  dash-pot 


DESCRIPTION  OF  THE  DIVIDING  ENGINES  695 

filled  with,  oil  is  to  dampen  any  vibrations  of  the  frame  which  carries 
the  diamond,  and  to  check  its  descent  on  the  plate. 

IV.  Corrector  mechanism.     See  Figs.  1,  4  and  5. 

The  wear  of  the  threads  contained  in  the  lignum  vitas  plugs  of  the 
split  nut-casing  is  taken  up  by  the  screws  in  the  adjusting  rings  (17), 
bringing  the  two  parts  of  the  nut  closer  to  the  feed-screw.  Each  side 
of  the  nut  is  provided  with  a  wing-shaped  lever,  the  lower  ends  of  which 
are  confined  in  guides  forming  part  of  the  lower  corrector  frame  (39); 
but  they  are  free  to  travel  in  the  direction  that  the  nut  moves.  When 
the  screw  is  turning  and  the  nut  advancing,  these  wings  are  pressed 
tight  against  the  guide-plate  (39  A)  of  the  corrector  frame;  and  thus 
the  nut  will  receive  additional  motions  from  any  displacement  of  the 
corrector.  In  this  manner  periodic  errors  of  the  screw  may  be  neutral- 
ized by  the  action  of  the  corrector.  The  precise  amount  of  correction 
is  controlled  by  the  adjustments  of  the  eccentric  (25).  This  gives  the 
requisite  amount  of  movement  at  the  proper  instants  to  the  corrector 
lever  (28),  which  in  turn  moves  the  rocking  shaft,  corrector  frame, 
crank,  lower  frame  and,  finally,  the  wings  of  the  nut.  The  disc  (24) 
may  be  adjusted  and  clamped,  as  shown  in  Fig.  4,  in  different  positions 
in  the  plane  of  the  graduated  ratchet-head;  and  the  position  of  the 
corrector  eccentric  (25)  with  respect  to  a  fixed  radius  of  the  graduated 
ratchet-head  must  be  such  as  to  make  the  phase  of  the  correction  oppo- 
site that  of  the  periodic  error.  The  amount  of  eccentricity  of  the  eccen- 
tric can  be  varied  by  means  of  set-screws,  as  is  evident  from  the  cut; 
and  this  must  be  regulated  so  that  the  amplitude  of  the  correction 
equals  that  of  the  periodic  error. 

DESCRIPTIVE  DRAWINGS  OF  DIVIDING  ENGINE  No.  3 

At  the  end  of  this  article  are  five  cuts  of  dividing  engine  No.  3,  drawn 
to  scale,  one  quarter  of  the  actual  size,  showing  different  views  and 
operations.  They  may  be  described  as  follows: 

Fig.  1.     Side  elevation,  showing  the  engine  in  a  ruling  position. 

Fig.  2.     Plan  view  of  the  foregoing. 

Fig.  3.  Plan  view,  showing  the  plate-carriage.  The  plate,  plate- 
holder  and  ruling-head  are  omitted. 

Fig.  4.  Side  elevation  opposite  to  Fig.  1,  showing  the  engine  in 
the  return  stroke  position. 

Fig.  5.  Transverse  sectional  elevation,  showing  the  feed-screw,  nut, 
etc.  The  mechanism  actuating  the  corrector-frame  is  shown  as  an 
end-view. 


696  HENRY  A.  EOWLAND 

Explanation  of  Numbers  in  the  Cuts 
(Similar  numerals  refer  to  like  parts  throughout  the  different  views.) 

1.  Euling  diamond. 

2.  Adjustable  diamond  holder. 

3.  Adjustable  support  for  the  axis  of  the  diamond-frame. 

4.  Euling-head,  carrying  ruling  mechanism. 

5.  Bods  of  the  ruling  carriage. 

6.  Plate  to  be  ruled. 

7.  Adjustable  box-wood  slides  of  ruling  carriage.     (N.  B. — There  are 

box-wood  slides  pressed  against  the  sides  as  well  as  the  top  of 
the  ways  of  the  frame.) 

8.  Plate-holder. 

9.  Clamps  for  plate-holder. 

10.  Bed-plate. 

11.  Plate-carriage,  which  is  moved  by  the  nut  and  which  rests  on  ways. 

(N.   B. — The   plate-carriage  has  a  cross-beam   below  the  feed- 
screw.    See  Fig.  5.) 

12.  Feed-screw. 

13.  Hardened  steel  step  in  end  of  feed-screw. 

14.  Hardened  steel  thrust-screw. 

15.  Casing  of  the  split  nut,  holding  the  plugs  16. 

16.  Lignum  vitas  plugs,  tapped  for  engaging  feed-screw. 

17.  Adjusting  rings  for  nut,  with  their  adjusting  screws. 

18  and  19.  Wings  of  the  nut,  controlled  by  the  corrector,  39  A. 

20.  Thrust  collar,  loosely  attached  to  plate-carriage,  11. 

21.  Abutting  lugs,  rigidly  attached  to  nut-casing  15,  and  in  contact 

with  collar  20. 

22.  Abutting  lugs   of   plate-carriage,  in   contact  with  screw-heads   in 

collar  20. 

23.  Graduated  ratchet-head  attached  to  the  feed-screw. 

24.  Disc  for  phase-adjustment  of  corrector,  being  movable  around  the 

axis  of  the  screw  in  the  plane  of  the  ratchet  wheel. 

25.  Eccentric   for   adjusting   amplitude    of    corrector,    being    movable 

around  an  axis  near  one  end  so  as  to  vary  the  eccentricity. 

26.  Pawl-lever,  which  raises  or  lowers  the  pawl,  when  it  is  disengaged 

or  engaged,  respectively,  in  the  ratchet  wheel  by  means  of  lever 
40. 

27.  Hollow  arbor,  serving  as  pivot  for  pawl-lever. 

28.  Corrector  lever,  resting  on  25,  and  pivoted  at  31. 

29.  Corrector  frame. 


DESCRIPTION  or  THE  DIVIDING  ENGINES  697 

30.  Hardened  steel  centres  for  corrector  frame. 

31.  Eocking  shaft,  rotated  by  means  of  lever  28. 

32.  Bearing  for  wrist-pin  of  lower  corrector  frame. 

33.  Crank  for  rocking  corrector;  a  slight  rotation  of  the  shaft  3?,  thus 

giving  a  slight  sidewise  motion  to  the  frame  39. 

34.  Hocking  stem,  which  moves  the  lifting-lever  56,  of  ruling  head. 

35.  Eod  to  communicate  reciprocating  motion  to  34. 

36.  Base-frame  of  engine. 

37.  Casings  of  ruling  carriage,  holding  the  adjustable  box-wood  slides,  7. 

38.  Adjustable  weight  for  corrector  lever. 

39.  Lower  corrector  frame,  moved  by  the  crank  33. 

39  A.  Corrector  guide-plate,  along  which  the  wings  of  the  nut  move. 

40.  Lever  for  engaging  and  disengaging  pawl,  by  means  of  bell-crank  42. 

41.  Pawl,  driving  ratchet  wheel. 

42.  Bell-crank  which  is  pivoted  on  26;  to  one  end  the  pawl  is  attached, 

and  the  other  is  raised  by  the  lever  40  and  lowered  by  the 
weight  45. 

43  and  44.  Adjusting  screws  attached  to  42,  for  regulating  the  pawl 
engagement.     The  stops  are  attached  to  26  and  40. 

45.  Weight  hanging  from  bell-crank. 

46.  Cam  operating  lever,  40;  attached  to  main  shaft. 

47.  Cam  operating  pawl-lever,  26;  attached  to  main  shaft. 

(These  two  cams  regulate  the  number  of  teeth  of  ratchet  wheel 
which  the  pawl  clears  each  revolution  of  the  main-shaft.) 

48.  Driving  pulley,  attached  to  main  shaft. 
48  A.  Main  shaft. 

49.  Connecting  rod  to  give  reciprocating  motion  to  diamond-holder  by 

means  of  52  and  37. 

50.  Crank  arm,  designed  to  vary  the  length  of  stroke  of  the  diamond. 

51.  Bar  connecting  cross-head  52,  and  ruling  frame  37. 

52.  Cross-head,  driven  by  connecting  rod  49. 

53.  Oscillating  rod,  connecting  35  and  54. 

54.  Lever  operating  stop  mechanism  for  lifting  diamond,  resting  on  55. 

55.  Cam  attached  to  main  shaft  and  operating  the  lever  54. 

56.  Lever  for  lifting  rod  57;  it  is  operated  by  the  rocking-stem  34. 
56  A.  Stop-plate  regulating  drop  of  rod  57. 

57.  Rod  for  lifting  diamond. 

58.  Dash-pot  attached  to  the  lever  which  carries  the  diamond-holder  2, 

and  which  is  pivoted  at  3. 

59.  Adjustments  for  holding  and  regulating  the  dashers. 


FIG.   i 

Side  elevation,  showing  the  engine  in  a  ruling  position 


SIDE   ELEVATION,  SHOWING  T 


L. 


:NGINE  IN  A  RULING  POSITION. 


FIG.  2 

Plan  view  of  the  foregoing 


LJ-T 


FIG.  2. 
PLAN    VIEW    OF  THE   FOREGOING. 


FIG.  3 

Plan  view,  showing  the  plate-carriage.     The  plate,  plate-holder  and 
ruling-head  are  omitted 


46 


:0  !  (O) 


-65 


LnJ 


FIG.  3. 

PLAN  VIEW,  SHOWING  THE  PLATE-CARRIAGE. 
THE  PLATE,  PLATE-HOLDER  AND  RULING-HEAD  ARE  OMITTED. 


FIG.  4 

Side  elevation  opposite  to  Fig.   i,  showing  the  engine  in  the  return 

stroke  position 


SIDE  ELEVATION   OPPOSITE  TO  FIG.  1,  SHOWINi 


HE  ENGINE  IN  THE  RETURN  STROKE  POSITION. 


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INDEX 


Numbers  refer  to  pages. 


Aberration   Problems,   674. 
Abney,  Sir  William  de  W.,  491,  499, 

574. 
Absorption,   Electric,   139,   297,  319, 

321. 
Absorption,    Electric,    of    Crystals, 

204. 
Academy    of    Arts    and     Sciences, 

American,  7,  343,  611. 
Academy  of  Sciences,  National,   1, 

15,  610. 

Academy,  French,  411. 
Aepinus,  626,  639. 
Air-thermometer,  358,  366. 
Alternating  Currents,  276,  280,  294, 

314,  661. 

Amagat,  E.  H.,  410. 
Amaury  (see  Jamin),  344,  388. 
Ames,  J.  S.,  525,  551,  691. 
Ampere,  627,  639. 
Anderson's    Method    of    Measuring 

Resistance,  308. 
Angstrom,  A.  J.,  512,  513,  546,  553, 

555. 

Angstrom's  Scale,  517,  553. 
Arago,  642. 

Archimedes,   619,   620,   621. 
Atmospheric  Electricity,  183,  212. 
Aurora,  Spectrum  of  the,  2,  31. 
Aurora,  Theory  of  the,  179. 
Ayrton,  W.  E.,  179,  182,  183,  213,  278. 


Barker,  George  F.,  3,  200,  364,  570. 
Barometer,    362. 
Basic  Lines  of  Lockyer,  524. 
Battery,  Water,  241. 
Baudin's    Thermometers,    364,    386, 
465. 
45 


Becquerel,  A.  C.,  184,  214. 

Beek,  A.  van,  411. 

Bell,  Graham,  574. 

Bell,  Louis,  242,  513  et  seq.,  545,  546, 

553  et  seq. 

Benzenberg,  J.  F.,  411. 
Berard,  J.  E.,  409,  410. 
Berlin,  University  of,  4,  128. 
Berlin  Academy,  4. 
Biot,  J.  B.,  39,  90,  114,  116,  626,  627, 

639. 

Bosscha,  J.,  408,  465. 
Boyle,  Eobert,  7. 
Brashear,  J.  A.,  9. 
Bravais,  A.,  411. 
Briggs,  L.  J.,  571,  573. 
B.  A.  Unit,  82,  84,  145,  146,  156,  217, 

239. 
Bruce,  Miss,  521. 

O. 

Calorimetry,  387. 

Canton,  John,  625. 

Capacity,  Electric,  297  et  seq.,  314 
et  seq. 

Carmichael,  N.  E.,  571,  573. 

Cathetometer,  361. 

Cavendish,  Henry,  626,  639. 

Cazin,  A.  A.,  36,  48,  410. 

Chapman  (see  Eutherfurd),  8. 

Chemical  Reaction,  Action  of  Mag- 
net on,  242. 

Clarke,  F.  W.,  570. 

Clausius,  E.  J.  E.,  204,  205,  210. 

Clement   (see  Desormes),  410. 

Colardeau,  249. 

Concave  Gratings,  488,  492,  505. 

Condenser,  Standard,  267. 

Convection,  Electric,  128,  138,  179, 
251. 

Copernicus,  614. 


700 


INDEX 


Coulomb,  C.  A.,  95,  96,  103,  119,  120, 

123,  626,  639,  645. 
Cremieu,  V.,  5. 
Crystals,    Electric    Absorption    of, 

204. 
Crystals,    Magnetic    Properties    of, 

187. 


B. 


Daniell,  J.  F.,  641. 

Davy,   Sir  Humphry,   638,   639,   644, 

650. 

De  Morgan,  619. 
Delaroche,    F.,   409,   410. 
Deluc,  J.  A.,  387. 
Desormes,  C.  B.,  410. 
Diamagnetism,  75,  184. 
Distribution,  Magnetic,  80,  85,  89. 
Dividing  Engines,  487,  508,  693. 
Doppler's  Principle,  674. 
Dub,  C.  J.,  36. 
Du  Fay,  639. 
Dulong,  P.  L.,  438. 
Duncan,  Louis,  283. 
Dupre,  Athanase,  410. 


Earths,  The  Rare,  565. 

Echelon  Spectroscope,  590. 

Edelmann,  M.  T.,  266. 

Edison's  Electric  Light,   200. 

Edlund,  E.,  408,  416,  632. 

Electric  Absorption,    139,    297,    319, 

321. 
Electric    Absorption    of    Crystals, 

204. 
Electric   Convection,    128,    138,    179, 

251. 

Electric  Currents,  Theory  of,  653. 
Electric  Light,  Edison's,  200. 
Electric  Units,  10. 
Electric  Units,  Ratio  of,  266. 
Electrical  Congresses,  10,  212,  217. 
Electricity,  Theories  of,  285,  635. 
Electricity,  Atmospheric,  183,  212. 
Electrodynamometer,  268,  284,   294, 

314. 

Electrometer,  Absolute,  266. 
Elements  in  the  Sun,  522. 
Ellis,   Wm.,   357. 

Energy,  Conservation  of,  2,  6,  24. 
Energy    of    Alternating    Currents, 

283. 


Ether,  Properties  of  the,  290  et 
seq.,  338,  580,  586,  632,  667,  673. 

Ethereal  Motion,  Resistance  to, 
338. 

Expansion  of  Air  under  Constant 
Volume,  410. 

F. 

Fairbairn,  Sir  Wm.,  416. 

Faraday,   M.,   24,   26,  40,   43,   56,   89, 

155,   184,  224,  242,   251,  286,  288, 

289,   596,   604,   616,   626,  629,   630, 

638  et  seq.,  660,  666. 
Faraday's   Lines  of  Force,   37,  127, 

286. 

Farrand,  12. 
Fastre's    Thermometers,    365,    386, 

416. 

Faure,  650. 

Favre,  P.  A.,  408,  410,  421. 
Fiske,  Lieut,,  238. 
Fitzgerald,  G.  F.,  229,  231. 
Flaugergues,  H.,  387. 
Fleming,  J.  A.,  278. 
Fletcher,  L.  B.,  266. 
Fortin-barometer,  362. 
Foster,  Henry,  411. 
Foucault,  J.  B.  L.,  674. 
Foucault-currents,  219,  234. 
Frankfort  -  Lauffen      Experiments, 

884. 
Franklin,    Benjamin,    625,    639,   663, 

665,  669. 

Fraunhofer,  J.,  7. 
Fresnel,  A.,  580. 
Friction  Brake,  423. 

G. 

Galileo,  614. 

Galvani,    626,    639. 

Galvanometers,  40,  159,  165,  268. 

Gaugain,  J.  M.,  42. 

Gauss,  97,  148,  181,  626. 

Gay  Lussac,  410. 

Geissler    Thermometers,    465,     478, 

481. 
Ghosts  in  Spectra,  490,  492,  510,  519, 

536. 

Gibbs,  O.  Walcott,  364,  570. 
Gilbert,  N.  E.,  338. 
Gilbert,  William,  624,  639. 
Gilman,  D.  C.,  14,  15. 
Glazebrook,  R.  T.,  240,  505. 


INDEX 


701 


Goldingham,  John,  411. 

Gramme    Armature,    222,    224,    227, 

228. 

Gratings,  7,  487,  492,  587,  525. 
Gratings,  Concave,  488,  492,  505. 
Gratings,  Nobert,  8,  555. 
Gratings,  Manufacture  of,  487,  508, 

693. 

Gratings,  Use  of,  519. 
Gratings,  Wandschaft's,  549. 
Grating-spectroscope,  489,  499,  512, 

551,  588. 

Gravitation,  Cause  of,  292. 
Gravitation,  Law  of,  670. 
Gray,  Stephen,  624,  639,  653. 
Green,  George,  39,  90,  108,  114,  115, 

116,  627,  630. 
Green,  James,  362. 
Grooves    in    Gratings,    Theory    of, 

529  et  seq. 
Guerricke,  Otto  v.,  639. 

H. 

Hall,  E.  H.,  197,  266. 

Hall  Effect,  The,  197. 

Harmonics  in  Alternating  Cur- 
rents, 276,  280,  300,  301. 

Harris  Unit  Jar,  208,  209. 

Harrison,  C.  N.,  685. 

Harvard  University,  5. 

Hastings,  C.  S.,  7,  503. 

Heat,  Mechanical  Equivalent  of,  5, 
343  et  seq.,  469. 

Heaviside,  Oliver,   674. 

Helmholtz,  H.  von,  4,  29,  83,  128, 
131,  138,  159,  167,  179,  251,  314, 
586,  630,  643. 

Henry,  Joseph,  53,  578,  657,  669. 

Hertz,  H.,  289,  580,  658,  659,  673,  674. 

Herwig,  H.  A.  B.,  416. 

Hidden,  570. 

Himstedt,   F.,   5. 

Him,  G.  A.,  344,  388,  408,  410,  416, 
418,  423,  424. 

Holman,  S.  W.,  364,  384.  . 

Hutchinson,  C.  T.,  4,  251. 
Hysteresis,  276  et  seq.,  281. 

I. 

Icilius,  Quintus,  36,  408,  418. 
Inductance,    Measurement    of,    294 

et  seq.,  314,  325. 
lonization  of  Gases,  579. 


J. 

Jacobi,  M.  H.  v.,  36. 

Jacobi    Unit,    147. 

Jacques,  W.  W.,  80,  81,  145,  174,  184, 

193. 
Jamin,  J.  C.,  71,  80,  81,  89,  90,  96,  97, 

122  et  seq.,  344,  388,  410. 
Jenkin,  Fleming,  150,  169. 
Jewell,  L.  E.,  524,  545,  550. 
Johns  Hopkins  University,  4. 
Jolly,  P.  G.,  410. 
Joule,  6,  7,  24,  27,  36,  52,  53,  146,  344, 

381,   408,   414,  416,  417,  419,   421, 

469. 
Joule's  Thermometers,  417,  469. 

K. 

Kelvin,    Lord     (see    Thomson,    Sir 

William). 

Kempf,  P.,  546,  553,  555. 
Kew  Thermometers,  363,   366,    381, 

466. 

Kimball,  A.  L.,  239. 
Kirchhoff,  G.  B.,  145,  156,  239,  419, 

628. 

Koenig,  Rudolph,  29,  217. 
Kohlrausch,  F.  W.,  4,  82,  83,  84,  146 

et  seq.,  410,  421,  628. 
Koyl,  C.  A.,  549,  555. 
Kriiss,  Dr.,  566,  570. 
Kurlbaum,  F.,  546,  553,  554,  555. 


Laboratories,   Physical,   614. 
Laboulaye,  C.  P.  L.  de,  410. 
Langley,  S.  P.,  491. 
Laplace,  626,  639,  671. 
Lecher,  E.,  4,  252. 
Lenard,  P.,  576,   585. 
Lenz,  H.  F.  E.,  36,  408,  418. 
Lightning,  236. 
Lightning-rods,  237,  663. 
Lippmann,  G.,  5. 
Lockyer,  Sir  J.  Norman,  487,  524. 
Lodge,  Sir  O.  J.,  662,  664,  674. 
Lorenz,  L.  V.,  146,  155,  156,  217,  239, 
419. 


Magnetic  Circuit,  3,  38,  89,  225,  276. 
Magnetic  Distribution,  80,  85,  89. 


702 


INDEX 


Magnetic  Induction,    Measurement 

of,  98. 

Magnetic  Permeability,  35,  56. 
Magnetic  Proof  Plane,  85. 
Magnetism  of  Earth,  179,  213. 
Magnetism,  Cause  of,  673. 
Magnets,  Lifting  Power  of,  52. 
Magnets    and   Chemical   Reactions, 

242. 

Magnetization,  Maximum,  35,  56. 
Magnetization,  Temporary,  49. 
Magnus,  H.  G.,  410. 
Marcou,  P.  B.,  216. 
Marianini,  S.  G.,  71. 
Martins,  C.  F.,  411. 
Mascart,  E.,  240. 
Masson,  A.  P.,  410. 
Matthiessen,  A.,  147. 
*Maxwell,  J.  C.,  3,  52,  57,  71,  83,  89, 

114,   128,   139,   149,   170,  198,   199, 

224,  251,  289,  580,  660,  673. 
Maxwell's     Electromagnetic     The- 

ory, 7,  198,  199,  289,  630,  631. 
Mayer,  Alfred  M.,  669. 
Mayer,  J.  R.,  24. 
McFarlane,  D.,  437,  438. 
McJunckin,  P.  C.,  338. 
Mechanical    Equivalent     of     Heat, 

343,  469. 

Mendenhall,  T.  C.,  1. 
Michelson,  A.  A.,  584,  590,  674. 
Michie,  Professor,  15. 
Moll,  G.,  411. 

Motors,  Electric,  280,  281. 
Miiller,  G.,  546,  553,  555. 
Miiller,  J.  H.  J.,  35,  36,  48. 
Miinchausen,  v.,  344,  389. 
Murphy,   Robert  626. 
Myrback,  v.,  411. 


National   Academy   of   Sciences,    1, 

15,  610. 
Nesbit,    53. 

Neumann,  F.  E.,  146,  387. 
Neumann's    Coefficient,    35,    57,    73, 

116. 
Newton,  Sir  Isaac,  56,  286,  293,  615, 

623,  638,  671. 

Nichol,  J.  P.,  435,  437,  438. 
Nichols,  E.  L.,  204,  249,  250. 


Niven's   Method   of   Measuring  In- 
ductance, 309. 
Nobert  Gratings,  8,  555. 

O. 

Oersted,  626,  639,  640. 

Ohm,  Determination  of  the,  217, 
239,  419,  628. 

Ohm's  Law  for  Currents,  139,  141, 
238,  640. 

Ohm's  Law  for  Magnetic  Induc- 
tion, 3,  38,  89,  90. 

P. 

Paine's     Electromagnetic     Engine, 

24. 

Parry,  E.,  Capt.,  411. 
Peirce,  C.  S.,  492,  494,  513  et  seq., 

545  et  seq. 

Penniman,  T.  D.,  297,  298,  314. 
Permeability,  Magnetic,   35,  56,  73. 
Perry,  John,  179,  182,  183,  213. 
Petit,  P.,  438. 

Pfaundler,  L.,  344,  351,  388,  467. 
Phillips  Academy,  Andover,  11. 
Pickering,  E.  C.,  364. 
Pickering,  W.,  343. 
Plante,  G.,  650. 
Platter    (see    Pfaundler),  344,  351, 

388,  467. 

Pliicker,  J.,  184. 
Poggendorff,  J.  C.,  348. 
Poisson,  626,  630,  639. 
Porous  Plug  Experiment,  346. 
Porter,  A.  W.,  580. 
Power,   Transmission    of,    280. 
Proof  Plane,  Magnetic,  85. 
Puluj,  J.,  408,  424. 
Pupin,  M.  L,  584,  585,  586. 


Radiation  of  Heat,  435. 

Rankine,  W.  J.  M.,  381. 

Rayleigh,    Lord,   240,   294,    525,    528, 

534,  588,  628. 

Rays,  Rontgen,  571,  573,  576. 
Recknagel,  G.  F.,  356,  358,  389. 
Regnault,  V.,  344,  353  et  seq.,  365, 

368,  376,  388  et  seq.,  409  et  seq., 

466,   607. 
Remsen,  Ira,  242  et  seq. 


*  References  to  Maxwell  are  so  numerous  that  only  the  more  important  ones  are  noted  here. 


INDEX 


703 


Rensselaer  Polytechnic  Institute, 
2,  12. 

Resistance,  Electrical;  Effect  of 
Magnetic  field  on,  338. 

Resistance,  Electrical;  Measure- 
ment of,  313. 

Resolving  Power,  502,  528,  588. 

Resonances,  2,  28. 

Richard  (see  Jamin),  410. 

Riecke,  E.,  36. 

Ritter,  J.  W.,  639,  650. 

Rontgen,  W.  C.^4,  252^  410,  414. 

Rontgen-rays,  571,  573,  576. 

Rogers,  W.  A.,  441,  507. 

Rosa,  E.  B.,  266. 

Royal   Society  of  London,   3. 

Ruling-  Engines,  8,  487,  508,  691. 

Rumford,  Count,  6,  408,  416,  669. 

Rumford-fund,  7,  343,   521,   548. 

Rutherfurd,  L.  W.,  8,  487,  494,  513. 


Savart,  F.,  411,  627. 

Schiller,  N.  N.,  252. 

Schneider,  Theodore,  9,  487,  692. 

Scott,  C.  F.,  237. 

Screws,  Perfect,  8,  487,  506. 

Sears,  David,  80,  98. 

Seebeck,  L.  F.  W.  A.,  134,  640. 

Shroder  v.  d.  Kolk,  411,  414. 

Siemens  Armature,  219,  221,.  222, 
228. 

Siemens  Unit,  4,  147,  152,  155,  156. 

Silbennann,  J.  T.,  408,  410,  421. 

"  Skin-Effect  "  of  Alternating  Cur- 
rents, 283,  661. 

Solar  Spectrum,  9,  512,  521. 

Sound,  Velocity  of,  411. 

Specific  Heats  of  Air,  Ratio  of,  410. 

Specific  Heats  of  Gases,  409,  410. 

Specific  Heat  of  Water,  387. 

Spectroscope,  Concave  Grating,  489, 
499,  512,  551,  589. 

Spectroscope,  Plane  Grating1,  588. 

Spectrum  of  the  Aurora,  2,  31. 

Spectrum,  Solar,  512,  521. 

Stampfer,  S.,  411. 

Stefan,  J.,  69. 

Steinheil,  160,  168. 

Steinmetz,  C.  P.,  278. 

Stokes,  Sir  G.  G.,  674. 


Stoletow,  A.  G.,  36,  48,  50,  71,  73,  91, 

105,   154. 
Sturgeon,  William,  53. 

T. 

Tate,  T.,  416. 

Tatnall,   R.   R.,    685. 

Telegraph,  Multiplex  Printing,  10. 

Temperature,    Absolute    Scale    of, 

381. 

Temperature,    Effect   of,    on    Mag- 
netization, 58,  65,  74. 
Tesla,  Nicola,  578. 
Thalgn,  T.  R.,  513,  546,  555. 
Thermometers,  Air,  358,  366. 
Thermometers,  Mercurial,  346,  363. 
Thermometers,   Mercurial  and  air, 

352. 
Thermometers,      Comparisons      of, 

477. 

Thermometers,  Standard,  363. 
Thermometry,  345,  439. 
Thiessen,  M.  F.,  481. 
Thompson,   S.  P.,  233,  234,  235. 
Thomson,  Elihu,  232,  235,   573,   574, 

584,  585. 

Thomson,   J.  J.,   579,   674. 
*Thomson,  Sir  William,  37,  77,  78. 

79,    148,   213,   346,    381,    414,    421, 

626,  649,  657. 

ThiTnderstorms,  Theory  of,  183,  213. 
Transformers,  Theory  of,  276,  280. 
Tresca,  H.  E.,  410,  513. 
Trowbridge,    John,    215,    364. 
Tyndall,  John,  26,  27,  97,  574,  641. 

V. 

Venetian  Institute;  Prize  Essay,  7. 

Verdet,  M.  E.,  58,  79. 

Violle,  J.  L.  G.,  408,  418. 

Vogel,  H.  C.,  549,  556,  557. 

Volta,  626,  639,  645. 

Vortex  in    Outlet   of   Water,    23. 


Waldo,  L.,  481. 
Waltenhofen,  A.  K,  421. 
Wandschaft's  Gratings,  549. 
Water,  Specific  Heat  of,  387. 
Water  Battery,  241. 


*  The  references  to  Lord  Kelvin  are  so  numerous  that  only  the  important  ones  are  noted 
here. 


704 


INDEX 


Wave-leng-ths,    Standard,    512,    517, 

521,  545,  548. 
Webb,  F.  C.,  38, 
Weber,  36,  48,  49,  125,  137,  147,  148, 

152,   153,   156,   160,   170.   184,  240, 

408,   418,   419,   626,   628. 
Weber,  H.  F.,  155,  408,  418,  419,  420. 
Weisbach,  J.,  410. 
Welsh's    Thermometers,    365. 
Welter,  J.  J.,  410. 
West  Point  Military  Academy,   14. 
Wheatstone,   C.,   649. 
Wiedemann,   E.,   409,  415. 


Wiedemann,   G.,   240. 
Wilke,  J.  K,  639. 
Wollaston,  W.  H.,  604. 
Wiillner,  A.,  368,  410. 

Y. 

Yale  University,  11. 
Young,  C.  A.,  487,  493. 
Young,  Thomas,  7. 

Z. 

Zieman  Effect,  672,  673 


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